Heat transfer in turbulent natural convection on a vertical permeable surface

A theoretical and experimental study is presented for heat transfer in turbulent natural convection on vertical surfaces with uniform and homogeneous air injection and withdrawal.     

Stability of a supersonic boundary layer on a permeable surface with heat transfer

The effect of cooling of a permeable surface on the stability of a supersonic boundary layer on it is investigated. As distinct from the case of an impermeable surface, deep cooling can reduce the critical Reynolds number. Common points of the continuous and discrete spectra are found in the region of the disturbance parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 41–46, January–February, 1977.The work was carried out at the Department of Applied Mathematics of the University of Western Ontario in Canada. I am grateful to the Head of the Department Professor J. Blackwell for suggesting the investigation of this problem.     

Free convection from a vertical permeable circular cone with non-uniform surface heat flux

 In this paper, the problem of laminar free convection from a vertical permeable circular cone maintained with non-uniform surface heat flux is considered. The governing boundary layer equations are reduced non-similar boundary layer equations with surface heat flux proportional to x ⁿ (where x is the distance measured from the leading edge). The solutions of the reduced equations are obtained by using three distinct solution methodologies; namely, (i) perturbation solution for small transpiration parameter, ξ, (ii) asymptotic solution for large ξ, and (iii) the finite difference solutions for all ξ. The solutions are presented in terms of local skin-friction and local Nusselt number for smaller values of Prandtl number and heat flux gradient and are displayed in tabular form as well as graphically. Effects of pertinent parameters on velocity and temperature profiles are also shown graphically. Solutions obtained by finite difference method are also compared with the perturbation solutions for small and large ξ and found to be in excellent agreement. Received on 1 October 1999     

Forced convection heat transfer on a heated bottom surface of cavity with different wall-height

Experiments to obtain the heat transfer characteristics of cavity, in which the downstream wall-heightD ₂ was changed from zero toD ₁ of upstream wall-height, have been performed. The vortex flow inside cavity was varied complicatedly depending on aspect-ratio of cavity and main flow velocity, and the flow pattern for cavity ofD ₂/D ₁=0.8 was altered entirely at theRe _H of about 1.5×10⁴. Three heat transfer regions ofNu _m versusRe _H were recognized for the cavity of large aspect-ratio. A close relation between those heat transfer behavior and approaching boundary layer flow was found. Heat transfer correlation was partially obtained for every cavities.     

Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties

This article presents a numerical solution for the steady two-dimensional mixed convection MHD flow of an electrically conducting viscous fluid over a vertical stretching sheet, in its own plane. The stretching velocity and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent fluid properties, namely, the fluid viscosity and the thermal conductivity are assumed to vary, respectively, as an inverse function of the temperature and a linear function of the temperature. A generalized similarity transformation is introduced to study the influence of temperature dependent fluid properties. The transformed boundary layer equations are solved numerically, using a finite difference scheme known as Keller Box method, for several sets of values of the physical parameters, namely, the stretching parameter, the temperature dependent viscosity parameter, the magnetic parameter, the mixed convection parameter, the temperature dependent thermal conductivity parameter and the Prandtl number. The numerical results thus obtained for the flow and heat transfer characteristics reveal many interesting behaviors. These behaviors warrant further study of the effects of the physical parameters on the flow and heat transfer characteristics. Here it may be noted that, in the case of the classical Navier-Stokes fluid flowing past a horizontal stretching sheet, McLeod and Rajagopal (1987) [42] showed that there exist an unique solution to the problem. This may not be true in the present case. Hence we would like to explore the non-uniqueness of the solution and present the findings in the subsequent paper.     

