A mathematical model is constructed to investigate the three-dimensional flow of a non-Newtonian fluid. An in-compressible viscoelastic fluid is used in mathematical formulation. The conjugate convective process （in ...A mathematical model is constructed to investigate the three-dimensional flow of a non-Newtonian fluid. An in-compressible viscoelastic fluid is used in mathematical formulation. The conjugate convective process （in which heat the transfer rate from the bounding surface with a finite capacity is proportional to the local surface temperature） in three-dimensional flow of a differential type of non-Newtonian fluid is analyzed for the first time. Series solutions for the nonlinear differential system are computed. Plots are presented for the description of emerging parameters entering into the problem. It is observed that the conjugate heating phenomenon causes an appreciable increase in the temperature at the stretching wall.展开更多
The magnetohydrodynamic(MHD) three-dimensional flow of Jeffrey fluid in the presence of Newtonian heating is investigated. Flow is caused by a bidirectional stretching surface. Series solutions are constructed for the...The magnetohydrodynamic(MHD) three-dimensional flow of Jeffrey fluid in the presence of Newtonian heating is investigated. Flow is caused by a bidirectional stretching surface. Series solutions are constructed for the velocity and temperature fields. Convergence of series solutions is ensured graphically and numerically. The variations of key parameters on the physical quantities are shown and discussed in detail. Constructed series solutions are compared with the existing solutions in the limiting case and an excellent agreement is noticed. Nusselt numbers are computed with and without magnetic fields. It is observed that the Nusselt number decreases in the presence of magnetic field.展开更多
The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equation...The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained.展开更多
Heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface were addressed.Analysis was performed in the presence of internal heat generation/absorption. Concentration and therm...Heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface were addressed.Analysis was performed in the presence of internal heat generation/absorption. Concentration and thermal buoyancy effects were accounted. Convective boundary conditions for heat and mass transfer analysis were explored. Series solutions of the resulting problem were developed. Effects of mixed convection, internal heat generation/absorption parameter and Biot numbers on the dimensionless velocity, temperature and concentration distributions were illustrated graphically. Numerical values of local Nusselt and Sherwood numbers were obtained and analyzed for all the physical parameters. It is found that both thermal and concentration boundary layer thicknesses are decreasing functions of stretching ratio. Variations of mixed convection parameter and concentration buoyancy parameter on the velocity profiles and associated boundary layer thicknesses are enhanced. Velocity profiles and temperature increase in the case of internal heat generation while they reduce for heat absorption. Heat transfer Biot number increases the thermal boundary layer thickness and temperature. Also concentration and its associated boundary layer are enhanced with an increase in mass transfer Biot number. The local Nusselt and Sherwood numbers have quite similar behaviors for increasing values of mixed convection parameter, concentration buoyancy parameter and Deborah number.展开更多
In this article, we present accurate analytical solutions for boundary layer flow and heat transfer of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface subject to a t...In this article, we present accurate analytical solutions for boundary layer flow and heat transfer of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface subject to a transverse uniform magnetic field using the homotopy analysis method （HAM） for two general types of non-isothermal boundary conditions. In addition, we demonstrate that the previously reported analytical solutions for the temperature field given in terms of Kummer＇s function do not converge at the boundary. We provide a graphical and numerical demonstration of the convergence of the HAM solutions and tabulate the effects of various parameters on the skin friction coefficient and wall heat transfer.展开更多
Analysis is carried out to study the existence, uniqueness and behavior of exact solutions of the fourth order nonlinear coupled ordinary differential equations arising in the flow and heat transfer of a viscoelastic,...Analysis is carried out to study the existence, uniqueness and behavior of exact solutions of the fourth order nonlinear coupled ordinary differential equations arising in the flow and heat transfer of a viscoelastic, electrically conducting fluid past a continuously stretching sheet. The ranges of the parametric values are obtained for which the system has a unique pair of solutions, a double pair of solutions and infinitely many solutions.展开更多
Exact solutions for an incompressible,viscoelas-tic,electrically conducting MHD aligned fluid are obtainedfor velocity components and temperature profiles.Lie Groupmethod is applied to obtain the solution and the symm...Exact solutions for an incompressible,viscoelas-tic,electrically conducting MHD aligned fluid are obtainedfor velocity components and temperature profiles.Lie Groupmethod is applied to obtain the solution and the symmetriesused are of translational type.展开更多
The present research explores the three-dimensional boundary layer flow of the Maxwell nanofluid. The flow is generated by a bidirectional stretching surface. The mathematical formulation is carried out through a boun...The present research explores the three-dimensional boundary layer flow of the Maxwell nanofluid. The flow is generated by a bidirectional stretching surface. The mathematical formulation is carried out through a boundary layer approach with the heat source/sink, the Brownian motion, and the thermophoresis effects. The newly developed boundary conditions requiring zero nanoparticle mass flux at the boundary are employed in the flow analysis for the Maxwell fluid. The governing nonlinear boundary layer equations through appropriate transformations are reduced to the coupled nonlin- ear ordinary differential system. The resulting nonlinear system is solved. Graphs are plotted to examine the effects of various interesting parameters on the non-dimensional velocities, temperature, and concentration fields. The values of the local Nusselt number are computed and examined numerically.展开更多
