The entransy theory developed in recent years is used to optimize the aspect ratio of a plate fin in heat convection.Based on a two-dimensional model,the theoretical analysis shows that the minimum thermal resistance ...The entransy theory developed in recent years is used to optimize the aspect ratio of a plate fin in heat convection.Based on a two-dimensional model,the theoretical analysis shows that the minimum thermal resistance defined with the concept of entransy dissipation corresponds to the maximum heat transfer rate when the temperature of the heating surface is fixed.On the other hand,when the heat flux of the heating surface is fixed,the minimum thermal resistance corresponds to the minimum average temperature of the heating surface.The entropy optimization is also given for the heat transfer processes.It is observed that the minimum entropy generation,the minimum entropy generation number,and the minimum revised entropy generation number do not always correspond to the best heat transfer performance.In addition,the influence factors on the optimized aspect ratio of the plate fin are also discussed.The optimized ratio decreases with the enhancement of heat convection,while it increases with fin thermal conductivity increasing.展开更多
Differential equation is very important in science and engineering, because it required the description of some measurable quantities (position, temperature, population, concentration, electrical current, etc.) in mat...Differential equation is very important in science and engineering, because it required the description of some measurable quantities (position, temperature, population, concentration, electrical current, etc.) in mathematical form of ordinary differential equations (ODEs). In this research, we determine heat transferred by convection in fluid problems by first-order ordinary differential equations. So in this research work first we discuss the solution of ordinary homogeneous and non-homogeneous differential equation and then apply the solution of first-order ODEs to heat transferring particularly in heat convection in fluid.展开更多
Numerical predictions are made for Laminar Forced convection heat transfer with and without buoyancy effects for Supercritical Nitrogen flowing over an isothermal horizontal flat plate with a heated surface facing dow...Numerical predictions are made for Laminar Forced convection heat transfer with and without buoyancy effects for Supercritical Nitrogen flowing over an isothermal horizontal flat plate with a heated surface facing downwards.Computations are performed by varying the value ofΔT from5 to 30 K and P_(∞)/P_(cr)ratio from1.1 to 1.5.Variation of all the thermophysical properties of supercritical Nitrogen is considered.The wall temperatures are chosen in such a way that two values of Tw are less than T∗(T*is the temperature at which the fluid has a maximum value of Cp for the given pressure),one value equal to T∗and two values greater than T∗.Three different values of U∞are used to obtain Re∞range of 3.6×10_(4)to 4.74×10^(5)for forced convection without buoyancy effects and Gr_(∞)/Re^(2)_(∞)range of 0.011 to 3.107 for the case where buoyancy effects are predominant.Six different forms of correlations are proposed based on numerical predictions and are compared with actual numerical predictions.It has been found that in all six forms of correlations,the maximum deviations are found to occur in those cases where the pseudocritical temperature TT∗lies between the wall temperature and bulk fluid temperature.展开更多
The behavior of single-phase flow and conjugate heat transfer in micro-channel heat sinks(MCHS)subjected to auniform heat flux is investigated by means of numerical simulations.Various geometrical configurations areex...The behavior of single-phase flow and conjugate heat transfer in micro-channel heat sinks(MCHS)subjected to auniform heat flux is investigated by means of numerical simulations.Various geometrical configurations areexamined,particularly,the combinations of rectangular solid and perforated blocks,used to create a disturbancein the flow.The analysis focuses on several key aspects and related metrics,including the temperature distribution,the mean Fanning friction factor,the pressure drop,the Nusselt number,and the overall heat transfer coefficientacross a range of Reynolds numbers(80–870).It is shown that the introduction of such blocks significantlyenhances the heat transfer performances of the MCHS compared to the straight-through flow channel.Specifically,a case is found where the Nusselt number increases by 2.3 times relative to the reference case.The integrationof perforated blocks facilitates the generation of vorticity within the channel,promoting the mixing of coldand hot fluids.Notably,MCHS incorporating perforated rectangular blocks exhibit more pronounced heat transferbenefits at Reynolds numbers smaller than 400.展开更多
After Bénard＇s experiment in 1900, Rayleigh formulated heat convection problems by the Oberbeck-Boussinesq approximation in the horizontal strip domain in 1916. The pattern formations have been investigated by t...After Bénard＇s experiment in 1900, Rayleigh formulated heat convection problems by the Oberbeck-Boussinesq approximation in the horizontal strip domain in 1916. The pattern formations have been investigated by the bifurcation theory, weakly nonlinear theories and computational approaches. The boundary conditions for the velocity on the upper and lower boundaries are usually assumed as stress-free or no-slip. In the first part of this paper, some bifurcation pictures for the case of the stress-free on the upper boundary and the no-slip on the lower boundary are obtained. In the second part of this paper, the bifurcation pictures for the case of the stress-free on both boundaries by a computer assisted proof are verified. At last., Bénard-Marangoni heat convections for the ease of the free surface of the upper boundary are considered.展开更多
