Effect of selected geometric parameters on natural convection in concentric square annulus

ABSTRACT

The research is focused on natural convection heat transfer in a concentric square annulus with tilted inner elliptic cylinder subjected to isothermal heating and cooling. Numerical method was adopted for the solution. The governing elliptic conservation equations were solved using Garlerkin Finite Element Method. Ranges of parameters considered for the study were orientation angle, aspect ratio and Rayleigh number. Physical model was generated using CorelDRAW 2019 version while meshing and simulation was done using COMSOL Multiphysics software. Results show that orientation angle had no significant effect on the average Nusselt number at low Rayleigh number. Beyond a critical Rayleigh number, average Nusselt number increases with an increase in orientation angle. Analyses of the results show that Rayleigh number, Nusselt number and orientation angle significantly influence the natural convection in concentric square annulus. The results presented in this study can be applied in heat exchanger devices, solar collectors, nuclear reactors and thermal storage systems.

KEYWORDS:

• Aspect ratio
• Nusselt number
• Rayleigh number
• Heat transfer
• Orientation angle

Nomenclature

A	=	Surface area for heat transfer
AR	=	Aspect ratio
a	=	Semi-major axis
b	=	Semi-minor axis
AS	=	Annular space
Fy	=	Body forces
g	=	Acceleration due to gravity
Gr	=	Grashof number
H	=	Width of the enclosure
L	=	Length of the enclosure
Nuavg	=	Average Nusselt number
Nuloc	=	Local Nusselt number
P	=	Pressure
Pr	=	Prandtl number
$\varphi$	=	Orientation angle
Ra	=	Rayleigh number
$T_c$	=	Temperature of the outer cold boundary
$T_h$	=	Temperature of the inner heated boundary
T	=	Dimensional temperature
$\theta$	=	Dimensionless temperature
$T_s$	=	Temperature of the surrounding air
$T_f$	=	Film temperature
u, U	=	Dimensional and dimensionless velocity in x direction
v, V	=	Dimensional and dimensionless velocity in y direction
x, X	=	Dimensional and dimensionless coordinate along horizontal direction
y,Y	=	Dimensional and dimensionless coordinate along the vertical direction
Greek symbol	=
$\alpha$	=	Fluid thermal diffusivity
$\beta$	=	Volume expansion coefficient
$v$	=	Fluid kinematic viscosity
$\mu$	=	Dynamic Viscosity
$\rho$	=	Fluid density
k	=	Thermal conductivity
Subscripts	=
c	=	Value at cold outer boundary
h	=	Value at hot inner boundary
i	=	Inner cylinder
o	=	Outer cylinder

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

I. K. Adegun

Ik Adegun is a lecture and Professor in the Department of Mechanical Engineering, University of Ilorin, Nigeria. His research interest in the area thermofluids, mathematical modeling and numerical simulation and he had published several peer reviewed journals in this area. Adegun is a registered professional Engineer with the Council for the Regulation of Engineering in Nigeria (COREN). He has supervised and graduated several undergraduate, masters and PhD students. Adegun is a member of Nigeria institute of Mechanical Engineering (MNIMechE) and Nigeria Society of Engineering (MNSE).

S. E. Ibitoye

SE Ibitoye is a lecturer in the Department of Mechanical Engineering, University of Ilorin, Nigeria. His research interest is in renewable energy, mechanical engineering design, numerical simulation and material characterisation. Ibitoye had published peer reviewed journals in this area. Ibitoye is a registered professional Engineer with the Council for the Regulation of Engineering in Nigeria (COREN).

A. Bala

A Bala just completed his masters’ degree in the Department of Mechanical Engineering, University of Ilorin, Nigeria. His area of specialization is in thermofluids and numerical simulation.