Numerical analysis of natural convection heat transfer and entropy generation in a porous quadrantal cavity

Nomenclature

c_p

= specific heat of the fluid, Jkg⁻¹K⁻¹;

Da

= Darcy number;

g

= acceleration due to gravity, ms⁻²;

h

= heat transfer coefficient, Wm⁻²K⁻¹;

k

= thermal conductivity, Wm⁻¹K⁻¹;

K

= permeability, m²;

L

= enclosure length, m;

Nu

= local Nusselt number;

$\overline{\text{Nu}}$

= average Nusselt number;

p

= pressure, Nm⁻²;

P

= non-dimensional pressure;

Pr

= Prandtl number;

Ra

= Rayleigh number;

S

= total dimensionless entropy;

S_θ

= dimensionless entropy generation due to heat transfer;

S_ψ

= dimensionless entropy generation due to fluid friction;

T

= temperature, K;

U, V

= Dimensionless x and y velocity components, respectively;

u, v

= x and y velocity components, respectively, ms⁻¹; and

x, y

= Horizontal and Vertical coordinates, respectively, m.

Greek symbols

α

= thermal diffusivity, m²s⁻¹;

β

= coefficient of thermal expansion, K⁻¹;

θ

= dimensionless temperature;

µ

= dynamic viscosity, kgm⁻¹s⁻¹;

ν

= kinematic viscosity, m²s⁻¹; and

ρ

= density of fluid, kgm⁻³.

Subscripts

avg

= average;

b

= bottom wall;

c

= cold wall;

min

= minimum; and

max

= maximum.

1. Introduction

The analysis of buoyancy induced convection in enclosures filled with porous media has been considered as one of the most important area of research investigation in the recent past due to its importance in a wide range of mechanical, chemical and civil engineering, applications, such as cooling of nuclear reactors, packed bed solar energy storage, grain storage, fibrous insulation systems, chemical catalytic converters, to name a few. The fundamental transport mechanism during the process of natural convection in porous enclosures and its applications are amply documented in the books and can be referred to: (Bejan and Kraus, 2003; Ingham and Pop, 2005; Nield and Bejan, 2013; Vafai, 2005; Bagchi and Kulacki, 2014; Narasimhan, 2013) and in the review article (Vafai and Hadim, 2000).

Recognizing the practical relevance of natural convection in a porous enclosure, a host of articles both theoretical and experimental had been reported in the recent past too. A thorough review in...

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