Numerical Simulation of Steady Mixed Convection Around Two Heated Circular Cylinders in a Square Enclosure

Abstract

In this paper, a numerical study has been carried out to investigate the steady-state mixed convection around two heated horizontal cylinders in a square two-dimensional enclosure. The cylinders are located at the middle of the enclosure height and the walls of the cavity are adiabatic. Streamlines and isotherms are produced and the effects of cylinder diameter, Reynolds number, and Richardson number on the heat transfer characteristics are numerically analyzed. The average Nusselt number over the surface of cylinders and average nondimensional temperature in the enclosure are also presented. The results show that both heat transfer rates from the heated cylinders and the dimensionless fluid temperature in the enclosure increase with increasing Richardson number and cylinder diameter. However, the trend of average Nusselt number and nondimensional temperature variation is completely opposite when Reynolds number increases. In addition, by increasing the cylinders diameter and Richardson number, the left cylinder is less affected by the inlet flow than right one.

NOMENCLATURE

d	=	diameter of cylinders, m
D	=	dimensionless diameter of cylinders, d/L
g	=	gravitational acceleration, m s−2
hφ	=	local heat transfer coefficient, w m−2 K−1
H	=	enclosure height, m
L	=	enclosure width, m
n	=	unit normal coordinate to the surface of the cylinders
Nuφ	=	local Nusselt number
	=	average Nusselt number
p	=	pressure, Pa
P	=	dimensionless pressure
Pr	=	Prandtl number
Re	=	Reynolds number
Ri	=	Richardson number
s	=	distance between cylinders, m
S	=	dimensionless distance between cylinders, s/L
TH	=	temperature of heated cylinders, K
Ti	=	temperature of inlet fluid, K
u, v	=	velocity components in the x and y directions, m s−1
ui	=	velocity of inlet fluid, m s−1
U, V	=	dimensionless velocities
V	=	volume of enclosure, m3
x, y	=	Cartesian coordinates
X, Y	=	dimensionless coordinates

Greek Symbols

ρ	=	density, kg m−3
α	=	thermal diffusivity, m2 s−1
β	=	thermal expansion coefficient, K−1
ν	=	kinematic viscosity, kg m−1 s−1
θ	=	dimensionless temperature
λ	=	thermal conductivity of the fluid, W m−1 K−1
φ	=	angular displacement from the front stagnation point, degree

Additional information

Notes on contributors

Fariborz Karimi

Fariborz Karimi is a Ph.D. student in the Institute of Thermophysics Engineering, School of Energy and Power Engineering, University of Shanghai for Science and Technology, China. He received his master's degree from the Mechanical Engineering Department, Isfahan University of Technology, Iran, in 2003, and his bachelor's degree from the same college in 2000. Currently, he is working on the numerical simulation of natural and mixed convection heat transfer problems.

Hongtao Xu

Hongtao Xu is a lecturer at the University of Shanghai for Science and Technology, China. He holds the M.S. and Ph.D. degrees from Xi'an Jiaotong University and Hong Kong Polytechnic University in 2002 and 2006, respectively. He specializes in heat and mass transfer and numerical simulation technologies.

Zhiyun Wang

Zhiyun Wang is a lecturer at the University of Shanghai for Science and Technology, China. He holds the M.S. and Ph.D. degrees from the University of Shanghai for Science and Technology, awarded in 2006 and 2011, respectively. His research interest is in the field of numerical simulation for heat and mass transfer.

Mo Yang

Mo Yang is a professor at the School of Energy and Power Engineering, University of Shanghai for Science and Technology, China. He received his M.S. and Ph.D. degrees from Northeast Dianli University and Xi'an Jiaotong University, China, in 1984 and 1991, respectively. He has published about 70 research papers in international journals and conferences. His research interests are mainly focused in the areas of numerical natural convection, forced and mixed convection, bifurcation and instability of fluid flow and heat transfer, optimization of heat exchangers, and thermal devices.

Yuwen Zhang

Yuwen Zhang is the James C. Dowell Professor in the Department of Mechanical and Aerospace Engineering at the University of Missouri. He has conducted research on micro- and nanoscale heat transfer, ultrafast and high-energy laser materials interactions, and sustainable and renewable energy, funded by the National Science Foundation (NSF), Office of Naval Research (ONR), Air Force Research Laboratory (AFRL), and U.S. Army PEO. He has published more than 200 journal papers and more than 130 conference papers, as well as two textbooks and two edited books. He is a fellow of the ASME and associate fellow of the AIAA.