Mixed convection heat transfer from a horizontal plate with variable surface heat flux in a porous medium

In this article nonsimilarity solution for mixed convection from a horizontal surface in a saturated porous medium was obtained for the case of variable surface heat flux. The entire mixed convection regime, ranging from pure forced convection to pure free convection, is considered by introducing a single nonsimilarity parameter. Heat transfer results are predicted by employing four different flow models, namely, Darcy's law, the Ergun model, and the Brinkman-Forchheimer-extended Darcy model with constant and variable porosity. The variable porosity effect is approximated by an exponential function. Effects of transverse thermal dispersion are taken into consideration in the energy equation, along with variable stagnant thermal conductivities. The formulation of the present problem shows that the flow and heat transfer characteristics depend on five parameters, that is, the power in the variation of surface heat flux, the nonsimilarity mixed-convection parameter, the inertia effect parameter, the boundary effect parameter, and the ratio of thermal conductivity of the fluid phase to that of the solid phase. Numerical results for the local Nusselt number variations, based on the various flow models, are presented for the entire mixed convection regime. The impacts␣of different governing parameters on the heat transfer results are thoroughly investigated. Received on 7 August 1997     

A simultaneous PIV and heat transfer study of bubble interaction with free convection flow

Whole field velocity and point temperature and surface heat flux measurements were performed to characterise the interaction of a single rising ellipsoidal air bubble with the free convection flow from a heated flat surface immersed in water at different angles of inclination. Two thermocouples and a hot film sensor were used to characterise heat transfer from the surface, while a time-resolved digital particle image velocimetry technique was used to map the bubble induced flow in a plane parallel to the surface. Heat flux fluctuations, preceding and following the bubble passage, were shown to correlate with the variation in both local flow velocities and fluid temperatures. The largest increases in heat transfer were recorded when both flow and temperature effects combined to enhance the convective cooling simultaneously. Such conditions were shown to be most likely met when the block was inclined at 45°, thus forcing the bubble to slide closer to the heated surface and hence to the thermal boundary layer.     

Radiation effects on Marangoni convection boundary layer over a permeable surface

The problem of Marangoni convection boundary layer flow that can be formed along the interface of two immiscible fluids when the wall is permeable, where there is suction or injection effect, is considered. Similarity equations are obtained through the application of similarity transformation techniques. The effects of suction/injection and radiation parameters on the heat transfer characteristics are numerically studied using the shooting method for a fixed value of the Prandtl number (Pr=0.7). Numerical results are obtained for the surface temperature gradient or the heat transfer rate as well as the temperature profiles for some values of the governing parameters. Comparisons with known results from the open literature show very good agreements. The results indicate that the heat transfer rate at the surface decreases as the radiation parameter increases. Further, results show that multiple (dual) solutions exist for a certain range of the governing parameters.     

Theoretical solution of simultaneous heat and mass transfer by free convection about a vertical flat plate

In this paper we present a numerical solution for stationary simultaneous heat and mass transfer in the laminar boundary layer on a vertical flat plate. The theory is based on a simple physical model that treats the two buoyancy effects (originating from temperature and concentration differences) as mutually independant and additional forces. Results are given for the case of Pr=0.71, Sc=0.63 and equally directed body forces. Our experimental data for the same conditions show close agreement and these seems to be no need for a more complicated theory.     

Mixed convection heat transfer from a horizontal channel with protruding heat sources

A numerical investigation is carried out to study fluid flow and heat transfer characteristics of conjugate mixed convection from a two dimensional horizontal channel with four protruding heat sources mounted on one of the finite thick channel walls. The flow is assumed as laminar, hydrodynamically and thermally developing. Water and FC70 are the fluids under consideration. The geometric parameters such as spacing between the channel walls (S), size of protruding heat sources (L_h×t_h), thickness of substrate (t) and spacing between heat sources (b) are fixed. Results are presented to show the effect of parameters such as Re_S, Gr_S^*, Pr, k_p/k_f and k_s/k_f on fluid flow and heat transfer characteristics. Using the method of asymptotic expansions, correlations are also presented for the maximum temperature of heat source.     