In this paper,transient and steady natural convection heat transfer in an elliptical annulus has been investigated.The annulus occupies the space between two horizontal concentric tubes of elliptic cross-section.The r...In this paper,transient and steady natural convection heat transfer in an elliptical annulus has been investigated.The annulus occupies the space between two horizontal concentric tubes of elliptic cross-section.The resulting velocity and thermal fields are predicted at different annulus orientations assuming isothermal surfaces.The full governing equations of mass,momentum and energy are solved numerically using the Fourier Spectral method.The heat convection process between the two tubes depends on Rayleigh number,Prandtl number,angle of inclination of tube axes and the geometry and dimensions of both tubes.The Prandtl number and inner tube axis ratio are fixed at 0.7 and 0.5,respectively.The problem is solved for the two Rayleigh numbers of 104 and 105 considering a ratio between the two major axes up to 3 while the angle of orientation of the minor axes varies from 0 to 90◦.The results for local and average Nusselt numbers are obtained and discussed together with the details of both flow and thermal fields.For isothermal heating conditions,the study has shown an optimum value for major axes ratio that minimizes the rate of heat transfer between the two tubes.Another important aspect of this paper is to prove the successful use of the Fourier Spectral Method in solving confined flow and heat convection problems.展开更多
Condensation of humid air along a vertical plate was numerically investigated, with the mathematical model built on the full boundary layer equations and the film-wise condensation assumption. The velocity, heat and m...Condensation of humid air along a vertical plate was numerically investigated, with the mathematical model built on the full boundary layer equations and the film-wise condensation assumption. The velocity, heat and mass transfer characteristics at the gas-liquid interface were numerical analyzed and the results indicated that it was not reasonable to neglect the condensate film from the point of its thickness only. The condensate film thickness, interface temperature drop and the interface tangential velocity affect the physical fields weakly. However, the subcooling and the interface normal velocity were important factors to be considered before the simplification was made. For higher wall temperature, the advective mass transfer contributed much to the total mass transfer. Therefore, the boundary conditions were the key to judge the rationality of neglecting the condensate film for numerical solutions. The numerical results were checked by comparing with experiments and correlations.展开更多
Heat transfer and entropy generation of developing laminar forced convection flow of water-Al_2O_3 nanofluid in a concentric annulus with constant heat flux on the walls is investigated numerically. In order to determ...Heat transfer and entropy generation of developing laminar forced convection flow of water-Al_2O_3 nanofluid in a concentric annulus with constant heat flux on the walls is investigated numerically. In order to determine entropy generation of fully developed flow, two approaches are employed and it is shown that only one of these methods can provide appropriate results for flow inside annuli. The effects of concentration of nanoparticles, Reynolds number and thermal boundaries on heat transfer enhancement and entropy generation of developing laminar flow inside annuli with different radius ratios and same cross sectional areas are studied. The results show that radius ratio is a very important decision parameter of an annular heat exchanger such that in each Re, there is an optimum radius ratio to maximize Nu and minimize entropy generation. Moreover, the effect of nanoparticles concentration on heat transfer enhancement and minimizing entropy generation is stronger at higher Reynolds.展开更多
Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or...Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.展开更多
Numerical study was performed to evaluate the characteristics of combined heat transfer of radiation, conduction and convection in indirect near infrared ray （N/R） heating chamber. The effects of important design pa...Numerical study was performed to evaluate the characteristics of combined heat transfer of radiation, conduction and convection in indirect near infrared ray （N/R） heating chamber. The effects of important design parameters such as the shape of heat absorbing cylinder and heat releasing fin on the pressure drop and heat transfer coefficient were analyzed with different Reynolds numbers. The Reynolds numbers were varied from 103 to 3x106, which was defined based on the hydraulic diameter of the heat absorbing cylinder. Analyses were performed to obtain the inner and outer flow and the temperature distributions in the heat absorbing cylinder and the rates of radiation heat transfer and convection heat transfer. As the Reynolds number increases, the convection heat transfer rate is increased while the radiation heat transfer rate is decreased. The average convection heat transfer rate follows a power rule of the Reynolds number. Addition of three-dimensional heat releasing fin to the outside of the heat absorbing cylinder enhances the convection heat transfer.展开更多
Convection heat transfer coefficient and air pressure drop in sinter layer are important factors for the design of sinter cooling craft. Due to the lack of necessary data, the two parameters are studied by experimenta...Convection heat transfer coefficient and air pressure drop in sinter layer are important factors for the design of sinter cooling craft. Due to the lack of necessary data, the two parameters are studied by experimental method. The experimental results show that heat conduction of sinter impacts the measurement of convection heat transfer coefficient. Convection heat transfer increases with the increase of air volumetric flow rate. Sinter layer without small particles(sample I) gives higher convection heat transfer coefficient than that with small particles(sample II). Under the considered conditions, volumetric convection heat transfer coefficient is in the range of 400-1800 W/(m3·°C). Air pressure drop in sinter layer increases with the increase of normal superficial velocity, as well as with the rise of air temperature. Additionally, air pressure drop also depends on sinter particle size distribution. In considered experimental conditions, pressure drop in sinter sample II is 2-3 times that in sinter sample I, which resulted from 17% small scale particles in sinter sample II.展开更多
