# ANALYSIS OF MIXED CONVECTION IN AN AIR FILLED SQUARE CAVITY by sdsdfqw21

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```									   ANALYSIS OF MIXED CONVECTION IN AN AIR FILLED
SQUARE CAVITY
∗
Deborah Ducasse
Department of Mathematical Sciences
University of KwaZulu-Natal
e-mail: debsducasse@yahoo.com

Prof P. Sibanda
Department of Mathematical Sciences
University of KwaZulu-Natal
e-mail: sibandap@ukzn.ac.za

SAMS Classiﬁcation: 13 Mathematical Physics
A steady state two-dimensional mixed convection problem in an air ﬁlled
square unit cavity has been numerically investigated. Two diﬀerent cases of
heating are investigated and compared. In the ﬁrst case, the bottom wall was
uniformly heated, the side walls were linearly heated and the top moving wall
was heated sinusoidally. The second case diﬀered from the ﬁrst in that the side
walls were instead uniformly cooled. This investigation is an extension of the
work by Basak et al. [1,2] who investigated mixed convection in a square cavity
with similar boundary conditions to the cases listed above with the exception
of the top wall which was well insulated. In this thesis, their work is extended
to include a sinusoidally heated top wall.
The nonlinear coupled equations are solved using the Penalty Galerkin Finite
Element Method. Stream function and isotherm results are found for various
values of the Reynolds number and the Grashof number. The strength of the
circulation is seen to increase with increasing Grashof number and to decrease
with increasing Reynolds number for both cases of heating. A comparison is
made between the stream function and isotherm results for the two cases.
The results for the rate of heat transfer in terms of the Nusselt number are
discussed. Both local and average Nusselt number results are presented and
discussed. The average Nusselt number is found using Simpson’s 1/3rd rule.
The rate of heat transfer is found to be higher at all four walls for the case of
cooled side walls than that of linearly heated side walls.

[1] T. Basak, S. Roy, P. K. Sharma, I. Pop, Analysis of mixed convection ﬂows
within a square cavity with linearly heated side wall(s), International Journal
of Heat and Mass Transfer 52 (2009) 2224-2242.
[2] T. Basak, S. Roy, P. K. Sharma, I. Pop, Analysis of mixed convection ﬂows
within a square cavity with uniform and non-uniform heating of bottom wall,
International Journal of Thermal Sciences 48 (2009) 891-912.

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