The effects of a magnetic dipole on a nonlinear thermally radiative ferromagnetic liquidflowing over a stretched surface in the presence of Brownian motion and thermophoresis are investigated.By means of a similarity t...The effects of a magnetic dipole on a nonlinear thermally radiative ferromagnetic liquidflowing over a stretched surface in the presence of Brownian motion and thermophoresis are investigated.By means of a similarity transformation,ordinary differential equations are derived and solved afterwards using a numerical(the BVP4C)method.The impact of various parameters,namely the velocity,temperature,concentration,is presented graphically.It is shown that the nanoparticles properties,in conjunction with the magnetic dipole effect,can increase the thermal conductivity of the engineered nanofluid and,consequently,the heat transfer.Comparison with earlier studies indicates high accuracy and effectiveness of the numerical approach.An increase in the Brow-nian motion parameter and thermophoresis parameter enhances the concentration and the related boundary layer.The skin-friction rises when the viscosity parameter is increased.A larger value of the ferromagnetic para-meter results in a higher skin-friction and,vice versa,in a smaller Nusselt number.展开更多
Motivated by the widespread applications of nanofluids,a nanofluid model is proposed which focuses on uniform magnetohydrodynamic(MHD)boundary layer flow over a non-linear stretching sheet,incorporating the Casson mod...Motivated by the widespread applications of nanofluids,a nanofluid model is proposed which focuses on uniform magnetohydrodynamic(MHD)boundary layer flow over a non-linear stretching sheet,incorporating the Casson model for blood-based nanofluid while accounting for viscous and Ohmic dissipation effects under the cases of Constant Surface Temperature(CST)and Prescribed Surface Temperature(PST).The study employs a two-phase model for the nanofluid,coupled with thermophoresis and Brownian motion,to analyze the effects of key fluid parameters such as thermophoresis,Brownian motion,slip velocity,Schmidt number,Eckert number,magnetic parameter,and non-linear stretching parameter on the velocity,concentration,and temperature profiles of the nanofluid.The proposed model is novel as it simultaneously considers the impact of thermophoresis and Brownian motion,along with Ohmic and viscous dissipation effects,in both CST and PST scenarios for blood-based Casson nanofluid.The numerical technique built into MATLAB’s bvp4c module is utilized to solve the governing system of coupled differential equations,revealing that the concentration of nanoparticles decreases with increasing thermophoresis and Brownian motion parameters while the temperature of the nanofluid increases.Additionally,a higher Eckert number is found to reduce the nanofluid temperature.A comparative analysis between CST and PST scenarios is also undertaken,which highlights the significant influence of these factors on the fluid’s characteristics.The findings have potential applications in biomedical processes to enhance fluid velocity and heat transfer rates,ultimately improving patient outcomes.展开更多
The results of this article can be useful in science and technology advancement, such as nanofluidics, micro mixing and energy conversion. The purpose of this article is to examine the impacts of nanoparticle shape on...The results of this article can be useful in science and technology advancement, such as nanofluidics, micro mixing and energy conversion. The purpose of this article is to examine the impacts of nanoparticle shape on Al2O3-water nanofluid and heat transfer over a non-linear radically stretching sheet in the existence of magnetic field and thermal radiation. The different shapes of Al2O3 nanoparticles that have under contemplation are column, sphere, hexahedron, tetrahedron, and lamina. The governing partial differential equations (PDEs) of the problem are regenerated into set of non-linear ordinary differential equations (ODEs) by using appropriate similarity transformation. The bvp4c program has used to solve the obtained non-linear ordinary differential equation (ODEs). The Nusselt number for all shapes of Al2O3 nanoparticle shapes in pure water with is presented in graphical form. It has reported that the heat transfer augmentation in lamina shapes nanoparticles is more than other shapes of nanoparticle. The relation of thermal boundary layer with shapes of nanoparticles, solid volume fraction, magnetic field and thermal radiation has also presented with the help of graphical representation. It is also demonstrated that lamina shape nanoparticles have showed large temperature distribution than other shapes of nanoparticles.展开更多
This paper investigates the boundary layer flow of the Maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field.The constitutive flow equations for the current...This paper investigates the boundary layer flow of the Maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field.The constitutive flow equations for the current physical problem are modeled and analyzed for the first time in the literature.The torsional motion of the cylinder is considered with the constant azimuthal velocity E.The partial differential equations(PDEs)governing the torsional motion of the Maxwell fluid together with energy transport are simplified with the boundary layer concept.The current analysis is valid only for a certain range of the positive Reynolds numbers.However,for very large Reynolds numbers,the flow becomes turbulent.Thus,the governing similarity equations are simplified through suitable transformations for the analysis of the large Reynolds numbers.The numerical simulations for the flow,heat,and mass transport phenomena are carried out in view of the bvp4c scheme in MATLAB.The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the flow penetrates shallower into the free stream fluid.It is also noted that the phenomenon of stress relaxation,described by the Deborah number,causes to decline the flow fields and enhance the thermal and solutal energy transport during the fluid motion.The penetration depth decreases for the transport of heat and mass in the fluid with the higher Reynolds numbers.An excellent validation of the numerical results is assured through tabular data with the existing literature.展开更多
