Free convection heat transfer from an isothermal plate with arbitrary inclination

Abstract

This paper presents a new formulation for the laminar free convection from an arbitrarily inclined isothermal plate to fluids of any Prandtl number between 0.00t and infinity. 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 equations. Moreover, the self-similar equations for the limiting cases of the horizontal and vertical plates are recovered from the transformed equations by setting ~ = 0 and ~ = 1, respectively. Heated upward-facing plates with positive and negative inclination angles are investigated. A very accurate correlation equation of the local Nusselt number is developed for arbitrary inclination angle and for 0.00t-< Pr< oe. Wiirmeiibertragung bei freier Konvektion an einer isothermen Platte mit beliebiger NeigungZusammenfasssung. Diese Untersuchung stellt eine neue Formulierung der laminaren freien Konvektion yon Fliissigkeiten mit einer Prandtl-Zahl zwischen 0,001 und unendlich an einer beliebig schrfiggestellten isothermen Platte dar. Ein neuer Neigungsparameter wird eingeftihrt, so dab alle Ffille der horizontalen, geneigten oder vertikalen Platte yon einem einzigen Satz transformierter Gleichungen beschrieben werden k6nnen. Die unabMngigen Gleichungen ftir die beiden Ffille der horizontalen and vertikalen Platte wurden fiir ~ = 0 und ~ = 1 aus den transformierten Gleichungen wieder abgeleitet. Es wurden erw/irmte aufwfirtsgerichtete Platten mit positiven und negativen Neigungswinkeln untersucht. Eine sehr genaue Gleichung wurde ftir die lokale Nusselt-Zahl bei beliebigen Neigungswinkeln und ftir 0,001 < Pr <: Go entwickelt.Nomenclature c, f

Free convection from an arbitrarily inclined plate in a porous medium

“…where Ra:gK (T w 9T )x/ is the Rayleigh number. This parameter is the porous medium analogue of the one proposed by Yu and Liu [8] in a viscous fluid. It describes the relative strength of the longitudinal to the normal components of the buoyancy force acting simultaneously on the boundary layer.…”

“…It may be noted to this end that important contributions to the problem of free convection from arbitrarily inclined plate in a viscous (non-porous) fluid were made by Yu and Liu [8], Lin et al [9], and Umemura and Law [10].…”

MHD mass transfer flow past an inclined plate with variable temperature and plate velocity embedded in a porous medium

“…Fujii and Imura described an experimental study concerning natural convection heat transfer from a plate with arbitrary inclination. Yu and Lin presented a new formulation for laminar free convection from an arbitrarily inclined isothermal plate to fluids of any Prandtl number between 0.001 and infinity. He investigated both the cases of positively inclined plate and negatively inclined plate at small angles to the horizontal.…”

Effects of Wall Shear Stress on MHD Conjugate Flow over an Inclined Plate in a Porous Medium with Ramped Wall Temperature

“…A solution for the boundary layer on a horizontal plate showing that if the plate is heated and faces downwards or is cooled and faces upwards was presented by Stewartson [2]. Free convection heat transfer from an isothermal plate with arbitrary inclination was investigated by [3]. Chen et al [4] have obtained a numerical solution for the problem of natural convection over an inclined plate with variable surface temperature.…”