Unsteady natural convection in horizontal channels with arbitrary wall temperatures

Abstract

Unsteady free convection flow in a horizontal channel with arbitrary wall temperatures has been discussed in general. A physically meaningful exact solution of the problem has been obtained in a closed form by the application of the standard finite sine transform technique. Influences of the governing parameters, the Prandtl number and the Rayleigh number, to bring the flow and heat transfer to final steady states have been discussed separately. For constant values of the arbitrary wall temperatures and of the function, determining the average axial velocity, the final steady state is approached in different times respectively for the cases when the Prandtl number Pr > 1 and Pr < 1. It is also seen that the function, representing the axial temperature gradient, is influenced by none of the governing parameters; but the steady state flow is influenced only by the Rayleigh number.