Two Coupled Forced‐Convection Boundary Layers of Counter‐Flow

In this study, the conjugate heat transfer problem of two forced‐convection boundary layers of counter‐laminar flow on plate sides is analyzed by employing the integral method. The analysis is conducted in a dimensionless way to generalize the solution. The dimensionless parameters governing the thermal coupling between the two convection layers are revealed from the analysis. These parameters give a measure of the relative importance of interactive heat transfer modes. Mean Nusselt number results are obtained for a wide range of the governing parameters.     

Conjugate film condensation and natural convection along the interface between a porous and an open space

This paper reports a theoretical investigation focusing on the interaction between film condensation and natural convection along a vertical wall separating a fluid reservoir from a fluid-saturated porous reservoir. The two reservoirs are maintained at different temperatures. The study consists of two parts: in the first part the condensation phenomenon takes place in the fluid reservoir and the natural convection phenomenon in the porous layer. In the second part, the opposite situation is considered. The main heat transfer and flow characteristics in the two counterflowing layers, namely, the condensation film and the natural convection boundary layer are documented for a wide range of the problem parameters. These parameters appear after boundary layer scaling of the governing equations. Important engineering results regarding the overall heat flux from the condensation side to the natural convection side are summarized in the course of the study. Finally, the effect of the thermal resistance of the wall constituting the interface separating the two reservoirs, on the overall heat flux from the condensation side to the natural convection side is determined.     

Effect of chemical reaction and thermal radiation on heat and mass transfer flow of MHD micropolar fluid in a rotating frame of reference

This paper studies the effect of first order chemical reaction and thermal radiation on hydromagnetic free convection heat and mass transfer flow of a micropolar fluid via a porous medium bounded by a semi-infinite porous plate with constant heat source in a rotating frame of reference. The plate is assumed to oscillate in time with constant frequency so that the solutions of the boundary layer are the same oscillatory type. The dimensionless governing equations for this investigation are solved analytically using small perturbation approximation. The effect of the various dimensionless parameters entering into the problem on the velocity, temperature and concentration profiles across the boundary layer are investigated through graphs. Also the results of the skin friction coefficient, couple stress coefficient, the rate of heat and mass transfer at the wall are prepared with various values of the parameters.     

Numerical investigation on mixed convection in a non-Newtonian fluid inside a vertical duct

This paper reports a numerical study of the thermal and fluid-dynamic behaviour of laminar mixed convection in a non-Newtonian fluid inside a vertical duct enclosed within two vertical plates that are plane and parallel, having linearly varying wall temperatures. The other inlet conditions consist of a parabolic distribution of the velocity field and a constant fluid temperature. The problem is assumed to be steady and two-dimensional. The formulation of a mathematical model in dimensionless co-ordinates and the discretisation of the governing equations by means of the finite difference method, have made it possible to create a numerical code developed in Matlab environment. The study was focused on the simultaneous presence and on the mutual interaction of natural and forced convection, starting from the effects of the re-circulation on the heat transfer. The quantitative results of the analysis, which are strongly affected by the variation of the Grashof number and of the exponent of the power law, are given in terms of graphic visualisations of the fluid velocity profiles and, when the governing parameters vary, of the various geometries characterising the heat transfer.     

Natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium

This work studies the natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium with uniform wall temperature. The two-velocity two-temperature formulation is used to derive the governing equations of this system. The Prandtl coordinate transformation is used to transform the wavy surface into a regular plane, and the obtained equations are then simplified further by the order-of-magnitude analysis to give the boundary layer equations. The cubic spline collocation method is used to solve the boundary layer governing equations. The effects of dimensionless amplitude, angle of inclination, inter-phase heat transfer parameter, modified thermal conductivity ratio, and permeability ratio on the heat transfer and flow characteristics are studied. Increasing the modified thermal conductivity ratio and the permeability ratio can effectively enhance the natural convection heat transfer of the inclined plate in bidisperse porous media. Moreover, the thermal non-equilibrium effects are significant for low values of the inter-phase heat transfer parameter. As the dimensionless amplitude increases, both the fluctuations of the local Nusselt number for the f-phase and the p-phase with the streamwise coordinate are enhanced.     