The laminar fully developed nanofluid flow and heat transfer in a horizonal channel are investigated. Highly accurate solutions for the temperature and nanopavticle concentration distributions are obtained. The effect...The laminar fully developed nanofluid flow and heat transfer in a horizonal channel are investigated. Highly accurate solutions for the temperature and nanopavticle concentration distributions are obtained. The effects of the Brownian motion parameter Nb, the thermophoresis parameter Nt, and the Lewis number Le on the temperature and nanoparticle concentration distributions are discussed. The current analysis shows that the nanoparticles can improve the heat transfer characteristics significantly for this flow problem.展开更多
This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or u...This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose.展开更多
Few studies jointly investigate thermal and turbulent effects. In general, these subjects are treated separately. The purpose of this paper is to use the Immersed Boundary Method (IBM) coupled with the Virtual Physica...Few studies jointly investigate thermal and turbulent effects. In general, these subjects are treated separately. The purpose of this paper is to use the Immersed Boundary Method (IBM) coupled with the Virtual Physical Model (VPM) to investigate incompressible two-dimensional Newtonian flow around a heated square cylinder at constant temperature on its surface with forced convection and turbulence. The VPM model dynamically evaluates the force that the fluid exerts on the immersed surface and the thermal exchange between both in the Reynolds numbers (Re) window 40 ≤ Re ≤ 5×103 . For simulations of turbulence the Smagorinsky and Spalart-Allmaras models are used. The first model uses the Large Eddy Simulation (LES) methodology and is based on the local equilibrium hypothesis for small scales associated with the Boussinesq hypothesis, such that the energy injected into the spectrum of the turbulence balances the energy dissipated by convective effects. The second model uses the concept Unsteady Reynolds Averaged Navier-Stokes Equations (URANS), with only one transport equation for turbulent viscosity, being calibrated in pressure gradient layers. The goal of this work is to analyse the combination of the heat-transfer phenomena with the turbulence for the thermo-fluid-structure interaction in a square cylinder. For this, it was developed a C/C++ code that requires low computational costs in regards to memory and computer facilities. It is observed that, with the increase of the Reynolds number, an increase of the drag coefficient occurs, as well as reinforces the influence of the pressure distribution downstream of the cylinder, which is strongly influenced by the formation and detachment of vortices on the upper and lower sides of the square cylinder.展开更多
In current research about nanofluid convection heat transfer, random motion of nanoparticles in the liquid distribution problem mostly was not considered. In order to study on the distribution of nanoparticles in liqu...In current research about nanofluid convection heat transfer, random motion of nanoparticles in the liquid distribution problem mostly was not considered. In order to study on the distribution of nanoparticles in liquid, nanofluid transport model in pipe is established by using the continuity equation, momentum equation and Fokker-Planck equation. The velocity distribution and the nanoparticles distribution in liquid are obtained by numerical calculation, and the effect of particle size and particle volume fraction on convection heat transfer coefficient of nanofluids is analyzed. The result shows that in high volume fraction （ 0 _-- 0.8% ）, the velocity distribution of nanofluids characterizes as a ＂cork-shaped＂ structure, which is significantly different from viscous fluid with a parabolic distribution. The convection heat transfer coefficient increases while the particle size of nanoparticle in nanofluids decreases. And the convection heat transfer coefficient of nanofluids is in good agreement with the experimental result both in low （0 ~〈 0.1% ） and high （ q = 0.6% ） volume fractions. In presented model, Brown motion, the effect of interactions between nanoparticles and fluid coupling, is also considered, but any phenomenological parameter is not introduced. Nanoparticles in liquid transport distribution can be quantitatively calculated by this model.展开更多
The aim of the thesis is to utilize essential theory of heat transfer,to use correlative expressions to calculate average convection heat change coefficient and heating temperature of strip in Jet Preheat Furnace (JPF...The aim of the thesis is to utilize essential theory of heat transfer,to use correlative expressions to calculate average convection heat change coefficient and heating temperature of strip in Jet Preheat Furnace (JPF),make the calculating results accordant with production data,and make the calculation to be used the process of production.The method is to collect:entry temperature and speed of strip,temperature and speed of N_2 - H_2,to analyse heat transfer according to length and thickness of strip,jet hole and mutual position of jet piping in JPF,to analyse heat transfer and built the physical model.In mathematic model, Martin correlative expressions are tried to calculate using the data from production,and are modified in part properly.At the same time,heat boundary condition is analysed with theory of impact jet and production data.The conclusion is obtained that boundary condition is rarely average numerical value of temperature of strip and N_2 - H_2 with impact jet condition,instead of a relation of function of temperature of strip, temperature and speed of N_2- H_2,array of jet holes,diameter of hole,distance between hole and strip,and acquired a calculating expression.In calculation of examples,the thesis collected and calculated 15 kinds of strips.The thickness of strips are 2=0.51~1.41 mm,material DQ - IF、DDQ,EDDQ,SEDDQ and 340DDQ.Main assess numerical value is temperature value after strip is heated with certain speed and within section of time.Maximum error in 9 groups of numerical value in the thesis is 3.36%comparing with production data.The correlative expressions can be used in production to adjust temperature of strip through changing speed and temperature of N_2 - H_2 and speed of strip.The correlative expressions are compiled computer process.The process can be applied in on line control of production by rapid calculating speed.展开更多
