The main objective of this work is to investigate analytically the steady nanofluid flow and heat transfer characteristics between nonparallel plane walls. Using appropriate transformations for the velocity and temper...The main objective of this work is to investigate analytically the steady nanofluid flow and heat transfer characteristics between nonparallel plane walls. Using appropriate transformations for the velocity and temperature, the basic nonlinear partial differential equations are reduced to the ordinary differential equations. Then, these equations have been solved analytically and numerically for some values of the governing parameters, Reynolds number, Re, channel half angle, α, Prandtl number, Pr, and Eckert number, Ec, using Adomian decomposition method and the Runge-Kutta method with mathematic package. Analytical and numerical results are searched for the skin friction coefficient, Nusselt number and the velocity and temperature profiles. It is found on one hand that the Nusselt number increases as Eckert number or channel half-angle increases, but it decreases as Reynolds number increases. On the other hand, it is also found that the presence of Cu nanoparticles in a water base fluid enhances heat transfer between nonparallel plane walls and in consequence the Nusselt number increases with the increase of nanoparticles volume fraction. Finally, an excellent agreement between analytical results and those obtained by numerical Runge-Kutta method is highly noticed.展开更多
Kerosene-alumina nanofluid flow and heat transfer in the presence of magnetic field are studied. The basic partial differential equations are reduced to ordinary differential equations which are solved semi analytical...Kerosene-alumina nanofluid flow and heat transfer in the presence of magnetic field are studied. The basic partial differential equations are reduced to ordinary differential equations which are solved semi analytically using differential transformation method. Velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number are determined analytically. The influence of pertinent parameters such as magnetic parameter, nanofluid volume fraction, viscosity parameter and Eckert number on the flow and heat transfer characteristics is discussed. Results indicate that skin friction coefficient decreases with increase of magnetic parameter, nanofluid volume fraction and viscosity parameter. Nusselt number increases with increase of magnetic parameter and nanofluid volume fraction while it decreases with increase of Eckert number and viscosity parameter.展开更多
An analysis was made to study the steady momentum and heat transfer characteristics of a viscous electrically conducting fluid near a stagnation point due to a stretching/shrinking sheet in the presence of a transvers...An analysis was made to study the steady momentum and heat transfer characteristics of a viscous electrically conducting fluid near a stagnation point due to a stretching/shrinking sheet in the presence of a transverse magnetic field and generalized slip condition. Two flow problems corresponding to the planar and axisymmetric stretching/shrinking sheet were considered. By means of similarity transformations, the obtained resultant nonlinear ordinary differential equations were solved numerically using a shooting method for dual solutions of velocity and temperature profiles. Some important physical features of the flow and heat transfer in terms of the fluid velocity, the temperature distribution, the skin friction coefficient and the local Nusselt number for various values of the controlling governing parameters like velocity slip parameter, critical shear rate, magnetic field, ratio of stretching/shrinking rate to external flow rate and Prandtl number were analyzed and discussed. An increase of the critical shear rate decreases the fluid velocity whereas the local Nusselt number increases. The comparison of the present numerical results with the existing literature in a limiting case is given and found to be in an excellent agreement.展开更多
Combined effects of Soret(thermal-diffusion) and Dufour(diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorpti...Combined effects of Soret(thermal-diffusion) and Dufour(diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorption and chemical reaction. The laws of conservation of mass, momentum, energy and concentration are found to lead to the mathematical development of the problem. Suitable transformations were used to convert the nonlinear partial differential equations into the ordinary differential equations. The series solutions of boundary layer equations through momentum, energy and concentration equations were obtained.Convergence of the developed series solutions was discussed via plots and numerical values. The behaviors of different physical parameters on the velocity components, temperature and concentration were obtained. Numerical values of Nusselt number, skin friction and Sherwood number with different parameters were computed and analyzed. It is found that Dufour and Soret numbers result in the enhancement of temperature and concentration distributions, respectively.展开更多
The thermal conduction behavior of the three-dimensional axisymmetric functionally graded circular plate was studied under thermal loads on its top and bottom surfaces. Material properties were taken to be arbitrary d...The thermal conduction behavior of the three-dimensional axisymmetric functionally graded circular plate was studied under thermal loads on its top and bottom surfaces. Material properties were taken to be arbitrary distribution functions of the thickness. A temperature function that satisfies thermal boundary conditions at the edges and the variable separation method were used to reduce equation governing the steady state heat conduction to an ordinary differential equation （ODE） in the thickness coordinate which was solved analytically. Next, resulting variable coefficients ODE due to arbitrary distribution of material properties along thickness coordinate was also solved by the Peano-Baker series. Some numerical examples were given to demonstrate the accuracy, efficiency of the present model, mad to investigate the influence of different distributions of material properties on the temperature field. The numerical results confirm that the influence of different material distributions, gradient indices and thickness of plate to temperature field in plate can not be ignored.展开更多