For new submarine pipeline maintenance lifting equipment,a specialized analysis model is constructed in this study.A pipeline can be divided into the lifted portion and the touch-down portion that lies on the seabed,a...For new submarine pipeline maintenance lifting equipment,a specialized analysis model is constructed in this study.A pipeline can be divided into the lifted portion and the touch-down portion that lies on the seabed,and each of these portions can be analyzed separately by converting the continuity conditions at the touch-down points to boundary conditions.The typical two-point sequence secant iterative technique is used to obtain the unknown lifted length and determine pipeline lifting confgurations.The BVP4C module in MATLAB software is used to solve this multiple-point boundary value problem issued from frst-order diferential equations.Also,the triple-point lifting mode of truncated maintenance and the two-point lifting mode of online maintenance are discussed.When the lifted heights at truss positions are shown,the lifting deformation,lifting forces,bending moment distribution,and axial force distribution can be analyzed using a dedicated analysis program.Numerical results can then be used to design a lifting strategy to protect the pipeline.展开更多
We study the coupled flow and heat transfer of power-law nanofluids on a non-isothermal rough rotating disk subjected to a magnetic field.The problem is formulated in terms of specified curvilinear orthogonal coordina...We study the coupled flow and heat transfer of power-law nanofluids on a non-isothermal rough rotating disk subjected to a magnetic field.The problem is formulated in terms of specified curvilinear orthogonal coordinate system.An improved BVP4C algorithm is proposed,and numerical solutions are obtained.The influence of volume fraction,types and shapes of nanoparticles,magnetic field and power-law index on the flow,and heat transfer behavior are discussed.The obtained results show that the power-law exponents(PLE),nanoparticle volume fraction(NVF),and magnetic field inclination angle(MFIA)have almost no effects on velocities in the wave surface direction,but have small or significant effects on the azimuth direction.The NVF has remarkable influences on local Nusselt number(LNN)and friction coefficients(FC)in the radial direction and the azimuth direction(AD).The LNN increases with NVF increasing while FC in AD decreases.The types of nanoparticles,magnetic field strength,and inclination have small effects on LNN,but they have remarkable influences on the friction coefficients with positively correlated heat transfer rate,while the inclination is negatively correlated with heat transfer rate.The size of the nanoparticle shape factor is positively correlated with LNN.展开更多
The purpose of this research is to investigate the influence that slip boundary conditions have on the rate of heat and mass transfer by examining the behavior of micropolar MHD flow across a porous stretching sheet.I...The purpose of this research is to investigate the influence that slip boundary conditions have on the rate of heat and mass transfer by examining the behavior of micropolar MHD flow across a porous stretching sheet.In addition to this,the impacts of thermal radiation and viscous dissipation are taken into account.With the use of various computing strategies,numerical results have been produced.Similarity transformation was utilized in order to convert the partial differential equations(PDEs)that regulated energy,rotational momentum,concentration,and momentum into ordinary differential equations(ODEs).As compared to earlier published research,MATLAB inbuilt solver solution shows an extremely good correlation in exceptional instances.In exceptional instances,the present MATLAB inbuilt solver solution has a very excellent connection with the findings of the previously published investigations.A variety of flow field factors impact the Nusselt number,the wall couple shear stress,the friction factor,Sherwood numbers the dimensionless distributions discussed in detail.When the Eckert number rises,the temperature rises,and the Schmidt number falls,the concentration falls.Velocity increases with increases in the material factor but drops with increases in the magnetic parameter and the surface condition factor.展开更多