This study characterizes and optimizes natural convection heat transfer of two Newtonian Al2O3 and Ti O2/water nano fluids in a cylindrical enclosure. Nusselt number(Nu) of nano fluids in relation to Rayleigh number(R...This study characterizes and optimizes natural convection heat transfer of two Newtonian Al2O3 and Ti O2/water nano fluids in a cylindrical enclosure. Nusselt number(Nu) of nano fluids in relation to Rayleigh number(Ra) for different concentrations of nano fluids is investigated at different con figurations and orientations of the enclosure.Results show that adding nanoparticles to water has a negligible or even adverse in fluence upon natural convection heat transfer of water: only a slight increase in natural convection heat transfer of Al2O3/water is observed,while natural convection heat transfer for TiO2/water nano fluid is inferior to that for the base fluid. Results also reveal that at low Ra, the likelihood of enhancement in natural convection heat transfer is more than at high Ra: at low Ra, inclination angle, aspect ratio of the enclosure and nanoparticle concentration in fluence natural convection heat transfer more pronouncedly than that in high Ra.展开更多
Turbulent forced convective heat transfer and flow con figurations in a square channel with wavy-ribs inserted diagonally are examined numerically. The in fluences of the 30° and 45° flow attack angles for w...Turbulent forced convective heat transfer and flow con figurations in a square channel with wavy-ribs inserted diagonally are examined numerically. The in fluences of the 30° and 45° flow attack angles for wavy-ribs, blockage ratio, R B= b/H = 0.05–0.25 with single pitch ratio, R P= P/H = 1 are investigated for the Reynolds number based on the hydraulic diameter of the square channel, Re = 3000–20000. The use of the wavy-ribs, which inserted diagonal in the square channel, is aimed to help to improve the thermal performance in heat exchange systems.The finite volume method and SIMPLE algorithm are applied to the present numerical simulation. The results are presented on the periodic flow and heat transfer pro files, flow con figurations, heat transfer characteristics and the performance evaluations. The mathematical results reveal that the use of wavy-ribs leads to a higher heat transfer rate and friction loss over the smooth channel. The heat transfer enhancements are around 1.97–5.14 and 2.04–5.27 times over the smooth channel for 30° and 45° attack angles, respectively. However, the corresponding friction loss values for 30° and 45° are around 4.26–86.55 and 5.03–97.98 times higher than the smooth square channel, respectively. The optimum thermal enhancement factor on both cases is found at R B= 0.10 and the lowest Reynolds number, Re = 3000, to be about 1.47 and 1.52, respectively, for 30° and 45° wavy-ribs.展开更多
In the absence of a simple technique to predict convection heat transfer on BIPV （building integrated photovoltaic） surfaces, a mobile probe with two thermocouples was designed. Thermal boundary layers on vertical f...In the absence of a simple technique to predict convection heat transfer on BIPV （building integrated photovoltaic） surfaces, a mobile probe with two thermocouples was designed. Thermal boundary layers on vertical flat surfaces ofa PV （photovoltaic） and a metallic plate were traversed. The plate consisted of twelve heaters where heat flux and surface temperature were controlled and measured. Uniform heat flux condition was developed on the heaters to closely simulate non-uniform temperature distribution on vertical PV modules. The two thermocouples on the probe measured local air temperature and contact temperature with the wall surface. Experimental results were presented in the forms of local Nusselt numbers versus Rayleigh numbers ＂Nu = a＇（Ra）b＇＇, and surface temperature versus dimensionless height （Ts - T∞ = c.（z/h）d）. The constant values for ＂a＂, ＂b＂, ＂c＂ and ＂d＂ were determined from the best curve-fitting to the power-law relation. The convection heat transfer predictions from the empirical correlations were found to be in consistent with those predictions made by a number of correlations published in the open literature. A simple technique is then proposed to employ two experimental data from the probe to refine empirical correlations as the operational conditions change. A flexible technique to update correlations is of prime significance requirement in thermal design and operation of BIPV modules. The work is in progress to further extend the correlation to predict the combined radiation and convection on inclined PVs and channels.展开更多
