Transient free convection in open-ended vertical channels

Abstract

The aim of the present work is to investigate the heat transfer for laminar natural convection of a fully developed flow in a chimney consisting of two parallel vertical plates with open ends, occurring due to a sudden change in temperature of one of the plates. The momentum conservation equation was analytically solved by applying the Laplace transform technique and the Green’s function method, resulting in the evaluation of the velocity field with a very low computational effort. The proposed analytical solution was adopted to assess the effect of the Prandtl number on the fluid behaviour of the flow. The results revealed that the steady-state velocity distribution is reached when the Fourier number became comparable with the Prandtl number, except for low values of the Prandtl number.