The objective of this paper is to study unsteady magneto hydrodynamic (MHD) free flow of viscoelastic fluid (Walter’s B) past an infinite vertical plate through porous medium. The temperature is assumed to be oscilla...The objective of this paper is to study unsteady magneto hydrodynamic (MHD) free flow of viscoelastic fluid (Walter’s B) past an infinite vertical plate through porous medium. The temperature is assumed to be oscillating with time. The solution obtained shows different profiles of effects of slip conditions on primary and secondary velocity. Also, the effects of various parameters on temperature, concentration, primary and secondary velocity profiles were presented graphically. The result indicated the secondary velocity is enhanced with increase in slip parameter. Primary velocity demonstrated opposite trend.展开更多
The aim of the present paper is to analyze the natural convection heat and mass transfer of nanofluids over a vertical plate embedded in a saturated Darcy porous medium subjected to surface heat and nanoparticle fluxe...The aim of the present paper is to analyze the natural convection heat and mass transfer of nanofluids over a vertical plate embedded in a saturated Darcy porous medium subjected to surface heat and nanoparticle fluxes. To carry out the numerical solution, two steps are performed. The governing partial differential equations are firstly simplified into a set of highly coupled nonlinear ordinary differential equations by appropriate similarity variables, and then numerically solved by the finite difference method. The obtained similarity solution depends on four non-dimensional parameters, i.e., the Brownian motion parameter （Nb）, the buoyancy ratio （Nr）, the thermophoresis parameter （Nt）, and the Lewis number （Le）. The variations of the reduced Nusselt number and the reduced Sherwood number with Nb and Nt for various values of Le and Nr are discussed in detail. Simulation results depict that the increase in Nb, Nt, or Nr decreases the reduced Nusselt number. An increase in the Lewis number increases both of the reduced Nusselt number and the Sherwood number. The results also reveal that the nanoparticle concentration boundary layer thickness is much thinner than those of the thermal and hydrodynamic boundary layers.展开更多
In this paper, an investigation of the effects of some physical parameters and Hall current on magneto hydrodynamics (MHD) fluid flow with heat flux over a porous medium was carefully examined, taking into considerati...In this paper, an investigation of the effects of some physical parameters and Hall current on magneto hydrodynamics (MHD) fluid flow with heat flux over a porous medium was carefully examined, taking into consideration Hall effects where the temperature and concentration are assumed to be oscillating with time. Furthermore, perturbation method is used in solving the governing equations. The profiles of velocity, temperature and concentration are presented graphically, going into the problem the primary and secondary velocity are presented and compute for some physical parameters such as mass Grashof number (<em>Gc</em>), Schmidt number <em>Sc</em>, Prandtl number (<em>Pr</em>) viscoelastic parameter (<em>K</em><sub>1</sub>) and hall current parameter (<em>m</em>). Results indicated that primary velocity increases with increase in values of <em>Gc</em> on one hand and on the other hand it decreases with increase in the values of <em>Pr</em>, <em>K</em><sub>1</sub> and <em>m</em>. Secondary velocity demonstrated opposite trend.展开更多
In this paper, the analytical solution of a viscous and incompressible fluid towards an exponentially stretching porous sheet with surface heat flux in porous medium, for the boundary layer and heat transfer flow, is ...In this paper, the analytical solution of a viscous and incompressible fluid towards an exponentially stretching porous sheet with surface heat flux in porous medium, for the boundary layer and heat transfer flow, is presented. The equations of continuity, momentum and the energy are transformed into non-linear ordinary differential by using similarity transformation. The solutions of these highly non-linear ordinary differential equations are found analytically by means of Homotopy Analysis Method (HAM). The result obtained by HAM is compared with numerical results presented in the literature. The accuracy of the HAM is indicated by close agreement of the two sets of results. By this method, an expression is obtained which is admissible for all values of effective parameters. This method has the ability to control the convergence of the solution.展开更多
In the present work we investigate the effects of Joule heating and viscous dissipation on MHD fluid flow. The viscous incompressible fluid flows over a stretching porous horizontal sheet subjected to power law heat f...In the present work we investigate the effects of Joule heating and viscous dissipation on MHD fluid flow. The viscous incompressible fluid flows over a stretching porous horizontal sheet subjected to power law heat flux in presence of heat source. The equations of momentum and heat transfer governing the problem are transformed into a system of dimensionless differential equations, which in turn solved numerically using shooting technique. The effects of the Joule heating parameter, permeability parameter, heat source parameter, Eckert number and Prandtl number are discussed and tabulated.展开更多
