Numerical analysis of natural
convection heat transfer and
entropy generation in a porous
quadrantal cavity
Shantanu Dutta and Arup Kumar Biswas
National Institute of Technology Durgapur, Durgapur, India, and
Sukumar Pati
Department of Mechanical Engineering,
National Institute of Technology Silchar, Silchar, India
Abstract
Purpose – The purpose of this paper is to analyze the natural convection heat transfer and irreversibility
characteristics in a quadrantal porous cavity subjected to uniform temperature heating from the bottom wall.
Design/methodology/approach – Brinkmann-extended Darcy model is used to simulate the
momentum transfer in the porous medium. The Boussinesq approximation is invoked to account for the
variation in density arising out of the temperature differential for the porous quadrantal enclosure subjected
to uniform heating on the bottom wall. The governing transport equations are solved using the finite element
method. A parametric study is carried out for the Rayleigh number (Ra) in the range of 10
3
to 10
6
and Darcy
number (Da) in the range of 10
5
-10
2
.
Findings – A complex interaction between the buoyant and viscous forces that govern the transport of heat
and entropy generation and the permeability of the porous medium plays a significant role on the same. The
effect of Da is almost insignificant in dictating the heat transfer for low values of Ra (10
3
, 10
4
), while there is a
significant alteration in Nusselt number for Ra 10
5
and moreover, the change is more intense for larger
values of Da. For lower values of Ra (#10
4
), the main contributor of irreversibility is the thermal
irreversibility irrespective of all values of Da. However, the fluid friction irreversibility is the dominant player
at higher values of Ra (=10
6
) and Da (=10
2
).
Practical implications – From an industrial point of view, the present study will have applications in
micro-electronic devices, building systems with complex geometries, solar collectors, electric machinery and
lubrication systems.
Originality/value – This research examines numerically the buoyancy driven heat transfer irreversibility
in a quadrantal porous enclosure that is subjected to uniform temperature heating from the bottom wall, that
was not investigated in the literature before.
Keywords Natural convection, Porous media, Entropy generation, Nusselt number, Quadrantal enclosure
Paper type Research paper
Nomenclature
c
p
= specific heat of the fluid, Jkg
1
K
1
;
Da = Darcy number;
g = acceleration due to gravity, ms
2
;
h = heat transfer coefficient, Wm
2
K
1
;
k = thermal conductivity, Wm
1
K
1
;
K = permeability, m
2
;
L = enclosure length, m;
HFF
29,12
4826
Received 25 November 2018
Revised 9 May 2019
1 June 2019
Accepted 1 June 2019
International Journal of Numerical
Methods for Heat & Fluid Flow
Vol. 29 No. 12, 2019
pp. 4826-4849
© Emerald Publishing Limited
0961-5539
DOI 10.1108/HFF-11-2018-0678
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