Experimental study was conducted to determine the effect of velocity of axial fan,outlet vent height,position,area,and aspect ratio(h/w)of ventilated enclosure on convection heat transfer.Rectangular wooden ventilated...Experimental study was conducted to determine the effect of velocity of axial fan,outlet vent height,position,area,and aspect ratio(h/w)of ventilated enclosure on convection heat transfer.Rectangular wooden ventilated enclosure having top and front transparent wall was made up of Perspex for visualization,and internal physical dimensions of box were 200 mm×200 mm×400 mm.Inlet vent was at bottom while outlet vents were at the side and top wall.Electrically heated cylindrical heat source having 6.1 slenderness ratio was fabricated and hanged at the centre of the enclosure.To calculate heat transfer rates,thermocouples were attached to the inner surface of heat source with silica gel.Heat source was operated at constant heat flux in order to quantify the effect of velocity of air on heat transfer.It was observed that average Nusselt number was increased from 68 to 216 by changing velocity from 0 to 3.34 m/s at constant modified Grashof number i.e.5.67E+09.While variation in outlet height at the front wall did not affect heat transfer in forced convection region.However,Nusselt number decreased to 5%by changing the outlet position from top to the front wall or by 50%reduction in outlet area during forced convection.Mean rise in temperature of enclosure increased from 8.19 K to 9.40 K by increasing aspect ratio of enclosure from 1.5 to 2 by operating heat source at constant heat flux i.e.541.20 w/m^(2).展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 51106082)the Tsinghua University Initiative Scientific Research Program
文摘The entransy theory developed in recent years is used to optimize the aspect ratio of a plate fin in heat convection.Based on a two-dimensional model,the theoretical analysis shows that the minimum thermal resistance defined with the concept of entransy dissipation corresponds to the maximum heat transfer rate when the temperature of the heating surface is fixed.On the other hand,when the heat flux of the heating surface is fixed,the minimum thermal resistance corresponds to the minimum average temperature of the heating surface.The entropy optimization is also given for the heat transfer processes.It is observed that the minimum entropy generation,the minimum entropy generation number,and the minimum revised entropy generation number do not always correspond to the best heat transfer performance.In addition,the influence factors on the optimized aspect ratio of the plate fin are also discussed.The optimized ratio decreases with the enhancement of heat convection,while it increases with fin thermal conductivity increasing.
文摘Differential equation is very important in science and engineering, because it required the description of some measurable quantities (position, temperature, population, concentration, electrical current, etc.) in mathematical form of ordinary differential equations (ODEs). In this research, we determine heat transferred by convection in fluid problems by first-order ordinary differential equations. So in this research work first we discuss the solution of ordinary homogeneous and non-homogeneous differential equation and then apply the solution of first-order ODEs to heat transferring particularly in heat convection in fluid.
文摘Numerical predictions are made for Laminar Forced convection heat transfer with and without buoyancy effects for Supercritical Nitrogen flowing over an isothermal horizontal flat plate with a heated surface facing downwards.Computations are performed by varying the value ofΔT from5 to 30 K and P_(∞)/P_(cr)ratio from1.1 to 1.5.Variation of all the thermophysical properties of supercritical Nitrogen is considered.The wall temperatures are chosen in such a way that two values of Tw are less than T∗(T*is the temperature at which the fluid has a maximum value of Cp for the given pressure),one value equal to T∗and two values greater than T∗.Three different values of U∞are used to obtain Re∞range of 3.6×10_(4)to 4.74×10^(5)for forced convection without buoyancy effects and Gr_(∞)/Re^(2)_(∞)range of 0.011 to 3.107 for the case where buoyancy effects are predominant.Six different forms of correlations are proposed based on numerical predictions and are compared with actual numerical predictions.It has been found that in all six forms of correlations,the maximum deviations are found to occur in those cases where the pseudocritical temperature TT∗lies between the wall temperature and bulk fluid temperature.
基金funded by the Project of the Hubei Provincial Department of Science and Technology(Grant No.2022CFB957)the Project of Hubei Engineering University of Teaching Research(Grant No.JY2024032)+1 种基金Ministry of Education University-Industry Cooperation Collaborative Education Project(Grant No.220903584161245)College Students’Innovation and Entrepreneurship Training Program(Grant Nos.DC2024031,DC2024032).
文摘The behavior of single-phase flow and conjugate heat transfer in micro-channel heat sinks(MCHS)subjected to auniform heat flux is investigated by means of numerical simulations.Various geometrical configurations areexamined,particularly,the combinations of rectangular solid and perforated blocks,used to create a disturbancein the flow.The analysis focuses on several key aspects and related metrics,including the temperature distribution,the mean Fanning friction factor,the pressure drop,the Nusselt number,and the overall heat transfer coefficientacross a range of Reynolds numbers(80–870).It is shown that the introduction of such blocks significantlyenhances the heat transfer performances of the MCHS compared to the straight-through flow channel.Specifically,a case is found where the Nusselt number increases by 2.3 times relative to the reference case.The integrationof perforated blocks facilitates the generation of vorticity within the channel,promoting the mixing of coldand hot fluids.Notably,MCHS incorporating perforated rectangular blocks exhibit more pronounced heat transferbenefits at Reynolds numbers smaller than 400.
文摘After Bénard＇s experiment in 1900, Rayleigh formulated heat convection problems by the Oberbeck-Boussinesq approximation in the horizontal strip domain in 1916. The pattern formations have been investigated by the bifurcation theory, weakly nonlinear theories and computational approaches. The boundary conditions for the velocity on the upper and lower boundaries are usually assumed as stress-free or no-slip. In the first part of this paper, some bifurcation pictures for the case of the stress-free on the upper boundary and the no-slip on the lower boundary are obtained. In the second part of this paper, the bifurcation pictures for the case of the stress-free on both boundaries by a computer assisted proof are verified. At last., Bénard-Marangoni heat convections for the ease of the free surface of the upper boundary are considered.