The present study numerically investigates the flow and heat transfer of porous Williamson hybrid nanofluid on an exponentially shrinking sheet with magnetohydrodynamic(MHD)effects.The nonlinear partial differential e...The present study numerically investigates the flow and heat transfer of porous Williamson hybrid nanofluid on an exponentially shrinking sheet with magnetohydrodynamic(MHD)effects.The nonlinear partial differential equations which governed the model are first reduced to a set of ordinary differential equations by using the similarity transformation.Next,the BVP4C solver is applied to solve the equations by considering the pertinent fluid parameters such as the permeability parameter,the magnetic parameter,the Williamson parameter,the nanoparticle volume fractions and the wall mass transfer parameter.The single(SWCNTs)and multi-walled carbon nanotubes(MWCNTs)nanoparticles are taken as the hybrid nanoparticles.It is found that the increase in magnetic parameter in SWCNT+MCWNT hybrid nanofluid results in an increase of 72.2%on skin friction compared to SWCNT nanofluid while maintaining reducing a small number of Nusselt number.This shows the potential of the Williamson hybrid nanofluid for friction application purposes especially in transportation like braking system,flushing fluid and mechanical engineering.展开更多
In current study,the numerical computations of Reiner–Rivlin nanofluid flow through a rotational disk under the influence of thermal radiation and Arrhenius activation energy is considered.For innovative physical sit...In current study,the numerical computations of Reiner–Rivlin nanofluid flow through a rotational disk under the influence of thermal radiation and Arrhenius activation energy is considered.For innovative physical situations,the motile microorganisms are incorporated too.The multiple slip effects are considered in the boundary conditions.The bioconvection of motile microorganism is utilized alongside nanofluids to provide stability to enhanced thermal transportation.The Bioconvection pattern in various nanoparticles accredits novel applications of biotechnology like the synthesis of biological polymers,biosensors,fuel cells,petroleum engineering,and the natural environment.By deploying some suitable similarity transformation functions,the governing partial differential equations(PDEs)of the flow problem are rehabilitated into dimensionless forms.The accomplished ordinary differential equations(ODEs)are solved numerically through the bvp4c scheme via a built-in function in computational MATLAB software.The upshots of some prominent physical and bioconvection parameters including wall slip parameters,thermophoresis parameter,Brownian motion parameter,Reiner–Revlin nanofluid parameter,Prandtl number,Peclet number,Lewis number,bioconvection Lewis number,and the mixed convection parameter against velocity,temperature,nanoparticles concentration,and density of motile microorganism profiles are dichotomized and pondered through graphs and tables.The presented computations show that the velocity profiles are de-escalated by the wall slip parameters while the thermal and solutal fields are upgraded with augmentation in thermophoresis number and wall slip parameters.The presence of thermal radiation enhances the temperature profile of nanofluid.The concentration profile of nanoparticles is boosted by intensification in activation energy.Furthermore,the increasing values of bioconvection Lewis number and Peclet number decay the motile microorganisms’field.展开更多
Entropy analysis can help to identify the sources of entropy generation in a heat transfer process more accurately than other methods,such as energy efficiency analysis.This is because entropy analysis takes into acco...Entropy analysis can help to identify the sources of entropy generation in a heat transfer process more accurately than other methods,such as energy efficiency analysis.This is because entropy analysis takes into account the quality of energy as well as its quantity.Na-nofluids have already been shown to have superior heat transfer characteristics compared to conventionalfluids.Stefan blowing can further enhance the heat transfer capabilities of nano-fluids by increasing the massflux and turbulence at the surface.This can be beneficial in a wide range of applications,such as heat exchangers,electronic cooling,and solar energy devices.The convective boundary condition accounts for heat transfer effects,influencing temperature distribution and the thermal boundary layer.Depending on the direction of heat transfer,the convective boundary condition can induce cooling or heating effects on the inclined plate.This has practical implications for various engineering applications,such as the cooling of electronic devices or heating in industrial processes.Carreau nanofluids have a wide range of potential applications in heat transfer,energy storage,drug delivery,and food processing.This research investigates how the presence of Stefan blowing affects the properties of Carreau nanofluid flow across a convectively heated tilted plate.Heat and mass transport phenomena are studied using quadratic thermal radiation and chemical reaction parameters.The mathematical model for this work is based on the Buongiorno model.The governing equations are converted into a system of ordinary differential equations and then solved using the bvp4c solver.Physical parameters such as the mass transfer rate can be visualized using bar graphs.The study’s primary findings are that when the Weissenberg number increases,the velocity rises and the concentration profile declines due to Brownian motion.It is discovered that,when 0.5≤γ≤3(the inverse porosity parameter),the friction factor declines by 0.34001(in the presence of Stefan blowing),and 0.3284(otherwise).It has been observed that as the Brinkman number and magnetic field parameters increase,there is an increase in entropy formation.Additionally,it has been noted that these same factors have an inverse effect on the Bejan number.At 0.1≤Nb≤0.6(Brownian motion),the Sherwood number is seen to rise at a rate of 0.113353(in the presence of Stefan blowing),and 0.479739(otherwise).When the Stefan blowing parameter is absent,the rate of heat transfer is observed to be noticeably faster than when it is present.Furthermore,when the heat source parameter is set to 0.1≤Hs≤0.6,the decrement rates in heat transfer rate are 0.12208(in the presence of Stefan blowing)and 0.02102(otherwise).展开更多
