Solar Radiation Assisted Natural Convection in Uniform Porous Medium Supported by a Vertical Flat Plate

1997 ◽  
Vol 119 (1) ◽  
pp. 89-96 ◽  
Author(s):  
A. J. Chamkha
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Solar Radiation ◽  
Flat Plate ◽  
Boussinesq Approximation ◽  
Incident Radiation ◽  
Temperature Fields ◽  
Convection Flow ◽  
Local Similarity ◽  
Vertical Flat Plate

Natural convection flow of an absorbing fluid up a uniform porous medium supported by a semi-infinite, ideally transparent, vertical flat plate due to solar radiation is considered. Boundary-layer equations are derived using the usual Boussinesq approximation and accounting for applied incident radiation flux. A convection type boundary condition is used at the plate surface. These equations exhibit no similarity solution. However, the local similarity method is employed for the solution of the present problem so as to allow comparisons with previously published work. The resulting approximate nonlinear ordinary differential equations are solved numerically by a standard implicit iterative finite-difference method. Graphical results for the velocity and temperature fields as well as the boundary friction and Nusselt number are presented and discussed.

scholarly journals Numerical study of the effects of natural convection in a thermoacoustic configuration

2019 ◽  
Vol 20 (8) ◽  
pp. 807
Author(s):  
Omar Hireche ◽  
Catherine Weisman ◽  
Diana Baltean-Carlès ◽  
Virginie Daru ◽  
Yann Fraigneau
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Numerical Study ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Acoustic Resonator ◽  
Operating Conditions ◽  
Temperature Fields ◽  
Convection Flow ◽  
Conductivity Anisotropy

This study focuses on natural convection flows within a cylindrical guide containing a porous medium. This configuration is applicable to standing-wave thermoacoustic engines, usually composed of an acoustic resonator where a (short) stack (or porous medium) is inserted, with a heat exchanger placed at one of its ends. The resulting horizontal temperature gradient, when high enough, triggers the onset of an acoustic wave. Natural convection effects are usually neglected in thermoacoustics so that axisymmetry is often assumed. Here a 3D numerical study of natural convection flow is performed using a finite volume code for solving mixed Navier-Stokes and Darcy-Brinkman equations under Boussinesq approximation. The influence of the porous medium’s physical characteristics (permeability, thermal conductivity, anisotropy) on the flow and temperature fields is investigated. It is shown that such flows are fully three-dimensional and therefore can modify significantly starting as well as steady operating conditions of the thermoacoustic engine.

Non-Darcian Boundary Layer Flow and Forced Convective Heat Transfer Over a Flat Plate in a Fluid-Saturated Porous Medium

1990 ◽  
Vol 112 (1) ◽  
pp. 157-162 ◽  
Author(s):  
A. Nakayama ◽  
T. Kokudai ◽  
H. Koyama
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Flat Plate ◽  
Similarity Solution ◽  
Temperature Fields ◽  
Solid Boundary ◽  
Local Similarity ◽  
Viscous Term ◽  
Inertia Term

The local similarity solution procedure was successfully adopted to investigate non-Darcian flow and heat transfer through a boundary layer developed over a horizontal flat plate in a highly porous medium. The full boundary layer equations, which consider the effects of convective inertia, solid boundary, and porous inertia in addition to the Darcy flow resistance, were solved using novel transformed variables deduced from a scale analysis. The results from this local similarity solution are found to be in good agreement with those obtained from a finite difference method. The effects of the convective inertia term, boundary viscous term, and porous inertia term on the velocity and temperature fields were examined in detail. Furthermore, useful asymptotic expressions for the local Nusselt number were derived in consideration of possible physical limiting conditions.

A Pseudospectral Analysis of Laminar Natural Convection Flow and Heat Transfer Between Two Inclined Parallel Plates

2006 ◽  
Author(s):  
Serkan Kasapoglu ◽  
Ilker Tari
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Boussinesq Approximation ◽  
Temperature Fields ◽  
Convection Flow ◽  
Parallel Plates ◽  
Natural Convection Flow ◽  
Constant Wall Temperature ◽  
Laminar Natural Convection

Three dimensional laminar natural convection flow of and heat transfer in incompressible air between two inclined parallel plates are analyzed with the Boussinesq approximation by using spectral methods. The plates are assumed to be infinitely long in streamwise (x) and spanwise (z) directions. For these directions, periodic boundary conditions are used and for the normal direction (y), constant wall temperature and no slip boundary conditions are used. Unsteady Navier-Stokes and energy equations are solved using a pseudospectral approach in order to obtain velocity and temperature fields inside the channel. Fourier series are used to expand the variables in × and z directions, while Chebyshev polynomials are used to expand the variables in y direction. By using the temperature distribution between the plates, local and average Nusselt numbers (Nu) are calculated. Nu values are correlated with φ, which is the inclination angle, and with Ra·cosφ to compare the results with the literature.

scholarly journals Mixed Convection Boundary Layer Flow over a Permeable Vertical Flat Plate Embedded in an Anisotropic Porous Medium

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Norfifah Bachok ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Mixed Convection ◽  
Flat Plate ◽  
Anisotropic Fluid ◽  
Convection Flow ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Vertical Flat Plate

An analysis is performed to study the heat transfer characteristics of steady mixed convection flow over a permeable vertical flat plate embedded in an anisotropic fluid-saturated porous medium. The effects of uniform suction and injection on the flow field and heat transfer characteristics are numerically studied by employing an implicit finite difference Keller-box method. It is found that dual solutions exist for both assisting and opposing flows. The results indicate that suction delays the boundary layer separation, while injection accelerates it.

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