The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible non-Newto- nian Casson fluid bounded by two parallel non-conducting porous plates has been studied with heat transfer consider...The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible non-Newto- nian Casson fluid bounded by two parallel non-conducting porous plates has been studied with heat transfer considering the Hall effect. The fluid is acted upon by a uniform and exponential decaying pressure gradient. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a uniform suction and injection. The lower plate is stationary and the upper plate is suddenly set into mo- tion and simultaneously suddenly isothermally heated to a temperature other than the lower plate temperature. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of unsteady pressure gradient, the Hall term, the parameter describing the non-Newtonian behavior on both the velocities and temperature distributions have been stud- ied.展开更多
Analytical solutions of temperature distributions and the Nusselt numbers in forced convection are reported for flow through infinitely long parallel plates, where the upper plate moves in the flow direction with cons...Analytical solutions of temperature distributions and the Nusselt numbers in forced convection are reported for flow through infinitely long parallel plates, where the upper plate moves in the flow direction with constant velocity and the lower plate is kept stationary. The flow is assumed to be laminar, both hydro-dynamically and thermally fully developed, taking into account the effect of viscous dissipation of the flowing fluid. Both the plates being kept at specified and at different constant heat fluxes are considered as thermal boundary conditions. The solutions obtained from energy equation are in terms of Brinkman number, dimensionless velocity and heat flux ratio. These parameters greatly influence and give complete understanding on heat transfer rates that has potentials for designing and analyzing energy equipment and processes.展开更多
Momentum and energy laminar boundary layers of an incompressible fluid with thermal radiation about a moving plate in a quiescent ambient fluid are investigated numerically. Also, it has been underlined that the analy...Momentum and energy laminar boundary layers of an incompressible fluid with thermal radiation about a moving plate in a quiescent ambient fluid are investigated numerically. Also, it has been underlined that the analysis of the roles of both velocity and temperature gradient at infinity is of key relevance for our results.展开更多
This communication reports,the flow of viscoelastic nanofluid with third order slip flow condition,Cattaneo-Christov heat and mass diffusion model.The joined non-linear ordinary differential equations(ODEs)were acquir...This communication reports,the flow of viscoelastic nanofluid with third order slip flow condition,Cattaneo-Christov heat and mass diffusion model.The joined non-linear ordinary differential equations(ODEs)were acquired from the partial differential equations,which are resulting from conservation of momentum,energy and species.By means of similarity transformations these ODEs were alerted into dimensionless form and solved numerically by means of bvp4c solver.The effects of different parameters on velocity,temperature,and concentration profiles were examined and discussed in depth by means of graphs and tables.The outcomes indicate that the velocity profile along both x and y directions augment with higher values of viscoelastic parameter.The results also confirm that an increment in the values of ratio parameter tends to grow up the velocity profile alongside y-direction.However,the velocity profile along x-direction slows down with increment in the value of third order slip parameter.Also,the results illustrate that diminution in temperature is observed for higher Sc in the region of boundary layer.Besides,both temperature and concentration can be improved via higher Biot number.The upshots also portrayed that the local skin friction coefficient augmented within mounting values of viscoelastic fluid parameter.Furthermore,for finer values of Biot number both local Nusselt number and the local Sherwood number are enlarged.In addition,the most favorable agreement is observed among the results of the present study and those of the earlier studies.展开更多
基金Project supported by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah(Grant No.10-130/1434HiCi)
文摘A mathematical model is constructed to investigate the three-dimensional flow of a non-Newtonian fluid. An in-compressible viscoelastic fluid is used in mathematical formulation. The conjugate convective process （in which heat the transfer rate from the bounding surface with a finite capacity is proportional to the local surface temperature） in three-dimensional flow of a differential type of non-Newtonian fluid is analyzed for the first time. Series solutions for the nonlinear differential system are computed. Plots are presented for the description of emerging parameters entering into the problem. It is observed that the conjugate heating phenomenon causes an appreciable increase in the temperature at the stretching wall.
文摘The magnetohydrodynamic(MHD) three-dimensional flow of Jeffrey fluid in the presence of Newtonian heating is investigated. Flow is caused by a bidirectional stretching surface. Series solutions are constructed for the velocity and temperature fields. Convergence of series solutions is ensured graphically and numerically. The variations of key parameters on the physical quantities are shown and discussed in detail. Constructed series solutions are compared with the existing solutions in the limiting case and an excellent agreement is noticed. Nusselt numbers are computed with and without magnetic fields. It is observed that the Nusselt number decreases in the presence of magnetic field.
文摘The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained.
