Free convection boundary layer correlations for a vertical plate with nonuniform heating

Abstract

An analytical study of a free convection boundary layer (BL) for a laminar and steady flow over a vertical flat plate (VFP) having nonuniform thermal conditions has been investigated. The plate is subjected to a variable wall heat flux of (Formula presented.) where (Formula presented.) is the distance along the VFP from the leading edge and (Formula presented.) is a reference heat flux. The boundary layer equations for nonuniform wall heat flux conditions have been formulated. These equations are then solved numerically for the range of exponents (Formula presented.) and Prandtl numbers ((Formula presented.)) of −0.25 to 1 and 0.01 to 1000 respectively. The effects of two physical parameters (Formula presented.) and (Formula presented.) on the characteristic of thermal boundary layer (TBL) and hydrodynamic boundary layer (VBL) are described. Moreover, correlations of TBL and VBL thicknesses have been presented as a function of Pr and (Formula presented.) The TBL and VBL thickness are more influenced by Pr as compared to (Formula presented.) These correlations are reasonably accurate for uniform heat flux (n = 0) proposed by A. Bejan using a scale analysis and no other such correlations are available for nonuniform heat flux for a wide range of Prandtl numbers (Pr). It has been found that when (Formula presented.) both the BL thicknesses decrease with the Pr till a value of (Formula presented.) is reached. For (Formula presented.) the growth of VBL and TBL thickness over the VFP increases and decreases respectively. Consequently, the local skin friction coefficient decreases and the local Nusselt number increases with the increase in (Formula presented.) and (Formula presented.) at a fixed value of modified Rayleigh number. © 2022 Taylor & Francis Group, LLC.