Composite heat transfer in case of steady laminar flow of a gray fluid with large optical density past a horizontal plate embedded in a saturated porous medium

Abstract

Abstract. The present paper discusses the problem of composite heat transfer and viscous friction of a moving gray medium with large optical density. Expressions for temperature and velocity distributions and the ratio of the radiative component to convective component of heat flux are obtained. It is observed that for a given value of B the ratio of radiative heat flux to convective heat flux is maximum at the edge of the boundary layer and tends to an asymptotic value as the boundary is reached. However, for a given value of K 6, the ratio of heat fluxes increases with increase in B (the porous parameter). The results also show that as the wall temperature approaches the value of free stream temperature, the ratio of heat fluxes decreases. Wiirmeiibergang eines Fluids mit groBer optiseher Dichte bei stationiirer laminarer Str6mung an einer horizontalen Platte eingebettet in einem gesiittigten por~isen MediumZusammenfassung. In der vorliegenden Arbeit wird das Problem des W/irmefibergangs und der viskosen Reibung eines bewegten grauen Mediums mit groger optischer Dichte er6rtert. Man erhfilt Formelausdrficke ffir Temperatur-und Geschwindigkeitsverteilungen und das Verhfiltnis yon dem Anteil der Strahlung zum konvektiven Anteil des Wfirmeflusses. Ffir einen gegebenen Wert yon B (dem por6sen Parameter) beobachtet man, dab das Verhfiltnis des Wfirmestroms durch Strahlung zum konvektiven W/irmestrom am Rand der Grenzflfiche maximal wird und sich dem Wert der Grenzfl/iche asymptotisch n/ihert. Jedoch erh6ht sich bei gegeOenem Wert yon K 6 das Verhfiltnis der Wfirmestr6me mit steigendem B. Die Ergebnisse zeigen auch, dab sich das Verhfiltnis der W/irmestr6me verringert, wenn die Wandtemperatur sich der Temperatur der freien Str6mung nfihert.

Velocity and temperature distributions on a semi-infinite flat plate embedded in a saturated porous medium

“…Chandrasekhara et al [3] obtained a similarity solutions for buoyancy induced flows in a saturated porous medium adjacent to impermeable horizontal surfaces. Chandrasekhara et al [4] obtained composite heat transfer in case of steady laminar flow of a gray fluid with large optical density past a horizontal plate embedded in a saturated porous medium. In all these analysis it is clear that a boundary layer of thickness 6 is formed and in this layer the streamwise component of the flow velocity 'u' varies from zero at the plate to 'u~' on the free stream.…”