基金support received from Department of Mechanical Engineering,UET Taxila,Pakistan and from King Fahd University of Petroleum&Minerals,Dhahran,Saudi Arabia is very highly appreciated.
文摘In this paper,transient and steady natural convection heat transfer in an elliptical annulus has been investigated.The annulus occupies the space between two horizontal concentric tubes of elliptic cross-section.The resulting velocity and thermal fields are predicted at different annulus orientations assuming isothermal surfaces.The full governing equations of mass,momentum and energy are solved numerically using the Fourier Spectral method.The heat convection process between the two tubes depends on Rayleigh number,Prandtl number,angle of inclination of tube axes and the geometry and dimensions of both tubes.The Prandtl number and inner tube axis ratio are fixed at 0.7 and 0.5,respectively.The problem is solved for the two Rayleigh numbers of 104 and 105 considering a ratio between the two major axes up to 3 while the angle of orientation of the minor axes varies from 0 to 90◦.The results for local and average Nusselt numbers are obtained and discussed together with the details of both flow and thermal fields.For isothermal heating conditions,the study has shown an optimum value for major axes ratio that minimizes the rate of heat transfer between the two tubes.Another important aspect of this paper is to prove the successful use of the Fourier Spectral Method in solving confined flow and heat convection problems.
基金Supported by the National Basic Research Program of China （2011CB706904） and Beijing Natural Science Foundation （3071001）
文摘Condensation of humid air along a vertical plate was numerically investigated, with the mathematical model built on the full boundary layer equations and the film-wise condensation assumption. The velocity, heat and mass transfer characteristics at the gas-liquid interface were numerical analyzed and the results indicated that it was not reasonable to neglect the condensate film from the point of its thickness only. The condensate film thickness, interface temperature drop and the interface tangential velocity affect the physical fields weakly. However, the subcooling and the interface normal velocity were important factors to be considered before the simplification was made. For higher wall temperature, the advective mass transfer contributed much to the total mass transfer. Therefore, the boundary conditions were the key to judge the rationality of neglecting the condensate film for numerical solutions. The numerical results were checked by comparing with experiments and correlations.
文摘Heat transfer and entropy generation of developing laminar forced convection flow of water-Al_2O_3 nanofluid in a concentric annulus with constant heat flux on the walls is investigated numerically. In order to determine entropy generation of fully developed flow, two approaches are employed and it is shown that only one of these methods can provide appropriate results for flow inside annuli. The effects of concentration of nanoparticles, Reynolds number and thermal boundaries on heat transfer enhancement and entropy generation of developing laminar flow inside annuli with different radius ratios and same cross sectional areas are studied. The results show that radius ratio is a very important decision parameter of an annular heat exchanger such that in each Re, there is an optimum radius ratio to maximize Nu and minimize entropy generation. Moreover, the effect of nanoparticles concentration on heat transfer enhancement and minimizing entropy generation is stronger at higher Reynolds.
基金This work was supported by the Natural Science Foundation of China(Grant Nos.61673169,11701176,11626101,11601485).
文摘Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.
基金supported by the Second Stage of Brain Korea 21 Projects
文摘Numerical study was performed to evaluate the characteristics of combined heat transfer of radiation, conduction and convection in indirect near infrared ray （N/R） heating chamber. The effects of important design parameters such as the shape of heat absorbing cylinder and heat releasing fin on the pressure drop and heat transfer coefficient were analyzed with different Reynolds numbers. The Reynolds numbers were varied from 103 to 3x106, which was defined based on the hydraulic diameter of the heat absorbing cylinder. Analyses were performed to obtain the inner and outer flow and the temperature distributions in the heat absorbing cylinder and the rates of radiation heat transfer and convection heat transfer. As the Reynolds number increases, the convection heat transfer rate is increased while the radiation heat transfer rate is decreased. The average convection heat transfer rate follows a power rule of the Reynolds number. Addition of three-dimensional heat releasing fin to the outside of the heat absorbing cylinder enhances the convection heat transfer.
基金Project(51306198)supported by the National Natural Science Foundation of China
文摘Convection heat transfer coefficient and air pressure drop in sinter layer are important factors for the design of sinter cooling craft. Due to the lack of necessary data, the two parameters are studied by experimental method. The experimental results show that heat conduction of sinter impacts the measurement of convection heat transfer coefficient. Convection heat transfer increases with the increase of air volumetric flow rate. Sinter layer without small particles(sample I) gives higher convection heat transfer coefficient than that with small particles(sample II). Under the considered conditions, volumetric convection heat transfer coefficient is in the range of 400-1800 W/(m3·°C). Air pressure drop in sinter layer increases with the increase of normal superficial velocity, as well as with the rise of air temperature. Additionally, air pressure drop also depends on sinter particle size distribution. In considered experimental conditions, pressure drop in sinter sample II is 2-3 times that in sinter sample I, which resulted from 17% small scale particles in sinter sample II.
