FLT-HPM for Two-dimensional Transient Natural Convection in a Horizontal Cylindrical Concentric Annulus

Abstract

A hybrid procedure FLT-HPM was proposed in this study, by combining the homotopy perturbation method (HPM) with Fourier transform and Laplace transform which aimed to find an approximate analytical solution to the problem of two-dimensional transient natural convection in a horizontal cylindrical concentric annulus bounded by two isothermal surfaces. The effect of the Grashof number, Prandtl number, and the radius ratio on fluid flow (air) and heat transfer with different values awreas discussed. Moreover, the velocity distributions and the mean Nusselt numbers were studied, and the Nusselt numbers were used to represent local and general heat transfer rates. Finally, the convergence of FLT-HPM was tested theoretically through the proof of some theorems. In addition, these theorems were applied to the results of the new solutions obtained using FLT-HPM.