Convection Analysis in Closed Cavity Via Fem Approach

Abstract

Thermal management in closed cavity is one of the most important analysis in recent decade. Such type of heat analysis in the presence of molecular movement is convection. The simulation of Heat and mass transfer through various type of convection in complex geometries is studied in this dissertation. The analysis of FEM on heat transportation in a two dimensional closed cavity is much challenging and depending upon the complex nature of the problem. However, to ensure the e - cient and accurate analysis, the following considerations of signi cant criteria may be taken as; Mesh density, Element type, Boundary Conditions, Material Properties of structure, the solution and its method and the criteria to check its convergence. Aim of this work is to develop various geometries (square, trapezoidal, circular, curved and corrugated) for engineering and industries as cooling equipment, thermal energy storage, thermal solar equipments etc. through ns, obstacles and lid walls. Mathematical non-linear Partial Di erential Equations (PDEs) and boundary conditions are developed. For such physical two dimensional problems, steady-state equations of continuity, momentum, energy and concentration are developed, which are nondimensionalized by using suitable dimensionless variables. For solution of strong non-linear PDEs in dimensionless form in this thesis, computational method as Finite Element Method (FEM) is adopted. For numerical approach, Glarekin residual approach of FEM is applied in which rst domain is discretized into sub-domain in the form of quadrilateral and triangular form etc. Each sub-domain formulation occurs with combination of nodes, which form elements. Acquired elements are solved in the form of simultaneous algebraic equations for unknown interior nodes, these elements of sub-domain develop sti ness matrix for numerical simulation. Union of elements form domain of the cavity or enclosure. Simulation of structure for natural, forced and mixed convection are taken in this thesis. Impact of various rising parameters on streamlines, isotherms, iso-concentration, velocity, tempera ture, local and average Nusselt number are presented in the form of graphs. The emphasis on heat transfer in cavity due to forced, natural and mixed convection are obtained. Numerical and graphical interpretation of problems are discussed in comparison with experimental and numerical results. Mesh analysis and grid independence test for various cavity are analysed for average Nusselt number. Number of nodes or response of meshes on rate of heat transfer are calculated. Validation of the current work with literature in limited cases are explored. In case of square cavity, size of heated n increases the heat transfer inside cavity. Convection process shows signi cant transfer rate of heat at mean position with increase in nanoparticles in enclosure. Heat driven through lid walls in case of forced convection in porous corrugated duct in the presence of heat generation. Partially lid driven of top lid walls move inside direction generate more heat in enclosure. In concentration of nano uids, Lewis number and buoyancy increase mass transfer and Re increases heat transfer inside enclosure. Forced convection in circular duct through triangular ns is signi cantly a ected with Re, Da and . Reynolds number increases heat in cavity while porosity and nanoparticle decrease heat in cavity with increasing the parameter. Q > 0 plays a vital role for heat generation inside cavity in all problems.