Numerical computation on Marangoni convective flow of two‐phase MHD dusty nanofluids under Brownian motion and thermophoresis effects

The current theoretical study describes the Marangoni thermal convective flow of magnetohydrodynamic dusty nanofluids along a wavy vertical surface. The two‐phase mathematical model is developed under the influence of thermal radiation and exponentially varying space‐dependent heat source. Pure and hybrid nanoparticles together with dust particle suspension in the base fluid are taken into consideration to characterize the behavior of the flow. Brownian motion and thermophoresis mechanisms are considered, since it enhances the convection features of dusty nanofluid. Appropriate transformations are adopted to modify the flow governing equations and boundary conditions to dimensionless form. The forward finite difference scheme is implemented to illustrate the resultant coupled partial differential equations. The Newton quasi‐linearization technique is utilized to reduce the nonlinear system into a linear form, which is solved thereafter by Thomas algorithm. The responses of velocity, temperature, concentration, friction factor, and heat and mass transfer rate profiles with various governing parameters are discussed and portrayed graphically. The study evidences that the radiation and space‐dependent heat generating parameters strengthen the temperature distribution. Also, the heat transfer rate appreciably rises with the increment in Marangoni convection. The solution methodology and accuracy of the model is validated by generating the earlier outcomes for nonradiating nanofluid flow without heat source/sink.     

Unsteady mixed convection from a rotating vertical slender cylinder in an axial flow

Unsteady mixed convection flow over a rotating vertical slender cylinder under the combined effects of buoyancy force and thermal diffusion with injection/suction has been studied where the slender cylinder is inline with the flow. The effect of surface curvature is also taken into account, especially for the applications such as wire and fiber drawing, where accurate predictions are desired. The governing boundary layer equations along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then resulting system of coupled nonlinear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. The effects of various parameters on velocity and temperature profiles and on skin friction coefficients and heat transfer rate at the wall are reported in the present study.     

Convection heat and mass transfer in a hydromagnetic flow of a second grade fluid in the presence of thermal radiation and thermal diffusion

The convection heat and mass transfer in a hydromagnetic flow of a second grade fluid past a semi-infinite stretching sheet in the presence of thermal radiation and thermal diffusion are considered. The governing coupled non-linear partial differential equations describing the flow problem are transformed into non-linear ordinary differential equations by method of similarity transformation. The resulting similarity equations are solved numerically using Runge-Kutta shooting method. The results are presented as velocity, temperature and concentration fields for different values of parameters entering into the problem. The skin friction, rate of heat transfer and mass transfer are presented numerically in tabular form. In addition, the results obtained showed that these parameters have significant influence on the flow, heat and mass transfer.     

Mixed Convection Over a Vertical Plate in a Doubly Stratified Fluid‐Saturated Non‐Darcy Porous Medium with Cross‐Diffusion Effects

The present article investigates the influence of Dufour and Soret effects on mixed convection heat and mass transfer over a vertical plate in a doubly stratified fluid‐saturated porous medium. The plate is maintained at a uniform and constant wall heat and mass fluxes. The Darcy–Forchheimer model is employed to describe the flow in porous medium. The nonlinear governing equations and their associated boundary conditions are initially transformed into dimensionless forms. The resulting system of nonlinear partial differential equations is then solved numerically by the Keller‐box method. The variation of the dimensionless velocity, temperature, concentration, heat, and mass transfer rates for different values of governing parameters involved in the problem are analyzed and presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21114     

Coupled heat and mass transfer by natural convection adjacent to a permeable horizontal cylinder in a saturated porous medium

The heat and mass transfer characteristics of free convection about a permeable horizontal cylinder embedded in porous media under the coupled effects of thermal and mass diffusion are numerically analyzed. The surface of the horizontal cylinder is maintained at a uniform wall temperature and uniform wall concentration. The transformed governing equations are obtained and solved by Keller box method. Numerical results for the dimensionless temperature profiles, the dimensionless concentration profiles, the Nusselt number and the Sherwood number are presented. Increasing the buoyancy ratio N and the transpiration parameter f_w increases the Nusselt number and the Sherwood number. For thermally assisting flow, when Lewis number Le increases, the Nusselt (Sherwood) number decreases (increases). Whereas, for thermally opposing flow, both the Nusselt number and the Sherwood number increase with increasing the Lewis number.     

