A semi-analytical solution for time-dependent natural convection flow with heat generation/absorption in an annulus partially filled with porous material
Multidiscipline Modeling in Materials and Structures
ISSN: 1573-6105
Article publication date: 27 July 2018
Issue publication date: 29 October 2018
Abstract
Purpose
The purpose of this paper is to present a semi-analytical solution for time-dependent natural convection flow with heat generation/absorption in an annulus partially filled with porous material.
Design/methodology/approach
The governing partial differential equations are transformed into the ordinary differential equations using the Laplace transform technique. The exact solution obtained is inverted from the Laplace domain to time domain using the Riemann-sum approximation approach. Justification of the Riemann-sum approximation approach is achieved by comparing the values obtained with those of the implicit finite difference method at both the transient state and the steady state at large time.
Findings
If is found that the peak axial velocity always occur in the clear fluid region. In addition, there is an indication that heat generating fluid is desirable for optimum mass flux in the annular gap most importantly when the convection current is enhanced by constant heat flux.
Originality/value
In view of the amount of works done on natural convection with internal heat generation/absorption, it becomes interesting to investigate the influence of this essential activity on natural convection flow in a vertical cylinder partially filled with porous material where the outer surface of the inner cylinder is either heated isothermally or with constant heat flux.
Keywords
Citation
Yusuf, T.S. and Jha, B.K. (2018), "A semi-analytical solution for time-dependent natural convection flow with heat generation/absorption in an annulus partially filled with porous material", Multidiscipline Modeling in Materials and Structures, Vol. 14 No. 5, pp. 1042-1063. https://doi.org/10.1108/MMMS-01-2018-0003
Publisher
:Emerald Publishing Limited
Copyright © 2018, Emerald Publishing Limited