In the present article,we perform the second law analysis of classical Blasius flow accounting the effects of nonlinear radiation and frictional heating.The two-dimensional boundary layer momentum and energy equations...In the present article,we perform the second law analysis of classical Blasius flow accounting the effects of nonlinear radiation and frictional heating.The two-dimensional boundary layer momentum and energy equations are converted to self-similar equations using similarity transformations.The set of resultant ordinary differential equations are solved numerically.The numerical results obtained from solutions of dimensionless momentum and energy equations are used to calculate the entropy generation number and Bejan number.The velocity profile f'(ξ),temperature distributionθ(ξ),entropy production number Ns and Bejan number Be are plotted against the physical flow parameters and are discussed in detail.Further,for the sake of validation of our numerical code,the obtained results are reproduced using Matlab built-in boundary value solver bvp4c resulting in an excellent agreement.It is observed that entropy generation is increasing function of heating parameter,Prandtl number,Eckert number and radiation parameter.Further,it is observed that entropy generation can be minimized by reducing the operating temperatureΔT=T_(w)−T_(∞).展开更多
In this article,three-dimensional mixed convection flow over an exponentially stretching sheet is investigated.Energy equation is modelled in the presence of viscous dissipation and variable thermal conductivity.Tempe...In this article,three-dimensional mixed convection flow over an exponentially stretching sheet is investigated.Energy equation is modelled in the presence of viscous dissipation and variable thermal conductivity.Temperature of the sheet is varying exponentially and is chosen in a form that facilitates the similarity transformations to obtain self-similar equations.Resulting nonlinear ordinary differential equations are solved numerically employing the Runge-Kutta shooting method.In order to check the accuracy of the method,these equations are also solved using bvp4c built-in routine in Matlab.Both solutions are in excellent agreement.The effects of physical parameters on the dimensionless velocity field and temperature are demonstrated through various graphs.The novelty of this analysis is the self-similar solution of the threedimensional boundary layer flow in the presence of mixed convection,viscous dissipation and variable thermal conductivity.展开更多
The aspiration of this research is to explore the impact of non-similar modeling for mixed convection in magnetized second-grade nanofluid flow.The flow is initiated by the stretching of a sheet at an exponential rate...The aspiration of this research is to explore the impact of non-similar modeling for mixed convection in magnetized second-grade nanofluid flow.The flow is initiated by the stretching of a sheet at an exponential rate in the upward vertical direction.The buoyancy effects in terms of temperature and concentration differences are inserted in the x-momentum equation.The aspects of heat and mass transfer are studied using dimensionless thermophoresis,Schmidt and Brownian motion parameters.The governing coupled partial differential system(PDEs)is remodeled into coupled non-similar nonlinear PDEs by introducing non-similar transformations.The numerical analysis for the dimensionless non-similar partial differential system is performed using a local non-similarity method via bvp4c.Finally,the quantitative effects of emerging dimensionless quantities on the nondimensional velocity,temperature and mass concentration in the boundary layer are conferred graphically,and inferences are drawn that important quantities of interest are substantially affected by these parameters.It is concluded that non-similar modeling,in contrast to similar models,is more general and more accurate in convection studies in the presence of buoyancy effects for second-grade non-Newtonian fluids.展开更多
In this paper,based on the finite element formulation,we focus on multiple solutions and their evolution with time for a laminar flow in a permeable channel with expanding or contracting walls.Both Newtonian fluid and...In this paper,based on the finite element formulation,we focus on multiple solutions and their evolution with time for a laminar flow in a permeable channel with expanding or contracting walls.Both Newtonian fluid and micropolar fluid are consid-ered.For the Newtonian fluid model,we find that the profile of the unique solution in the case of injection remains the same for long time,which indicates that the solution may be stable.On the other hand,in the case of large suction,the profile of multiple solutions changes in time,which suggests that the multiple solutions may be unstable.Similar behaviors and conclusions are observed for the micropolar fluid model under different boundary parameters.展开更多