Laminar combined magnetoconvection in a wavy enclosure with the effect of heat conducting cylinder

In the current work, a numerical study of the flow characteristics on combined magnetoconvection in a lid-driven square enclosure, differentially heated, is carried out. This problem is solved by using finite element method of the partial differential equations, which are the heat transfer and stream function in Cartesian coordinates. The tests are performed for different solid–fluid thermal conductivity ratio, cylinder location and Richardson number while the Prandtl number, Reynolds number, magnetic and Joule heating parameters are kept constant. One geometrical configuration is used namely two undulations. The outcome obtained shows that the heat conducting inner square cylinder affects the flow and the heat transfer rate in the enclosure. The trend of the local heat transfer is found to follow a wavy pattern. Results are presented in terms of streamlines, isotherms, average Nusselt number at the heated wavy wall, average temperature of the fluid in the enclosure and dimensionless temperature at the cylinder center for different combinations of the governing parameters.     

Numerical analysis of convective heat transport in a porous semi‐trapezoidal enclosure with radiation effect

A theoretical and numerical study of natural convection of two‐dimensional laminar incompressible flow in a semi‐trapezoidal porous enclosure in the presence of thermal radiation is conducted. The semi‐trapezoidal enclosure has an inclined left wall that in addition to the right vertical wall is maintained at a constant temperature, whereas the remaining (horizontal) walls are adiabatic. The Darcy‐Brinkman isotropic model is utilized. The governing partial differential equations are transformed using a vorticity stream function and nondimensional quantities and the resulting governing nonlinear dimensionless equations are solved using the finite difference method with incremental steps. The impacts of the different model parameters (Rayleigh number [Ra], Darcy number [Da], and radiation parameter [Rd]) on the thermofluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with the greater Darcy parameter (permeability). The flow is accelerated with the increasing buoyancy effect (Rayleigh number) and heat transfer is also increased with a greater radiative flux. The present numerical simulations are more relevant to hybrid porous media solar collectors.     

Effect of Heat-Generating Solid Body on Mixed Convection Flow in a Ventilated Cavity

The mixed convection flow and heat transfer characteristics inside a square ventilated cavity with a heat-generating solid circular body located at the center have been investigated numerically. The inlet opening is at the bottom of the left wall, while the outlet one is at the top of the right wall, and all the walls of the cavity are considered to be adiabatic. A Galerkin weighted residual finite element method is used to solve the governing equations of mass, momentum, and energy. The behavior of the fluid in the ranges of dimensionless cylinder diameter from 0.1 to 0.6 of the heat generating body, thermal conductivity ratio range from 0.2 to 50 between solid and fluid, and heat generating parameter range from 1 to 5 is described in detail. The medium considered is air with a Prandtl number of 0.71. It is found that the flow and temperature field is strongly dependent on the already-mentioned parameters for the ranges considered. The variation of the mean Nusselt number, the dimensionless average drag force, and the average temperature of the fluid versus Richardson number are presented for these parameters.     

The skin friction in the MHD mixed convection stagnation point with mass transfer

Numerical results are presented for the effects of mass transfer on steady two-dimensional laminar MHD mixed convection owing to the stagnation flow against a heated vertical semi-infinite permeable surface. These results are obtained by solving the coupled nonlinear partial differential equations describing the conservation of mass, momentum and energy by a perturbation technique. These results are presented to illustrate the influence of the Hartmann number, wall mass transfer coefficient, heat absorption coefficient, Prandtl number and the mixed convection or buoyancy parameter. Numerical results for the dimensionless velocity profiles, the temperature profiles, the local friction coefficient and the local Nusselt number are presented for various parameters. These effects of the different parameters on the velocity and temperature as well as the skin friction and wall heat transfer are presented graphically.     

Uncertainties in physical property effects on viscous flow and heat transfer over a nonlinearly stretching sheet with nanofluids

The purpose of this paper is to investigate a numerical analysis for the flow and heat transfer in a viscous fluid over a nonlinear stretching sheet utilizing nanofluid. The governing partial differential equations are converted into highly nonlinear ordinary differential equations by a similarity transformation. Different water-based nanofluids containing Cu, Ag, CuO, Al₂O₃, and TiO₂ are considered in our problem. Furthermore, four different models of nanofluid based on different formulas for thermal conductivity and dynamic viscosity on the flow and heat transfer characteristics are discussed. The variations of dimensionless surface temperature, dimensionless surface temperature gradient as well as the flow and heat transfer characteristics with the governing parameters are graphed and tabulated. Comparison with published results for pure fluid flow is presented and it is found to be in excellent agreement.     

