Three-Dimensional Mixed Convection Flow past an Infinite Vertical Plate with Constant Surface Heat Flux

Bhupendra Kumar Sharma,R C Chaudhary,Tara Chand

doi:10.5923/j.ajcam.20110101.06

Abstract

The present paper contains a mathematical analysis of the mixed convection three dimensional steady lami- nar flow of a viscous incompressible fluid past an infinite vertical porous plate. The three-dimensional flow is caused by the transverse sinusoidal suction at the plate. A constant heat flux is prescribed at the plate. Assuming the plate velocity to be uniform, analytical solutions are obtained for the flow field, the temperature field and the skin-friction. Effects of Prandtl number and Grashof number on the flow characteristics are explored and illustrated graphically. In view of the importance of the problems of laminar flow control (LFC), especially in the field of aeronautical engineering, various theoretical and experimental studies of different arrangements and configurations of suction holes and slits have been compiled by Lachmann(1). The suction of the fluid is also an acknowledged technique for control- ling the undesirable features in the boundary layer theory. Further, from the technological point of view, free convec- tion flow and heat transfer problems are always important, for they have many practical applications. The phenomenon of free-convection arises when the difference between the plate temperature and the free stream temperature apprecia- bly large which causes density variations leading to buoyancy forces acting on the fluid elements. This process of heat transfer is encountered in cooling of nuclear reactors, providing heat sinks in turbine blades and aeronautics. Free convection flow past vertical plate has been studied exten- sively by many researchers and some of them are Os- trach(2-3), Stewartson et. al.(4), Sparrow et. al.(5-6), Ma- buchi(7), Riley et. al.(8), Berezovsky et.al.(9), Na(10), Dey et al (11), Kawase et al(12), Martynenko et.al.(13), Weiss et.al.(14) and Pantokratoras(15-16) in numerous ways to include various physical effects. In their work they have restricted themselves to two-dimensional flow only. There may arise situations where the flow fields may be essential- ly three-dimensional, for example when variations in the suction velocity distribution is transverse to the flow direc- tion. Gersten and Gross(17) have studied the effect of such

Highlights

In view of the importance of the problems of laminar flow control (LFC), especially in the field of aeronautical engineering, various theoretical and experimental studies of different arrangements and configurations of suction holes and slits have been compiled by Lachmann[1]
We present an approximate analytical solution to the problem of the laminar three-dimensional steady mixed convection flow past an infinite vertical porous plate with constant heat flux, (CHF), from which the fluid is extracted at a uniform rate
The fluid velocity takes its maximum value inside the thermal boundary layer due to the convection currents and as the distance from the vertical plate increases it decays to its limiting value

Summary

Introduction

In view of the importance of the problems of laminar flow control (LFC), especially in the field of aeronautical engineering, various theoretical and experimental studies of different arrangements and configurations of suction holes and slits have been compiled by Lachmann[1]. Free convection flow past vertical plate has been studied extensively by many researchers and some of them are Ostrach[2,3], Stewartson et al.[4], Sparrow et al.[5,6], Mabuchi[7], Riley et al.[8], Berezovsky et al.[9], Na[10], Dey et al [11], Kawase et al[12], Martynenko et al.[13], Weiss et al.[14] and Pantokratoras[15,16] in numerous ways to include various physical effects In their work they have restricted themselves to two-dimensional flow only. We present an approximate analytical solution to the problem of the laminar three-dimensional (caused by sinusoidally varying suction) steady mixed convection flow past an infinite vertical porous plate with constant heat flux, (CHF), from which the fluid is extracted at a uniform rate

Mathematical Analysis

Solution

Pr 2 Pr

Results and Discussion