Abstract
This paper presents a numerical study of natural convection within a wavy enclosure heated via corner heating. The considered enclosure is a square enclosure with left wavy side wall. The vertical wavy wall of the enclosure and both of the corner heaters are maintained at constant temperature, T c and T h, respectively, with T h > T c while the remaining horizontal, bottom, top and side walls are insulated. A penalty element-free Galerkin approach with reduced gauss integration scheme for penalty terms is used to solve momentum and energy equations over the complex domain with wide range of parameters, namely, Rayleigh number (Ra), Prandtl number (Pr), and range of heaters in the x- and y-direction. Numerical results are represented in terms of isotherms, streamlines, and Nusselt number. It is observed that the rate of heat transfer depends to a great extent on the Rayleigh number, Prandtl number, length of the corner heaters and the shape of the heat transfer surface. The consistent performance of the adopted numerical procedure is verified by comparison of the results obtained through the present meshless technique with those existing in the literature.
Highlights
Natural convection within closed cavities with different fluids has attracted considerable attention of many researchers [1,2,3,4,5,6] due to its immense applications in engineering such as the cooling of electronic devices, refrigerators, room ventilating, heat exchangers, and solar collectors
The flow and temperature fields are graphically presented in terms of stream lines and isotherm contours, respectively
The meshfree element free Galerkin model is demonstrated as an alternative approach to eliminate the well known drawbacks of grid based methods such as FDM and finite element method (FEM)
Summary
Natural convection within closed cavities with different fluids has attracted considerable attention of many researchers [1,2,3,4,5,6] due to its immense applications in engineering such as the cooling of electronic devices, refrigerators, room ventilating, heat exchangers, and solar collectors. Many authors [4,5,6] studied the impact of different boundary conditions on convection phenomenon within an enclosure In these studies, different shapes of heat transfer surfaces were not considered. There has been considerable interest in the intentional roughening of the surface to enhance the heat transfer This small scale roughness may be represented by periodic functions (sine and cosines). The system of equations is linearized by incorporating known functions U, V, θ as given in (29), which is solved using Gauss elimination method. This gives a new set of values of unknowns U, V, θ and the process continues till the required accuracy (0.0005) is achieved
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