On laminar hydromagnetic mixed convection flow in a vertical channel with symmetric and asymmetric wall heating conditions

The problem of hydromagnetic fully developed laminar mixed convection flow in a vertical channel with symmetric and asymmetric wall heating conditions in the presence or absence of heat generation or absorption effects is considered. Through proper choice of dimensionless variables, the governing equations are developed and three types of thermal boundary conditions are prescribed. These thermal boundary conditions are isothermal-isothermal, isoflux-isothermal, and isothermal-isoflux for the left-right walls of the channel. Analytical solutions for the velocity and temperature profiles for various special cases of the problem are reported. In addition, closed-form expressions for the Nusselt numbers and reversal flow conditions at both the left and right channel walls are derived. The general problem which includes the effects of both viscous dissipation and Joule heating is solved numerically by an implicit finite-difference scheme. Favorable comparisons of special cases with previously published work are obtained. A selected set of graphical results illustrating the effects of the various parameters involved in the problem including viscous and magnetic dissipations on the velocity and temperature profiles as well as flow reversal situations and Nusselt numbers is presented and discussed.     

理想流体对流传热问题的理论解

研究理想流体受迫对流传热和自然对流传热问题的理论解。采用流体无垂直于壁面法线方向运动(即无穿透)的条件取代黏性流体在壁面无滑移条件，解决了流体在边界上有滑移时计算对流传热系数的困难，给出了理想流体与平壁受迫对流传热、理想流体与竖直壁面自然对流传热和理想流体在管内受迫对流传热的理论解。结果表明：理想流体的对流传热与黏性流体同样存在着热边界层。在外部流动的情况下，无论受迫对流传热还是自然对流传热，对流传热系数都与流体的导热系数、密度和比热三乘积的二分之一次方成正比。在管内受迫对流的情况下，当无因次长度大于0．05时，局部Nu和界面无因次温度分布都不再变化，对于恒热流边界条件，Nu等于8，截面无因次平均温度等于2；对于恒壁温边界条件，Nu等于5．782，截面无因次平均温度等于2．316。     

Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate

The combined free convection boundary layer flow with thermal radiation and mass transfer past a permeable vertical plate is studied when the plate moves in its own plane. The plate is maintained at a uniform temperature with uniform species concentration and the fluid is considered to be gray, absorbing–emitting. The coupled unsteady non-linear momentum, energy and concentration equations governing the problem is obtained and made similar by introducing a time-dependent length scale. The similarity equations are solved numerically using superposition method. The resulting velocity, temperature and concentration distributions are shown graphically for different values of parameters entering into the problem. The numerical values of the local wall shear stress, local surface heat and mass flux are shown in tabular form.     

Effect of Viscous Dissipation and Internal Heat Generation/Absorption on Heat Transfer Flow Over a Moving Wedge With Convective Boundary Condition

In this study, the effects of viscous dissipation and internal heat generation/absorption on heat transfer viscous flow over a moving wedge in the presence of suction or injection with a convective boundary condition have been carried out numerically for various values of dimensionless parameters. With the help of similarity transformation, the momentum and energy equations are reduced to a set of coupled non‐linear ordinary differential equations. These equations are solved using the Runge–Kutta fourth‐order method with a shooting technique. The variation in the dimensionless temperature, velocity, heat transfer coefficient, and shear stress have been presented in tabular as well as in graphical form for a range of controlling parameters. It is shown that the dimensionless heat transfer rate is a strong function of viscous dissipation and convective parameters and heat transfer shows an enhanced behavior with the stretching parameter for both the favorable and unfavorable regimes. It is also shown that in the presence of a heat source, the dimensionless temperature and its gradients in thermal boundary layers are found to be high for a high value of the convection parameter. The comparison of present results with the available data shows a good agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(7): 589–602, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21055     

Unsteady mixed convection flow over a vertical wedge

The behavior of unsteady mixed convection flow of an incompressible viscous fluid over a vertical wedge with constant suction/injection have been investigated. The unsteadiness is due to the time-dependent free stream velocity. The governing boundary layer equations along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then resulting system of coupled non-linear partial differential equations is solved by an implicit finite-difference scheme in combination with the quasi-linearization technique. Numerical results for the effects of various parameters on velocity, temperature and concentration profiles and on their gradient at the wall are reported in the present study. The buoyancy force causes considerable velocity overshoot for low Prandtl number (Pr) fluids. Skin friction coefficient, heat and concentration transfer rates are found to alter significantly due to injection/suction for both accelerating and decelerating flow.