Numerical study on magneto-hydrodynamic mixed convection in a lid driven cavity with wavy top wall and rectangular heaters at the bottom wall

Abstract

In this thesis, the problem of mixed convection and heat transfer in a wavy top wall and rectangular heaters at the bottom wall enclosure in the presence of a magnetic field with lid driven has been studied. The two dimensional steady state Navier-Stokes equations, energy equation and continuity equation are modified to account for the presence of thermal buoyancy and magnetic field. The physical problems are represented mathematically with different sets of governing equations along with the corresponding boundary conditions. The equations are transformed into non-dimensional form with the help of suitable dimensionless variables. The dimensionless parameters appear in the equations are the Reynolds number (Re), Hartmann number (Ha) and Grashof number (Gr). The non-dimensional governing equations are solved by using Galerkin weighted residual method of finite element formulation. MHD mixed convection in a wavy top wall with three heaters at the bottom wall has been studied with two different lid-driven conditions. All boundaries and heaters are considered to be rigid. For case-1, the lower wall has three rectangular heaters having a hot temperature (Th) while the top wall is maintained partially cold temperature (Tc) and remaining parts are kept adiabatic. Moreover, both left and right walls are sliding upward and downward respectively with considered velocity. On the other hand, for case-2, the lower wall has three rectangular heaters with temperature Th while the side walls are maintained cold temperature and the top wall is also partially cold and remaining parts are kept adiabatic. Moreover, the top wall is sliding from left to right and the side walls moving downward. Results are presented in terms of streamlines, isotherms, average Nusselt number and local Nusselt number along the rectangular heaters as required for different combinations of the non-dimensional governing parameters namely Reynolds number (Re) varying from 50 to 1000, Hartmann number (Ha) varying from 0 to 100 and Grashof number (Gr) for 104 and 105 where Prandtl number kept in constant at 0.733. Moreover, comparisons with previously published work are performed and the results are found to be in excellent agreement. The significant effect of the magnetic field is observed in the heat transfer mechanisms and flow characteristics inside the enclosure. However, streamlines variation for different dimensionless numbers is noticeable a lot rather than temperature variation. Also, with increasing Ha number, flow velocity as well as heat transfer in the enclosure decrease. In case-2, it is observed that the variations of results due to the changes of dimensionless numbers are more prominent than that of in case-1.