Free convection from an arbitrarily inclined plate in a porous medium

Abstract

A mathematical model for the flow and heat transfer in the free convection from an arbitrary inclined isothermal flat plate embedded in a porous medium is presented, in which the Darcy-Boussinesq approximation is adopted to account for bouyancy force. A novel inclination parameter is proposed such that all cases of the horizontal, inclined and vertical plates can be described by a single set of transformed boundary layer equations. Moreover, the similarity equations for the limiting cases of the horizontal and vertical plates are recovered from the transformed equations by setting :0 and :1, respectively. Detailed results for the skin friction coefficient and Nusselt number as well as for the dimensionless velocity and temperature profiles are presented for a wide range of the parameter. A comparison with similarity solution shows excellent agreement.

Natural Convection Boundary Layer Along Impermeable Inclined Surfaces Embedded in Porous Medium

“…2. The solution was obtained by using the inclination parameter defined by Pop and Na [9] and defining a new coordinate system for both positive and negative inclinations of the plate. The numerical Keller box scheme implemented to discrete equations.…”

“…To convert Eqs. ( 1), ( 8) and ( 9) to the equations that could describe natural convection flow from an arbitrarily inclined plate in a porous medium, the parameter which was introduced by Pop and Na [9], is used ( ) ( )…”

“…Jang and Chang [8] studied free convection on an inclined plate with power function distribution of wall temperature, while its angle varies between 0 to close to 90 degrees from horizontal. While Pop and Na [9] have solved the free convection of an isothermal inclined surface. Their solution included all horizontal to vertical cases.…”

“…Coordinate system introduced by Pop and Na [9] is used in the solution. Then the system of two equations can be solved by finite difference technique proposed by Keller [13] for both the cases of positively inclined plate ( )…”

Conjugate Free Convection from a Slightly Inclined Plate Embedded in a Porous Medium

“…In the previous studies of free and mixed convection flow along inclined plates embedded in a porous medium, studies by Ingham et al [11], Rees and Riley [12], Kumari et al [13], Pop and Na [14], Weidman and Amberg [15], and Hossain et al [16], there are two types of formulation for the theoretical analysis. The first type is based on the similarity variables for a horizontal plate and provides solutions that are valid for small angles of inclination of the plate from the horizontal.…”