基金Project supported by the National Natural Science Foundation of China （No. 10972136） and the Doctoral Fund for New Teachers of Higher Eduation of China （No. 20090073120014）
文摘The laminar fully developed nanofluid flow and heat transfer in a horizonal channel are investigated. Highly accurate solutions for the temperature and nanopavticle concentration distributions are obtained. The effects of the Brownian motion parameter Nb, the thermophoresis parameter Nt, and the Lewis number Le on the temperature and nanoparticle concentration distributions are discussed. The current analysis shows that the nanoparticles can improve the heat transfer characteristics significantly for this flow problem.
文摘This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose.
基金the partial support by CMUP(UID/MAT/00144/2013),which is funded by FCT(Portugal)with national(MCTES)and European structural funds(FEDER),under the partnership agreement PT2020-ext.to 2018the financial support by CAPES(Brazil)SG acknowledges the Project STRIDE-NORTE-01-0145-FEDER-000033,funded by ERDF NORTE 2020.
文摘Few studies jointly investigate thermal and turbulent effects. In general, these subjects are treated separately. The purpose of this paper is to use the Immersed Boundary Method (IBM) coupled with the Virtual Physical Model (VPM) to investigate incompressible two-dimensional Newtonian flow around a heated square cylinder at constant temperature on its surface with forced convection and turbulence. The VPM model dynamically evaluates the force that the fluid exerts on the immersed surface and the thermal exchange between both in the Reynolds numbers (Re) window 40 ≤ Re ≤ 5×103 . For simulations of turbulence the Smagorinsky and Spalart-Allmaras models are used. The first model uses the Large Eddy Simulation (LES) methodology and is based on the local equilibrium hypothesis for small scales associated with the Boussinesq hypothesis, such that the energy injected into the spectrum of the turbulence balances the energy dissipated by convective effects. The second model uses the concept Unsteady Reynolds Averaged Navier-Stokes Equations (URANS), with only one transport equation for turbulent viscosity, being calibrated in pressure gradient layers. The goal of this work is to analyse the combination of the heat-transfer phenomena with the turbulence for the thermo-fluid-structure interaction in a square cylinder. For this, it was developed a C/C++ code that requires low computational costs in regards to memory and computer facilities. It is observed that, with the increase of the Reynolds number, an increase of the drag coefficient occurs, as well as reinforces the influence of the pressure distribution downstream of the cylinder, which is strongly influenced by the formation and detachment of vortices on the upper and lower sides of the square cylinder.
基金supported by National Natural Science Foundation of China(Grant No.51375090)
文摘In current research about nanofluid convection heat transfer, random motion of nanoparticles in the liquid distribution problem mostly was not considered. In order to study on the distribution of nanoparticles in liquid, nanofluid transport model in pipe is established by using the continuity equation, momentum equation and Fokker-Planck equation. The velocity distribution and the nanoparticles distribution in liquid are obtained by numerical calculation, and the effect of particle size and particle volume fraction on convection heat transfer coefficient of nanofluids is analyzed. The result shows that in high volume fraction （ 0 _-- 0.8% ）, the velocity distribution of nanofluids characterizes as a ＂cork-shaped＂ structure, which is significantly different from viscous fluid with a parabolic distribution. The convection heat transfer coefficient increases while the particle size of nanoparticle in nanofluids decreases. And the convection heat transfer coefficient of nanofluids is in good agreement with the experimental result both in low （0 ~〈 0.1% ） and high （ q = 0.6% ） volume fractions. In presented model, Brown motion, the effect of interactions between nanoparticles and fluid coupling, is also considered, but any phenomenological parameter is not introduced. Nanoparticles in liquid transport distribution can be quantitatively calculated by this model.
文摘The aim of the thesis is to utilize essential theory of heat transfer,to use correlative expressions to calculate average convection heat change coefficient and heating temperature of strip in Jet Preheat Furnace (JPF),make the calculating results accordant with production data,and make the calculation to be used the process of production.The method is to collect:entry temperature and speed of strip,temperature and speed of N_2 - H_2,to analyse heat transfer according to length and thickness of strip,jet hole and mutual position of jet piping in JPF,to analyse heat transfer and built the physical model.In mathematic model, Martin correlative expressions are tried to calculate using the data from production,and are modified in part properly.At the same time,heat boundary condition is analysed with theory of impact jet and production data.The conclusion is obtained that boundary condition is rarely average numerical value of temperature of strip and N_2 - H_2 with impact jet condition,instead of a relation of function of temperature of strip, temperature and speed of N_2- H_2,array of jet holes,diameter of hole,distance between hole and strip,and acquired a calculating expression.In calculation of examples,the thesis collected and calculated 15 kinds of strips.The thickness of strips are 2=0.51~1.41 mm,material DQ - IF、DDQ,EDDQ,SEDDQ and 340DDQ.Main assess numerical value is temperature value after strip is heated with certain speed and within section of time.Maximum error in 9 groups of numerical value in the thesis is 3.36%comparing with production data.The correlative expressions can be used in production to adjust temperature of strip through changing speed and temperature of N_2 - H_2 and speed of strip.The correlative expressions are compiled computer process.The process can be applied in on line control of production by rapid calculating speed.