This study examines theoretically and computationally the non-Newtonian boundary layer flow and heat transfer for a viscoelastic fluid over a stretching continuous sheet embedded in a porous medium with variable fluid...This study examines theoretically and computationally the non-Newtonian boundary layer flow and heat transfer for a viscoelastic fluid over a stretching continuous sheet embedded in a porous medium with variable fluid properties, slip velocity, and internal heat generation/absorption. The flow in boundary layer is considered to be generated solely by the stretching of the sheet adjacent to porous medium with boundary wall slip condition. Highly nonlinear momentum and thermal boundary layer equations governing the flow and heat transfer are reduced to set of nonlinear ordinary differential equations by appropriate transformation. The resulting ODEs are successfully solved numerically with the help of shooting method. Graphical results are shown for non-dimensional velocities and temperature. The effects of heat generation/absorption parameter, the porous parameter, the viscoelastic parameter, velocity slip parameter, variable thermal conductivity and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction coefficient and Nusselt number are presented. Comparison of numerical results is made with the earlier published results under limiting cases.展开更多
The magnetohydrodynamic(MHD) boundary layer flow of Casson fluid in the presence of nanoparticles is investigated.Convective conditions of temperature and nanoparticle concentration are employed in the formulation. Th...The magnetohydrodynamic(MHD) boundary layer flow of Casson fluid in the presence of nanoparticles is investigated.Convective conditions of temperature and nanoparticle concentration are employed in the formulation. The flow is generated due to exponentially stretching surface. The governing boundary layer equations are reduced into the ordinary differential equations. Series solutions are presented to analyze the velocity, temperature and nanoparticle concentration fields. Temperature and nanoparticle concentration fields decrease when the values of Casson parameter enhance. It is found that the Biot numbers arising due to thermal and concentration convective conditions yield an enhancement in the temperature and concentration fields. Further, we observed that both the thermal and nanoparticle concentration boundary layer thicknesses are higher for the larger values of thermophoresis parameter. The effects of Brownian motion parameter on the temperature and nanoparticle concentration are reverse.展开更多
The steady two-dimensional flow of Powell-Eyring fluid is investigated. The flow is caused by a stretching surface with homogeneous-heterogeneous reactions. The governing nonlinear differential equations are reduced t...The steady two-dimensional flow of Powell-Eyring fluid is investigated. The flow is caused by a stretching surface with homogeneous-heterogeneous reactions. The governing nonlinear differential equations are reduced to the ordinary differential equations by similarity transformations. The analytic solutions are presented in series forms by homotopy analysis method(HAM). Convergence of the obtained series solutions is explicitly discussed. The physical significance of different parameters on the velocity and concentration profiles is discussed through graphical illustrations. It is noticed that the boundary layer thickness increases by increasing the Powell-Eyring fluid material parameter(ε) whereas it decreases by increasing the fluid material parameter(δ). Further, the concentration profile increases when Powell-Eyring fluid material parameters increase. The concentration is also an increasing function of Schmidt number and decreasing function of strength of homogeneous reaction. Also mass transfer rate increases for larger rate of heterogeneous reaction.展开更多
文摘The main objective of this work is to investigate analytically the steady nanofluid flow and heat transfer characteristics between nonparallel plane walls. Using appropriate transformations for the velocity and temperature, the basic nonlinear partial differential equations are reduced to the ordinary differential equations. Then, these equations have been solved analytically and numerically for some values of the governing parameters, Reynolds number, Re, channel half angle, α, Prandtl number, Pr, and Eckert number, Ec, using Adomian decomposition method and the Runge-Kutta method with mathematic package. Analytical and numerical results are searched for the skin friction coefficient, Nusselt number and the velocity and temperature profiles. It is found on one hand that the Nusselt number increases as Eckert number or channel half-angle increases, but it decreases as Reynolds number increases. On the other hand, it is also found that the presence of Cu nanoparticles in a water base fluid enhances heat transfer between nonparallel plane walls and in consequence the Nusselt number increases with the increase of nanoparticles volume fraction. Finally, an excellent agreement between analytical results and those obtained by numerical Runge-Kutta method is highly noticed.
文摘Kerosene-alumina nanofluid flow and heat transfer in the presence of magnetic field are studied. The basic partial differential equations are reduced to ordinary differential equations which are solved semi analytically using differential transformation method. Velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number are determined analytically. The influence of pertinent parameters such as magnetic parameter, nanofluid volume fraction, viscosity parameter and Eckert number on the flow and heat transfer characteristics is discussed. Results indicate that skin friction coefficient decreases with increase of magnetic parameter, nanofluid volume fraction and viscosity parameter. Nusselt number increases with increase of magnetic parameter and nanofluid volume fraction while it decreases with increase of Eckert number and viscosity parameter.