文摘Heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface were addressed.Analysis was performed in the presence of internal heat generation/absorption. Concentration and thermal buoyancy effects were accounted. Convective boundary conditions for heat and mass transfer analysis were explored. Series solutions of the resulting problem were developed. Effects of mixed convection, internal heat generation/absorption parameter and Biot numbers on the dimensionless velocity, temperature and concentration distributions were illustrated graphically. Numerical values of local Nusselt and Sherwood numbers were obtained and analyzed for all the physical parameters. It is found that both thermal and concentration boundary layer thicknesses are decreasing functions of stretching ratio. Variations of mixed convection parameter and concentration buoyancy parameter on the velocity profiles and associated boundary layer thicknesses are enhanced. Velocity profiles and temperature increase in the case of internal heat generation while they reduce for heat absorption. Heat transfer Biot number increases the thermal boundary layer thickness and temperature. Also concentration and its associated boundary layer are enhanced with an increase in mass transfer Biot number. The local Nusselt and Sherwood numbers have quite similar behaviors for increasing values of mixed convection parameter, concentration buoyancy parameter and Deborah number.
文摘In this article, we present accurate analytical solutions for boundary layer flow and heat transfer of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface subject to a transverse uniform magnetic field using the homotopy analysis method （HAM） for two general types of non-isothermal boundary conditions. In addition, we demonstrate that the previously reported analytical solutions for the temperature field given in terms of Kummer＇s function do not converge at the boundary. We provide a graphical and numerical demonstration of the convergence of the HAM solutions and tabulate the effects of various parameters on the skin friction coefficient and wall heat transfer.
文摘Analysis is carried out to study the existence, uniqueness and behavior of exact solutions of the fourth order nonlinear coupled ordinary differential equations arising in the flow and heat transfer of a viscoelastic, electrically conducting fluid past a continuously stretching sheet. The ranges of the parametric values are obtained for which the system has a unique pair of solutions, a double pair of solutions and infinitely many solutions.
文摘Exact solutions for an incompressible,viscoelas-tic,electrically conducting MHD aligned fluid are obtainedfor velocity components and temperature profiles.Lie Groupmethod is applied to obtain the solution and the symmetriesused are of translational type.
文摘The present research explores the three-dimensional boundary layer flow of the Maxwell nanofluid. The flow is generated by a bidirectional stretching surface. The mathematical formulation is carried out through a boundary layer approach with the heat source/sink, the Brownian motion, and the thermophoresis effects. The newly developed boundary conditions requiring zero nanoparticle mass flux at the boundary are employed in the flow analysis for the Maxwell fluid. The governing nonlinear boundary layer equations through appropriate transformations are reduced to the coupled nonlin- ear ordinary differential system. The resulting nonlinear system is solved. Graphs are plotted to examine the effects of various interesting parameters on the non-dimensional velocities, temperature, and concentration fields. The values of the local Nusselt number are computed and examined numerically.
文摘The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible non-Newto- nian Casson fluid bounded by two parallel non-conducting porous plates has been studied with heat transfer considering the Hall effect. The fluid is acted upon by a uniform and exponential decaying pressure gradient. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a uniform suction and injection. The lower plate is stationary and the upper plate is suddenly set into mo- tion and simultaneously suddenly isothermally heated to a temperature other than the lower plate temperature. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of unsteady pressure gradient, the Hall term, the parameter describing the non-Newtonian behavior on both the velocities and temperature distributions have been stud- ied.
文摘Analytical solutions of temperature distributions and the Nusselt numbers in forced convection are reported for flow through infinitely long parallel plates, where the upper plate moves in the flow direction with constant velocity and the lower plate is kept stationary. The flow is assumed to be laminar, both hydro-dynamically and thermally fully developed, taking into account the effect of viscous dissipation of the flowing fluid. Both the plates being kept at specified and at different constant heat fluxes are considered as thermal boundary conditions. The solutions obtained from energy equation are in terms of Brinkman number, dimensionless velocity and heat flux ratio. These parameters greatly influence and give complete understanding on heat transfer rates that has potentials for designing and analyzing energy equipment and processes.
文摘Momentum and energy laminar boundary layers of an incompressible fluid with thermal radiation about a moving plate in a quiescent ambient fluid are investigated numerically. Also, it has been underlined that the analysis of the roles of both velocity and temperature gradient at infinity is of key relevance for our results.
文摘This communication reports,the flow of viscoelastic nanofluid with third order slip flow condition,Cattaneo-Christov heat and mass diffusion model.The joined non-linear ordinary differential equations(ODEs)were acquired from the partial differential equations,which are resulting from conservation of momentum,energy and species.By means of similarity transformations these ODEs were alerted into dimensionless form and solved numerically by means of bvp4c solver.The effects of different parameters on velocity,temperature,and concentration profiles were examined and discussed in depth by means of graphs and tables.The outcomes indicate that the velocity profile along both x and y directions augment with higher values of viscoelastic parameter.The results also confirm that an increment in the values of ratio parameter tends to grow up the velocity profile alongside y-direction.However,the velocity profile along x-direction slows down with increment in the value of third order slip parameter.Also,the results illustrate that diminution in temperature is observed for higher Sc in the region of boundary layer.Besides,both temperature and concentration can be improved via higher Biot number.The upshots also portrayed that the local skin friction coefficient augmented within mounting values of viscoelastic fluid parameter.Furthermore,for finer values of Biot number both local Nusselt number and the local Sherwood number are enlarged.In addition,the most favorable agreement is observed among the results of the present study and those of the earlier studies.