Free convection heat transfer from an isothermal wavy surface in a porous enclosure

The coupled streamfuction–temperature equations governing the Darcian flow and convection process in a fluid-saturated porous enclosure with an isothermal sinusoidal bottom sun face, has been numerically analyzed using a finite element method (FEM). No restrictions have been imposed on the geometrical non-linearity arising from the parameters like wave amplitude (a), number of waves per unit length (N), wave phase (Φ), aspect ratio (A) and also on the flow driving parameter Rayleigh number (Ra). The numerical simulations for varying values of Ra bring about interesting flow features, like the transformation of a unicellular flow to a multicellular flow. Both with increasing amplitude and increasing number of waves per unit length, owing to the shift in the separation and reattachment points, a row–column pattern of multicellular flow transforms to a simple row of multicellular flow. A cycle of n celluar and n+1 cellular flows, with the flow in adjacent cells in the opposite direction, periodically manifest with phase varying between 0 and 360°. The global heat transfer into the system has been found to decrease with increasing amplitude and increasing number of waves per unit length. Only marginal changes in the global heat flux are observed, either with increasing Ra or varying Φ. Effectively, sinusoidal bottom surface undulations of the isothermal wall of a porous enclosure reduces the heat transfer into the system. © 1998 John Wiley & Sons, Ltd.     

Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux

The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field. It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field. The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF). The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method. Moreover, the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method, for the whole range of the local transpiration parameter ζ. Consideration is also given to the regions where the local transpiration parameter ζ is small or large enough. However, in these particular regions, solutions are acquired with the aid of a regular perturbation method. The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number Pr (= 0.005, 0.01, 0.05). Furthermore, the velocity and temperature profiles are also drawn from various values of the local transpiration parameter ζ.     

Effect of Hall current on MHD natural convection flow from vertical permeable fiat plate with uniform surface heat flux

The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field.It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field.The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF).The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method.Moreover,the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method,for the whole range of the local transpiration parameter ζ.Consideration is also given to the regions where the local transpiration parameter ζis small or large enough.However,in these particular regions,solutions are acquired with the aid of a regular perturbation method.The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number Pr (=0.005,0.01,0.05).Furthermore,the velocity and temperature profiles are also drawn from various values of the local transpiration parameterζ.     

Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux

The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field.It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field.The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF).The parabolic equations obtained from FVF are numer...     

A numerical study on heat transfer of a ferrofluid flow in a square cavity under simultaneous gravitational and magnetic convection

Theoretical and Computational Fluid Dynamics - Thermomagnetic convection is based on the use of external magnetic fields to better control heat transfer fluxes in ferrofluids, finding important...     

Thermal radiation effect on a mixed convection flow and heat transfer of the Williamson fluid past an exponentially shrinking permeable sheet with a convective boundary condition

The thermal radiation effect on a steady mixed convective flow with heat transfer of a nonlinear (non-Newtonian) Williamson fluid past an exponentially shrinking porous sheet with a convective boundary condition is investigated numerically. In this study, both an assisting flow and an opposing flow are considered. The governing equations are converted into nonlinear ordinary differential equations by using a suitable transformation. A numerical solution of the problem is obtained by using the Matlab software package for different values of the governing parameters. The results show that dual nonsimilar solutions exist for the opposing flow, whereas the solution for the assisting flow is unique. It is also observed that the dual nonsimilar solutions exist only if a certain amount of mass suction is applied through the porous sheet, which depends on the Williamson parameter, convective parameter, and radiation parameter.     

Transient forced convection heat transfer in a channel

A numerical analysis is made of incompressible transient turbulent flow heat transfer between two parallel plates when there is a step jump in space along the channel in wall heat flux or wall temperature. The variation of the fluid velocity and effective diffusivity over the channel cross section are accounted for. The fluid is assumed to have a fully-developed turbulent velocity profile throughout the length of the channel. The thermal responses of the system are obtained by solving energy equation for air by a digital computer. The results are presented in graphical forms. The stability of the finite difference solution is studied and condition for the stability of the difference solution is derived. A method is given to obtain velocity distributions from the distribution of turbulent eddy diffusivity of momentum. Variations of Nusselt numbers are obtained as a function of time and space. Steady-state values are also given and compared with the published results.