The role of the Cattaneo-Christov heat flux theory in the two-dimensional laminar flow of the Jeffrey liquid is discussed with a vertical sheet. The salient feature in the energy equation is accounted due to the imple...The role of the Cattaneo-Christov heat flux theory in the two-dimensional laminar flow of the Jeffrey liquid is discussed with a vertical sheet. The salient feature in the energy equation is accounted due to the implementation of the Cattaneo-Christov heat flux. A liquid with variable thermal conductivity is considered in the Darcy-Forchheimer porous space. The mathematical expressions of momentum and energy are coupled due to the presence of mixed convection. A highly nonlinear coupled system of equations is tackled with the homotopic algorithm. The convergence of the homotopy expressions is calculated graphically and numerically. The solutions of the velocity and temperature are expressed for various values of the Deborah number, the ratio of the relaxation time to the retardation time, the porosity parameter, the mixed convective parameter, the Darcy-Forchheimer parameter, and the conductivity parameter. The results show that the velocity and temperature are higher in Fourier＇s law of heat conduction cases in comparison with the Cattaneo-Christov heat flux model.展开更多
A three-dimensional finite-element model has been established to investigate the thermal behavior of the medium-thick slab copper casting mold with different cooling water slot designs. The mold wall temperatures meas...A three-dimensional finite-element model has been established to investigate the thermal behavior of the medium-thick slab copper casting mold with different cooling water slot designs. The mold wall temperatures measured using thermocouples buried in different positions of the mold with the original designed cooling system were analyzed to determine the corresponding heat flux profile. This profile was then used for simulation to predict the temperature distribution and the thermal stress distribution of the molds. The predicted temperatures during operation matched the plant measurements. The results showed that the maximum temperature, about 635 K in the wide hot surface, was found about 60 mm below the meniscus and 226 mm from the center of the mold. For the mold with the type I modified design, there was an insignificant decrease in temperature of about 5 K, and for the mold with the type II modified design, the maximum temperature was decreased by about 15 K and the temperature of the hot surface was distributed more uniformly along the length of the mold. The corresponding maximum thermal stress at the hot surface of the mold was reduced from 408 MPa to 386 MPa with the type II modified design. The results indicated that the modified design II is beneficial to the increase of mold life and the quality of casting slabs.展开更多
文摘The objective of this paper is to study unsteady magneto hydrodynamic (MHD) free flow of viscoelastic fluid (Walter’s B) past an infinite vertical plate through porous medium. The temperature is assumed to be oscillating with time. The solution obtained shows different profiles of effects of slip conditions on primary and secondary velocity. Also, the effects of various parameters on temperature, concentration, primary and secondary velocity profiles were presented graphically. The result indicated the secondary velocity is enhanced with increase in slip parameter. Primary velocity demonstrated opposite trend.
基金Shahid Chamran University of Ahvaz for its support of this paper
文摘The aim of the present paper is to analyze the natural convection heat and mass transfer of nanofluids over a vertical plate embedded in a saturated Darcy porous medium subjected to surface heat and nanoparticle fluxes. To carry out the numerical solution, two steps are performed. The governing partial differential equations are firstly simplified into a set of highly coupled nonlinear ordinary differential equations by appropriate similarity variables, and then numerically solved by the finite difference method. The obtained similarity solution depends on four non-dimensional parameters, i.e., the Brownian motion parameter （Nb）, the buoyancy ratio （Nr）, the thermophoresis parameter （Nt）, and the Lewis number （Le）. The variations of the reduced Nusselt number and the reduced Sherwood number with Nb and Nt for various values of Le and Nr are discussed in detail. Simulation results depict that the increase in Nb, Nt, or Nr decreases the reduced Nusselt number. An increase in the Lewis number increases both of the reduced Nusselt number and the Sherwood number. The results also reveal that the nanoparticle concentration boundary layer thickness is much thinner than those of the thermal and hydrodynamic boundary layers.
