Numerical investigation of MHD mixed convective nanofluid flow in a lid-driven enclosure with internal heat source and sinusoidal

Abstract

Numerical investigation of MHD mixed convective nanofluid flow in a lid-driven enclosure with internal heat source and sinusoidal boundary has been studied by solving steady state two-dimensional incompressible mass and momentum equations along with energy equations. The physical problems are represented mathematically by the governing equations along with the corresponding boundary conditions. With proper choice of the nondimensional variables the equations are transformed to non-dimensional form. To calculate the numerical results finite element approach based on Galerkin’s weighted residual method is used. The results for fluid flow, heat transfer phenomena and temperature distribution are presented through streamlines, isothermal lines and numerical graphs. Comparisons with previously published works are performed and the results arefound to be an excellent agreement. The study is executed by analyzing different ranges of geometrical, physical and nondimensional parameters such as the ratio of wave amplitude and cavity length,the ratio of heat source circumference and cavity length, magnetic strength, number of undulations of sinusoidal wall, amount of solid fraction of nanoparticle, Richardson number etc. Keeping into account the significant role of internal heat source shape on heat transfer, three different shaped such as circular, square and rectangular sheet shaped heat sources are investigated elaborately to summarize which type of heat source is more effective. In all the cases water is considered as the base fluid and equal amount of Cuand〖Al〗_2 O_3 solid particle is considered as nanoparticle of hybrid nanofluid.Data analysis reveals that, heat transfer rate decreases with the increasing value of heat sourcecircumference and cavity length ratio irrespective of heat source shape. On theother hand, heat transfer rate is maximum for circular shaped heat source andminimum for rectangular sheet shaped heat source. Wave amplitude of sinusoidal wall plays a key role on heat transfer rate. The significance of the effect of wave amplitude and cavity length ratio is analyzed elaborately in comparison with flat surface. Results show that, in the mixed convection region in absence of magnetic field, heat transfer rate increases up to a limit of A/L=0.09 but for further increase of A/L heat transfer rate started to decrease. Considering the prominent role of magnetic field on heat transfer rate effect of Hartmann number is analyzed for all types of heat sources. Results show that heat transfer rate decreases with the increasing strength of magnetic field irrespective of heat source shape and size. Since the amount of solid nanoparticles has a leading role on heat transfer rate, the effect ofφ is also investigated for all types of heat sources and the result depicts that heat transfer rate increases with the increasing amount of solid nanoparticles irrespective of heat source shape and size. Analyzed results are verified and optimized through sensitivity analysis. The various ideas and results have been discussed distinctly in detail in the relevant chapters of this thesis work. An effort is given to summarize the results of whole investigation to get a clear picture of this research work at a glance.