SIMILARITY SOLUTION FOR UNSTEADY FREE CONVECTION OF POWER LAW FLUIDS ON HORIZONTAL PLATE
B. BAGHERIAN *
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Azadisquare, Mashhad, Iran
A. R. TEYMORTASH
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Azadisquare, Mashhad, Iran
*Author to whom correspondence should be addressed.
Abstract
The transformation group theoretic approach is applied to present an analysis of the problem of unsteady free convection flow over a horizontal flat plate immersed in a power law fluid. Thermal boundary layer is induced within a horizontal semi-infinite layer. The system of governing partial differential equations reduces to a system of ordinary differential equations with appropriate boundary conditions by using the two-parameter group theory. The obtained ordinary differential equations are solved numerically for the velocity, pressure and temperature profiles. Effect of Prandtl number and viscosity index on the thermal boundary-layer, velocity boundary-layer, normalized Nusselt number and normalized skin friction has been investigated. The result showed thermal boundary-layer and velocity boundary-layer are a function of viscosity index.
Keywords: Unsteady free convection flow, group theoretic method, power law fluid, horizontal plate