文摘In this paper, an investigation of the effects of some physical parameters and Hall current on magneto hydrodynamics (MHD) fluid flow with heat flux over a porous medium was carefully examined, taking into consideration Hall effects where the temperature and concentration are assumed to be oscillating with time. Furthermore, perturbation method is used in solving the governing equations. The profiles of velocity, temperature and concentration are presented graphically, going into the problem the primary and secondary velocity are presented and compute for some physical parameters such as mass Grashof number (<em>Gc</em>), Schmidt number <em>Sc</em>, Prandtl number (<em>Pr</em>) viscoelastic parameter (<em>K</em><sub>1</sub>) and hall current parameter (<em>m</em>). Results indicated that primary velocity increases with increase in values of <em>Gc</em> on one hand and on the other hand it decreases with increase in the values of <em>Pr</em>, <em>K</em><sub>1</sub> and <em>m</em>. Secondary velocity demonstrated opposite trend.
文摘In this paper, the analytical solution of a viscous and incompressible fluid towards an exponentially stretching porous sheet with surface heat flux in porous medium, for the boundary layer and heat transfer flow, is presented. The equations of continuity, momentum and the energy are transformed into non-linear ordinary differential by using similarity transformation. The solutions of these highly non-linear ordinary differential equations are found analytically by means of Homotopy Analysis Method (HAM). The result obtained by HAM is compared with numerical results presented in the literature. The accuracy of the HAM is indicated by close agreement of the two sets of results. By this method, an expression is obtained which is admissible for all values of effective parameters. This method has the ability to control the convergence of the solution.
文摘In the present work we investigate the effects of Joule heating and viscous dissipation on MHD fluid flow. The viscous incompressible fluid flows over a stretching porous horizontal sheet subjected to power law heat flux in presence of heat source. The equations of momentum and heat transfer governing the problem are transformed into a system of dimensionless differential equations, which in turn solved numerically using shooting technique. The effects of the Joule heating parameter, permeability parameter, heat source parameter, Eckert number and Prandtl number are discussed and tabulated.
文摘The role of the Cattaneo-Christov heat flux theory in the two-dimensional laminar flow of the Jeffrey liquid is discussed with a vertical sheet. The salient feature in the energy equation is accounted due to the implementation of the Cattaneo-Christov heat flux. A liquid with variable thermal conductivity is considered in the Darcy-Forchheimer porous space. The mathematical expressions of momentum and energy are coupled due to the presence of mixed convection. A highly nonlinear coupled system of equations is tackled with the homotopic algorithm. The convergence of the homotopy expressions is calculated graphically and numerically. The solutions of the velocity and temperature are expressed for various values of the Deborah number, the ratio of the relaxation time to the retardation time, the porosity parameter, the mixed convective parameter, the Darcy-Forchheimer parameter, and the conductivity parameter. The results show that the velocity and temperature are higher in Fourier＇s law of heat conduction cases in comparison with the Cattaneo-Christov heat flux model.
基金financially supported by the National Natural Science Foundation of China(Nos.51525401,51274054,U1332115,51401044)the Science and Technology Planning Project of Dalian(No.2013A16GX110)+1 种基金the China Postdoctoral Science Foundation(2015M581331)the Fundamental Research Funds for the Central Universities
文摘A three-dimensional finite-element model has been established to investigate the thermal behavior of the medium-thick slab copper casting mold with different cooling water slot designs. The mold wall temperatures measured using thermocouples buried in different positions of the mold with the original designed cooling system were analyzed to determine the corresponding heat flux profile. This profile was then used for simulation to predict the temperature distribution and the thermal stress distribution of the molds. The predicted temperatures during operation matched the plant measurements. The results showed that the maximum temperature, about 635 K in the wide hot surface, was found about 60 mm below the meniscus and 226 mm from the center of the mold. For the mold with the type I modified design, there was an insignificant decrease in temperature of about 5 K, and for the mold with the type II modified design, the maximum temperature was decreased by about 15 K and the temperature of the hot surface was distributed more uniformly along the length of the mold. The corresponding maximum thermal stress at the hot surface of the mold was reduced from 408 MPa to 386 MPa with the type II modified design. The results indicated that the modified design II is beneficial to the increase of mold life and the quality of casting slabs.