文摘This study characterizes and optimizes natural convection heat transfer of two Newtonian Al2O3 and Ti O2/water nano fluids in a cylindrical enclosure. Nusselt number(Nu) of nano fluids in relation to Rayleigh number(Ra) for different concentrations of nano fluids is investigated at different con figurations and orientations of the enclosure.Results show that adding nanoparticles to water has a negligible or even adverse in fluence upon natural convection heat transfer of water: only a slight increase in natural convection heat transfer of Al2O3/water is observed,while natural convection heat transfer for TiO2/water nano fluid is inferior to that for the base fluid. Results also reveal that at low Ra, the likelihood of enhancement in natural convection heat transfer is more than at high Ra: at low Ra, inclination angle, aspect ratio of the enclosure and nanoparticle concentration in fluence natural convection heat transfer more pronouncedly than that in high Ra.
基金Supported by College of Industrial Technology,King Mongkut's University of Technology North Bangkok,Thailand
文摘Turbulent forced convective heat transfer and flow con figurations in a square channel with wavy-ribs inserted diagonally are examined numerically. The in fluences of the 30° and 45° flow attack angles for wavy-ribs, blockage ratio, R B= b/H = 0.05–0.25 with single pitch ratio, R P= P/H = 1 are investigated for the Reynolds number based on the hydraulic diameter of the square channel, Re = 3000–20000. The use of the wavy-ribs, which inserted diagonal in the square channel, is aimed to help to improve the thermal performance in heat exchange systems.The finite volume method and SIMPLE algorithm are applied to the present numerical simulation. The results are presented on the periodic flow and heat transfer pro files, flow con figurations, heat transfer characteristics and the performance evaluations. The mathematical results reveal that the use of wavy-ribs leads to a higher heat transfer rate and friction loss over the smooth channel. The heat transfer enhancements are around 1.97–5.14 and 2.04–5.27 times over the smooth channel for 30° and 45° attack angles, respectively. However, the corresponding friction loss values for 30° and 45° are around 4.26–86.55 and 5.03–97.98 times higher than the smooth square channel, respectively. The optimum thermal enhancement factor on both cases is found at R B= 0.10 and the lowest Reynolds number, Re = 3000, to be about 1.47 and 1.52, respectively, for 30° and 45° wavy-ribs.
文摘In the absence of a simple technique to predict convection heat transfer on BIPV （building integrated photovoltaic） surfaces, a mobile probe with two thermocouples was designed. Thermal boundary layers on vertical flat surfaces ofa PV （photovoltaic） and a metallic plate were traversed. The plate consisted of twelve heaters where heat flux and surface temperature were controlled and measured. Uniform heat flux condition was developed on the heaters to closely simulate non-uniform temperature distribution on vertical PV modules. The two thermocouples on the probe measured local air temperature and contact temperature with the wall surface. Experimental results were presented in the forms of local Nusselt numbers versus Rayleigh numbers ＂Nu = a＇（Ra）b＇＇, and surface temperature versus dimensionless height （Ts - T∞ = c.（z/h）d）. The constant values for ＂a＂, ＂b＂, ＂c＂ and ＂d＂ were determined from the best curve-fitting to the power-law relation. The convection heat transfer predictions from the empirical correlations were found to be in consistent with those predictions made by a number of correlations published in the open literature. A simple technique is then proposed to employ two experimental data from the probe to refine empirical correlations as the operational conditions change. A flexible technique to update correlations is of prime significance requirement in thermal design and operation of BIPV modules. The work is in progress to further extend the correlation to predict the combined radiation and convection on inclined PVs and channels.
文摘Experimental study was conducted to determine the effect of velocity of axial fan,outlet vent height,position,area,and aspect ratio(h/w)of ventilated enclosure on convection heat transfer.Rectangular wooden ventilated enclosure having top and front transparent wall was made up of Perspex for visualization,and internal physical dimensions of box were 200 mm×200 mm×400 mm.Inlet vent was at bottom while outlet vents were at the side and top wall.Electrically heated cylindrical heat source having 6.1 slenderness ratio was fabricated and hanged at the centre of the enclosure.To calculate heat transfer rates,thermocouples were attached to the inner surface of heat source with silica gel.Heat source was operated at constant heat flux in order to quantify the effect of velocity of air on heat transfer.It was observed that average Nusselt number was increased from 68 to 216 by changing velocity from 0 to 3.34 m/s at constant modified Grashof number i.e.5.67E+09.While variation in outlet height at the front wall did not affect heat transfer in forced convection region.However,Nusselt number decreased to 5%by changing the outlet position from top to the front wall or by 50%reduction in outlet area during forced convection.Mean rise in temperature of enclosure increased from 8.19 K to 9.40 K by increasing aspect ratio of enclosure from 1.5 to 2 by operating heat source at constant heat flux i.e.541.20 w/m^(2).
