Numerical investigation of mixed convection heat transfer in presence of magnetic field in a lid-driven wavy cavity having vertical fin

Abstract

Mixed convection heat transfer in presence of magnetic field in a lid-driven wavy cavity having vertical fin has been studied numerically in this thesis. The horizontal bottom and top walls are kept at constant heated temperature Th while the vertical wavy walls are kept at constant cold temperature Tc maintaining Th > Tc. A heated fin of length (l) is attached to the hot bottom wall at a position (d) from the left wall having thickness (b). The top wall moves right to left with constant velocity. The gravitational force acts in vertically downward direction and a uniform magnetic field with a constant magnitude in the direction of the moving lid is applied. The physical problems are presented mathematically by different sets of governing equations along with the corresponding boundary conditions. Using a set of appropriate transformations, the governing equations along with the boundary conditions are transformed into non-dimensional form, which is then solved by employing a Finite-element method based on Galerkin weighted residuals. The investigations are conducted for different values of Richardson number (Ri), Hartmann number (Ha), fin lengths (L) but for fixed fin thickness, fin position, amplitude, number of oscillations with Re = 100 whereas Prandtl number is kept constant at 0.71. Various characteristics such as streamlines, isotherms, velocity profiles, local Nusselt number, fin effectiveness (εf) and heat transfer rate in terms of the average Nusselt number (Nuav) and average fluid temperature (θav) are presented for the aforementioned parameters. The results indicate that the mentioned parameters strongly affect the flow phenomenon and temperature field inside the wavy cavity whereas on the fin length these effects are more significant. Results of this study conformed very well with the published ones.