Author : M. Mohamed, Esam
journal of kerbala university,
2012, Volume 8, Issue 2, Pages 304-319
A numerical study has been performed on mixed convection heat transfer inside a square cavity with sinusoidal wavy upper and lower surfaces, the vertical walls are insulated. The lower surface was maintained at uniform temperature higher than the upper surface.
Vorticity-stream function method has been used to write the dimensionless governing equations, which consist of parabolic vorticity and energy equations that are solved by (explicit) method and elliptic stream function equation solved by successive over- relaxation method (S.O.R). The system of equations was solved using finite difference discretization. The Body Fitted Coordinate system (B.F.C) has been used with the grid generation technique to solve the flow equations because of the complexity of the upper and lower surfaces shape. Two elliptic differential equations had been solved to generate the internal grid.
In the present study, the effect of number and amplitude of undulations (λ & A) of the wavy surfaces, the Richardson number (Ri) and Grashof number (Gr) on the flow structure inside the cavity and Nusselt number of the heated wall are reported for (λ=0 to 3), (A=0, 0.02, 0.04 and 0.06), (Ri =0.01, 0.1, 1 & 10), (Gr=103 ,103.5,104 & 104.5) and Pr=0.71. A two-dimensional laminar viscous non-compressible fluid flow was considered.
From the present analysis, it is found that local Nusselt number increases with increasing the number of waves of the wavy surfaces. While, the mean and local Nusselt number decreases with increasing the amplitude of undulation (A) and Richardson number (Ri) and increases with increasing the Grashof number (Gr). Higher mean Nusselt number is observed at (A=0.02 & Gr=104.5) at low Richardson number value (Ri=0.01). The validity of the numerical code is verified by comparison with published results.