الفهرس 
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Abstract
33
A finite element model is developed to solve the steady state two-dimensional natural convection heat transfer and buoyancy-driven flow in enclosures containing cavities.
The enclosure has two vertical outside walls maintained at constant, but different temperatures and two horizontal insulated walls. Simplified boundary conditions of perfectly insulated connecting walls and perfectly conducting connecting walls are first studied. The effect of finite walls conduction is then considered.
The stream function-vorticity formulation is adopted in the present investigation. Flow and energy equations are solved using the finite element method. The method allows the use of irregular grid for complicated geometries; thus predictions are made for enclosures with square as well as circular cavities.
The results include the temperature fields in both the solid walls and the fluid-filled cavity in addition to the flow field in the cavity.
The model is verified by comparing the present results of the isothermal contour lines within the cavity, with the experimental contours of kim {28}. Excellent agreement is found.
Heat transfer calculations have been performed for modified Rayleigh number R* from 1.0E+3 to 0.64E+5. The results show that the effect of solid walls conductance and the interaction between the convection in the fluid-filled cavity and conduction in the solid walls can be neglected.
The results also show that the average dimensionless heat transfer rates through the enclosures containing square cavities is less than those parameters used. K*=10,, A*=0.36 and Ra*=1.0E+5, the heat transfer through the walls is reduced by 33%, when using a circular cavity and by 36%, when using a square cavity. Thus for the same area ratioA*, enclosures containing square cavities are better insulators than the enclosure containing circular cavities .
The isothermal contour line clearly indicate that the top and bottom walls of the square cavity are nowhere perfectly insulated, and heat is transferred between the walls and the fluid withen the cavity. The temperature distribution on the top and bottom walls of the cavity deviates from the linear one, especially at high Ra*
The comparison of the local number at the hot wall of the square cavity for the simplified boundary condtions (perfectly insulated connecting walls and perfectly conducting connecting walls ) and for walls with finite conductance , show that the perfectly conducting connecting walls gives closer results to the finite conductance case.