The current article investigates the numerical study of the micropolar nanofluid flow through a 3D rotating surface.This communication may manipulate for the aim such as the delivery of the drug,cooling of electronic ...The current article investigates the numerical study of the micropolar nanofluid flow through a 3D rotating surface.This communication may manipulate for the aim such as the delivery of the drug,cooling of electronic chips,nanoscience and the fields of nanotechnology.The impact of heat source/sink is employed.Brownian motion and thermophoresis aspects are discussed.The rotating sheet with the impacts of Darcy-Forchheimer law is also scrutinized.Furthermore,the influence of activation energy is analyzed in the current article.The numerical analysis is simplified with the help of befitted resemblance transformations.The succor of the shooting algorithm with built-in solver bvp4c MATLAB software is used for the numerical solution of nonlinear transformed equations.The consequences of different physical factors on the physical engineering quantities and the subjective fields were examined and presented.According to outcomes,it can be analyzed that the flow profile declined with the rotational parameter.It is observed that angular velocity diminishes via a larger porosity parameter.Furthermore,the temperature gradient is declined via a larger magnitude of the Prandtl number.The heat transfer is enhanced in the occurrence of Brownian motion.The activations energy parameter causes an increment in the volumetric concentration field.Moreover,the local Nusselt number is reduced via a greater estimation of the porosity parameter.展开更多
文摘The effects of a magnetic dipole on a nonlinear thermally radiative ferromagnetic liquidflowing over a stretched surface in the presence of Brownian motion and thermophoresis are investigated.By means of a similarity transformation,ordinary differential equations are derived and solved afterwards using a numerical(the BVP4C)method.The impact of various parameters,namely the velocity,temperature,concentration,is presented graphically.It is shown that the nanoparticles properties,in conjunction with the magnetic dipole effect,can increase the thermal conductivity of the engineered nanofluid and,consequently,the heat transfer.Comparison with earlier studies indicates high accuracy and effectiveness of the numerical approach.An increase in the Brow-nian motion parameter and thermophoresis parameter enhances the concentration and the related boundary layer.The skin-friction rises when the viscosity parameter is increased.A larger value of the ferromagnetic para-meter results in a higher skin-friction and,vice versa,in a smaller Nusselt number.
基金funded by Universiti Teknikal Malaysia Melaka and Ministry of Higher Education(MoHE)Malaysia,grant number FRGS/1/2024/FTKM/F00586.
文摘Motivated by the widespread applications of nanofluids,a nanofluid model is proposed which focuses on uniform magnetohydrodynamic(MHD)boundary layer flow over a non-linear stretching sheet,incorporating the Casson model for blood-based nanofluid while accounting for viscous and Ohmic dissipation effects under the cases of Constant Surface Temperature(CST)and Prescribed Surface Temperature(PST).The study employs a two-phase model for the nanofluid,coupled with thermophoresis and Brownian motion,to analyze the effects of key fluid parameters such as thermophoresis,Brownian motion,slip velocity,Schmidt number,Eckert number,magnetic parameter,and non-linear stretching parameter on the velocity,concentration,and temperature profiles of the nanofluid.The proposed model is novel as it simultaneously considers the impact of thermophoresis and Brownian motion,along with Ohmic and viscous dissipation effects,in both CST and PST scenarios for blood-based Casson nanofluid.The numerical technique built into MATLAB’s bvp4c module is utilized to solve the governing system of coupled differential equations,revealing that the concentration of nanoparticles decreases with increasing thermophoresis and Brownian motion parameters while the temperature of the nanofluid increases.Additionally,a higher Eckert number is found to reduce the nanofluid temperature.A comparative analysis between CST and PST scenarios is also undertaken,which highlights the significant influence of these factors on the fluid’s characteristics.The findings have potential applications in biomedical processes to enhance fluid velocity and heat transfer rates,ultimately improving patient outcomes.
文摘The results of this article can be useful in science and technology advancement, such as nanofluidics, micro mixing and energy conversion. The purpose of this article is to examine the impacts of nanoparticle shape on Al2O3-water nanofluid and heat transfer over a non-linear radically stretching sheet in the existence of magnetic field and thermal radiation. The different shapes of Al2O3 nanoparticles that have under contemplation are column, sphere, hexahedron, tetrahedron, and lamina. The governing partial differential equations (PDEs) of the problem are regenerated into set of non-linear ordinary differential equations (ODEs) by using appropriate similarity transformation. The bvp4c program has used to solve the obtained non-linear ordinary differential equation (ODEs). The Nusselt number for all shapes of Al2O3 nanoparticle shapes in pure water with is presented in graphical form. It has reported that the heat transfer augmentation in lamina shapes nanoparticles is more than other shapes of nanoparticle. The relation of thermal boundary layer with shapes of nanoparticles, solid volume fraction, magnetic field and thermal radiation has also presented with the help of graphical representation. It is also demonstrated that lamina shape nanoparticles have showed large temperature distribution than other shapes of nanoparticles.