文摘An analysis was made to study the steady momentum and heat transfer characteristics of a viscous electrically conducting fluid near a stagnation point due to a stretching/shrinking sheet in the presence of a transverse magnetic field and generalized slip condition. Two flow problems corresponding to the planar and axisymmetric stretching/shrinking sheet were considered. By means of similarity transformations, the obtained resultant nonlinear ordinary differential equations were solved numerically using a shooting method for dual solutions of velocity and temperature profiles. Some important physical features of the flow and heat transfer in terms of the fluid velocity, the temperature distribution, the skin friction coefficient and the local Nusselt number for various values of the controlling governing parameters like velocity slip parameter, critical shear rate, magnetic field, ratio of stretching/shrinking rate to external flow rate and Prandtl number were analyzed and discussed. An increase of the critical shear rate decreases the fluid velocity whereas the local Nusselt number increases. The comparison of the present numerical results with the existing literature in a limiting case is given and found to be in an excellent agreement.
文摘Combined effects of Soret(thermal-diffusion) and Dufour(diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorption and chemical reaction. The laws of conservation of mass, momentum, energy and concentration are found to lead to the mathematical development of the problem. Suitable transformations were used to convert the nonlinear partial differential equations into the ordinary differential equations. The series solutions of boundary layer equations through momentum, energy and concentration equations were obtained.Convergence of the developed series solutions was discussed via plots and numerical values. The behaviors of different physical parameters on the velocity components, temperature and concentration were obtained. Numerical values of Nusselt number, skin friction and Sherwood number with different parameters were computed and analyzed. It is found that Dufour and Soret numbers result in the enhancement of temperature and concentration distributions, respectively.
基金Project(11102136)supported by the National Natural Science Foundation of ChinaProject(2012ZDK04)supported by the Open Project of Guangxi Key Laboratory of Disaster Prevention and Structural Safety,China
文摘The thermal conduction behavior of the three-dimensional axisymmetric functionally graded circular plate was studied under thermal loads on its top and bottom surfaces. Material properties were taken to be arbitrary distribution functions of the thickness. A temperature function that satisfies thermal boundary conditions at the edges and the variable separation method were used to reduce equation governing the steady state heat conduction to an ordinary differential equation （ODE） in the thickness coordinate which was solved analytically. Next, resulting variable coefficients ODE due to arbitrary distribution of material properties along thickness coordinate was also solved by the Peano-Baker series. Some numerical examples were given to demonstrate the accuracy, efficiency of the present model, mad to investigate the influence of different distributions of material properties on the temperature field. The numerical results confirm that the influence of different material distributions, gradient indices and thickness of plate to temperature field in plate can not be ignored.
文摘This study examines theoretically and computationally the non-Newtonian boundary layer flow and heat transfer for a viscoelastic fluid over a stretching continuous sheet embedded in a porous medium with variable fluid properties, slip velocity, and internal heat generation/absorption. The flow in boundary layer is considered to be generated solely by the stretching of the sheet adjacent to porous medium with boundary wall slip condition. Highly nonlinear momentum and thermal boundary layer equations governing the flow and heat transfer are reduced to set of nonlinear ordinary differential equations by appropriate transformation. The resulting ODEs are successfully solved numerically with the help of shooting method. Graphical results are shown for non-dimensional velocities and temperature. The effects of heat generation/absorption parameter, the porous parameter, the viscoelastic parameter, velocity slip parameter, variable thermal conductivity and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction coefficient and Nusselt number are presented. Comparison of numerical results is made with the earlier published results under limiting cases.
文摘The magnetohydrodynamic(MHD) boundary layer flow of Casson fluid in the presence of nanoparticles is investigated.Convective conditions of temperature and nanoparticle concentration are employed in the formulation. The flow is generated due to exponentially stretching surface. The governing boundary layer equations are reduced into the ordinary differential equations. Series solutions are presented to analyze the velocity, temperature and nanoparticle concentration fields. Temperature and nanoparticle concentration fields decrease when the values of Casson parameter enhance. It is found that the Biot numbers arising due to thermal and concentration convective conditions yield an enhancement in the temperature and concentration fields. Further, we observed that both the thermal and nanoparticle concentration boundary layer thicknesses are higher for the larger values of thermophoresis parameter. The effects of Brownian motion parameter on the temperature and nanoparticle concentration are reverse.
文摘The steady two-dimensional flow of Powell-Eyring fluid is investigated. The flow is caused by a stretching surface with homogeneous-heterogeneous reactions. The governing nonlinear differential equations are reduced to the ordinary differential equations by similarity transformations. The analytic solutions are presented in series forms by homotopy analysis method(HAM). Convergence of the obtained series solutions is explicitly discussed. The physical significance of different parameters on the velocity and concentration profiles is discussed through graphical illustrations. It is noticed that the boundary layer thickness increases by increasing the Powell-Eyring fluid material parameter(ε) whereas it decreases by increasing the fluid material parameter(δ). Further, the concentration profile increases when Powell-Eyring fluid material parameters increase. The concentration is also an increasing function of Schmidt number and decreasing function of strength of homogeneous reaction. Also mass transfer rate increases for larger rate of heterogeneous reaction.