文摘This paper investigates the boundary layer flow of the Maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field.The constitutive flow equations for the current physical problem are modeled and analyzed for the first time in the literature.The torsional motion of the cylinder is considered with the constant azimuthal velocity E.The partial differential equations(PDEs)governing the torsional motion of the Maxwell fluid together with energy transport are simplified with the boundary layer concept.The current analysis is valid only for a certain range of the positive Reynolds numbers.However,for very large Reynolds numbers,the flow becomes turbulent.Thus,the governing similarity equations are simplified through suitable transformations for the analysis of the large Reynolds numbers.The numerical simulations for the flow,heat,and mass transport phenomena are carried out in view of the bvp4c scheme in MATLAB.The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the flow penetrates shallower into the free stream fluid.It is also noted that the phenomenon of stress relaxation,described by the Deborah number,causes to decline the flow fields and enhance the thermal and solutal energy transport during the fluid motion.The penetration depth decreases for the transport of heat and mass in the fluid with the higher Reynolds numbers.An excellent validation of the numerical results is assured through tabular data with the existing literature.
基金This paper was financially supported by the National Natural Science Foundation of China(Grant No.51679251)the authors would like to express their sincere thanks.
文摘For new submarine pipeline maintenance lifting equipment,a specialized analysis model is constructed in this study.A pipeline can be divided into the lifted portion and the touch-down portion that lies on the seabed,and each of these portions can be analyzed separately by converting the continuity conditions at the touch-down points to boundary conditions.The typical two-point sequence secant iterative technique is used to obtain the unknown lifted length and determine pipeline lifting confgurations.The BVP4C module in MATLAB software is used to solve this multiple-point boundary value problem issued from frst-order diferential equations.Also,the triple-point lifting mode of truncated maintenance and the two-point lifting mode of online maintenance are discussed.When the lifted heights at truss positions are shown,the lifting deformation,lifting forces,bending moment distribution,and axial force distribution can be analyzed using a dedicated analysis program.Numerical results can then be used to design a lifting strategy to protect the pipeline.
基金supported by the National Natural Science Foundations of China(Grant No.11772046)。
文摘We study the coupled flow and heat transfer of power-law nanofluids on a non-isothermal rough rotating disk subjected to a magnetic field.The problem is formulated in terms of specified curvilinear orthogonal coordinate system.An improved BVP4C algorithm is proposed,and numerical solutions are obtained.The influence of volume fraction,types and shapes of nanoparticles,magnetic field and power-law index on the flow,and heat transfer behavior are discussed.The obtained results show that the power-law exponents(PLE),nanoparticle volume fraction(NVF),and magnetic field inclination angle(MFIA)have almost no effects on velocities in the wave surface direction,but have small or significant effects on the azimuth direction.The NVF has remarkable influences on local Nusselt number(LNN)and friction coefficients(FC)in the radial direction and the azimuth direction(AD).The LNN increases with NVF increasing while FC in AD decreases.The types of nanoparticles,magnetic field strength,and inclination have small effects on LNN,but they have remarkable influences on the friction coefficients with positively correlated heat transfer rate,while the inclination is negatively correlated with heat transfer rate.The size of the nanoparticle shape factor is positively correlated with LNN.
文摘The purpose of this research is to investigate the influence that slip boundary conditions have on the rate of heat and mass transfer by examining the behavior of micropolar MHD flow across a porous stretching sheet.In addition to this,the impacts of thermal radiation and viscous dissipation are taken into account.With the use of various computing strategies,numerical results have been produced.Similarity transformation was utilized in order to convert the partial differential equations(PDEs)that regulated energy,rotational momentum,concentration,and momentum into ordinary differential equations(ODEs).As compared to earlier published research,MATLAB inbuilt solver solution shows an extremely good correlation in exceptional instances.In exceptional instances,the present MATLAB inbuilt solver solution has a very excellent connection with the findings of the previously published investigations.A variety of flow field factors impact the Nusselt number,the wall couple shear stress,the friction factor,Sherwood numbers the dimensionless distributions discussed in detail.When the Eckert number rises,the temperature rises,and the Schmidt number falls,the concentration falls.Velocity increases with increases in the material factor but drops with increases in the magnetic parameter and the surface condition factor.
文摘The present study numerically investigates the flow and heat transfer of porous Williamson hybrid nanofluid on an exponentially shrinking sheet with magnetohydrodynamic(MHD)effects.The nonlinear partial differential equations which governed the model are first reduced to a set of ordinary differential equations by using the similarity transformation.Next,the BVP4C solver is applied to solve the equations by considering the pertinent fluid parameters such as the permeability parameter,the magnetic parameter,the Williamson parameter,the nanoparticle volume fractions and the wall mass transfer parameter.The single(SWCNTs)and multi-walled carbon nanotubes(MWCNTs)nanoparticles are taken as the hybrid nanoparticles.It is found that the increase in magnetic parameter in SWCNT+MCWNT hybrid nanofluid results in an increase of 72.2%on skin friction compared to SWCNT nanofluid while maintaining reducing a small number of Nusselt number.This shows the potential of the Williamson hybrid nanofluid for friction application purposes especially in transportation like braking system,flushing fluid and mechanical engineering.
基金supported by the Government College University,Faisalabad,and Higher Education Commission,Pakistan.
文摘In current study,the numerical computations of Reiner–Rivlin nanofluid flow through a rotational disk under the influence of thermal radiation and Arrhenius activation energy is considered.For innovative physical situations,the motile microorganisms are incorporated too.The multiple slip effects are considered in the boundary conditions.The bioconvection of motile microorganism is utilized alongside nanofluids to provide stability to enhanced thermal transportation.The Bioconvection pattern in various nanoparticles accredits novel applications of biotechnology like the synthesis of biological polymers,biosensors,fuel cells,petroleum engineering,and the natural environment.By deploying some suitable similarity transformation functions,the governing partial differential equations(PDEs)of the flow problem are rehabilitated into dimensionless forms.The accomplished ordinary differential equations(ODEs)are solved numerically through the bvp4c scheme via a built-in function in computational MATLAB software.The upshots of some prominent physical and bioconvection parameters including wall slip parameters,thermophoresis parameter,Brownian motion parameter,Reiner–Revlin nanofluid parameter,Prandtl number,Peclet number,Lewis number,bioconvection Lewis number,and the mixed convection parameter against velocity,temperature,nanoparticles concentration,and density of motile microorganism profiles are dichotomized and pondered through graphs and tables.The presented computations show that the velocity profiles are de-escalated by the wall slip parameters while the thermal and solutal fields are upgraded with augmentation in thermophoresis number and wall slip parameters.The presence of thermal radiation enhances the temperature profile of nanofluid.The concentration profile of nanoparticles is boosted by intensification in activation energy.Furthermore,the increasing values of bioconvection Lewis number and Peclet number decay the motile microorganisms’field.
基金funding this research through Researchers Supporting Project number:RSPD2024R650,King Saud University,Riyadh,Saudi Arabia.
文摘Entropy analysis can help to identify the sources of entropy generation in a heat transfer process more accurately than other methods,such as energy efficiency analysis.This is because entropy analysis takes into account the quality of energy as well as its quantity.Na-nofluids have already been shown to have superior heat transfer characteristics compared to conventionalfluids.Stefan blowing can further enhance the heat transfer capabilities of nano-fluids by increasing the massflux and turbulence at the surface.This can be beneficial in a wide range of applications,such as heat exchangers,electronic cooling,and solar energy devices.The convective boundary condition accounts for heat transfer effects,influencing temperature distribution and the thermal boundary layer.Depending on the direction of heat transfer,the convective boundary condition can induce cooling or heating effects on the inclined plate.This has practical implications for various engineering applications,such as the cooling of electronic devices or heating in industrial processes.Carreau nanofluids have a wide range of potential applications in heat transfer,energy storage,drug delivery,and food processing.This research investigates how the presence of Stefan blowing affects the properties of Carreau nanofluid flow across a convectively heated tilted plate.Heat and mass transport phenomena are studied using quadratic thermal radiation and chemical reaction parameters.The mathematical model for this work is based on the Buongiorno model.The governing equations are converted into a system of ordinary differential equations and then solved using the bvp4c solver.Physical parameters such as the mass transfer rate can be visualized using bar graphs.The study’s primary findings are that when the Weissenberg number increases,the velocity rises and the concentration profile declines due to Brownian motion.It is discovered that,when 0.5≤γ≤3(the inverse porosity parameter),the friction factor declines by 0.34001(in the presence of Stefan blowing),and 0.3284(otherwise).It has been observed that as the Brinkman number and magnetic field parameters increase,there is an increase in entropy formation.Additionally,it has been noted that these same factors have an inverse effect on the Bejan number.At 0.1≤Nb≤0.6(Brownian motion),the Sherwood number is seen to rise at a rate of 0.113353(in the presence of Stefan blowing),and 0.479739(otherwise).When the Stefan blowing parameter is absent,the rate of heat transfer is observed to be noticeably faster than when it is present.Furthermore,when the heat source parameter is set to 0.1≤Hs≤0.6,the decrement rates in heat transfer rate are 0.12208(in the presence of Stefan blowing)and 0.02102(otherwise).
文摘In the present article,we perform the second law analysis of classical Blasius flow accounting the effects of nonlinear radiation and frictional heating.The two-dimensional boundary layer momentum and energy equations are converted to self-similar equations using similarity transformations.The set of resultant ordinary differential equations are solved numerically.The numerical results obtained from solutions of dimensionless momentum and energy equations are used to calculate the entropy generation number and Bejan number.The velocity profile f'(ξ),temperature distributionθ(ξ),entropy production number Ns and Bejan number Be are plotted against the physical flow parameters and are discussed in detail.Further,for the sake of validation of our numerical code,the obtained results are reproduced using Matlab built-in boundary value solver bvp4c resulting in an excellent agreement.It is observed that entropy generation is increasing function of heating parameter,Prandtl number,Eckert number and radiation parameter.Further,it is observed that entropy generation can be minimized by reducing the operating temperatureΔT=T_(w)−T_(∞).
文摘In this article,three-dimensional mixed convection flow over an exponentially stretching sheet is investigated.Energy equation is modelled in the presence of viscous dissipation and variable thermal conductivity.Temperature of the sheet is varying exponentially and is chosen in a form that facilitates the similarity transformations to obtain self-similar equations.Resulting nonlinear ordinary differential equations are solved numerically employing the Runge-Kutta shooting method.In order to check the accuracy of the method,these equations are also solved using bvp4c built-in routine in Matlab.Both solutions are in excellent agreement.The effects of physical parameters on the dimensionless velocity field and temperature are demonstrated through various graphs.The novelty of this analysis is the self-similar solution of the threedimensional boundary layer flow in the presence of mixed convection,viscous dissipation and variable thermal conductivity.
文摘The aspiration of this research is to explore the impact of non-similar modeling for mixed convection in magnetized second-grade nanofluid flow.The flow is initiated by the stretching of a sheet at an exponential rate in the upward vertical direction.The buoyancy effects in terms of temperature and concentration differences are inserted in the x-momentum equation.The aspects of heat and mass transfer are studied using dimensionless thermophoresis,Schmidt and Brownian motion parameters.The governing coupled partial differential system(PDEs)is remodeled into coupled non-similar nonlinear PDEs by introducing non-similar transformations.The numerical analysis for the dimensionless non-similar partial differential system is performed using a local non-similarity method via bvp4c.Finally,the quantitative effects of emerging dimensionless quantities on the nondimensional velocity,temperature and mass concentration in the boundary layer are conferred graphically,and inferences are drawn that important quantities of interest are substantially affected by these parameters.It is concluded that non-similar modeling,in contrast to similar models,is more general and more accurate in convection studies in the presence of buoyancy effects for second-grade non-Newtonian fluids.
基金This work is partially supported by the National Natural Science Foundations of China(No.91430106)the Fundamental Research Funds for the Cen-tral Universities(No.06500073).
文摘In this paper,based on the finite element formulation,we focus on multiple solutions and their evolution with time for a laminar flow in a permeable channel with expanding or contracting walls.Both Newtonian fluid and micropolar fluid are consid-ered.For the Newtonian fluid model,we find that the profile of the unique solution in the case of injection remains the same for long time,which indicates that the solution may be stable.On the other hand,in the case of large suction,the profile of multiple solutions changes in time,which suggests that the multiple solutions may be unstable.Similar behaviors and conclusions are observed for the micropolar fluid model under different boundary parameters.
基金the Deanship of Scientific Research at King Khalid University,Abha,Saudi Arabia for funding this work through Large Groups Project under Grant Number RGP.2/51/44.
文摘The current article investigates the numerical study of the micropolar nanofluid flow through a 3D rotating surface.This communication may manipulate for the aim such as the delivery of the drug,cooling of electronic chips,nanoscience and the fields of nanotechnology.The impact of heat source/sink is employed.Brownian motion and thermophoresis aspects are discussed.The rotating sheet with the impacts of Darcy-Forchheimer law is also scrutinized.Furthermore,the influence of activation energy is analyzed in the current article.The numerical analysis is simplified with the help of befitted resemblance transformations.The succor of the shooting algorithm with built-in solver bvp4c MATLAB software is used for the numerical solution of nonlinear transformed equations.The consequences of different physical factors on the physical engineering quantities and the subjective fields were examined and presented.According to outcomes,it can be analyzed that the flow profile declined with the rotational parameter.It is observed that angular velocity diminishes via a larger porosity parameter.Furthermore,the temperature gradient is declined via a larger magnitude of the Prandtl number.The heat transfer is enhanced in the occurrence of Brownian motion.The activations energy parameter causes an increment in the volumetric concentration field.Moreover,the local Nusselt number is reduced via a greater estimation of the porosity parameter.
