Thermal Radiation Effects On Fluid Flow And Heat Transfer Of Participating MHD In Enclosed Cavities

Magnetohydrodynamics(MHD)has received considerable attention by the researchers,due to its importance many fields ranging from several natural phenomena like geophysics,astrophysics to many engineering applications such as nuclear power plants,gas turbines,electromagnetic stirring and so on.In general,the above mentioned fields involving the high temperature process,and the thermal radiative heat transfer cannot be ignored or avoided in many application of MHD.Therefore,the radiation magnetohydrodynamics(Radiation-Magnetohydrodynamics,Radiation-MHD or R-MHD)has been investigated and developed.Among the various researches for the R-MHD problems at home and abroad,most works were focused on the boundary layer;however,few were in a square cavity.The CSM has the characteristics of exponential convergence,simple calculation process,easy implementation and good stability,etc.Based on above mentioned advantages,the CSM is used to simulate thermal radiation effects on fluid flow and heat transfer of participating MHD in enclosed cavities.The main contents of this thesis are as follows:(1)Our researches are restricted in the Cartesian coordinate systems.The mathematical models of the R-MHD are presented for two-dimensional and three-dimensional enclosed cavities,respectively.For generality,the governing equations are translated into the dimensionless forms.The steady flow is treated as the unsteady one here to ensure numerical stability and the convenient application to unsteady flow in the future.Therefore,the unsteady terms are added to the momentum and energy equations.The combination of Adams-Bashforth and backward difference,which is second-order-accurate and semi-implicit,is adopted to treat the temporal discretization.The improved projection scheme is applied to deal with the coupling of the velocity and the pressure.The same scheme of the temporal discretization is applied to the energy equation,also.The radiative transfer equation is angularly discretized by the Spherical Rings Arithmetic Progressing(SRAPN)quadrature scheme,based on the discrete ordinates method.Finally,all the governing equations are discretized spatially discretization by using the Chebyshev CSM.(2)The two-dimensional mathematical model of the R-MHD is adopted.The responding programs are designed.Considering the calculation time and accuracy,the grid and angular direction number of RTE independency tests are conducted,respectively.In order to validate the codes,computation is performed for natural convection,MHD free convection and simplified coupling of radiation and natural convection,respectively.The results of the CSM show good agreement with previous numerical results.The validation shows that the numerical methods and the codes are all credible.After validation of the codes,the effects of the various parameters,such as inclination angle of the magnetic field,Hartmann number,optical thickness,scatter albedo,and emissivity of walls,Grashof number and Planck number on streamlines,isotherms,and Nusselt number are analyzed.(3)The three-dimensional mathematical model of the R-MHD is adopted.The relevant numerical validations are performed.Thereafter,the thermal radiation effects on fluid flow and heat transfer of participating MHD in an enclosed cubical cavity are investigated.The effects of various Hartmann numbers on fluid flow and heat transfer of participating MHD are comparatively analyzed with and without thermal radiation for fixed Prandtl number,Pr = 0.733.The combined effects of thermal radiation and magnetic field on fluid flow and heat transfer of participating MHD are further investigated.The Rayleigh number(Ra = 105)and Prandtl number(Pr=13.6)are fixed.The isothermal surfaces,the projection of streamlines and isotherms on the three different mid-plane(i.e.,X = 0.5,Y = 0.5,and Z = 0.5,respectively)of the cubic cavity,the rate of heat transfer,three-dimensional transverse flow,and the maximum value of the transverse velocity show the effects of the Hartmann number,the optical thickness and the conduction-radiation interaction parameter on flow and heat transfer process.The main innovations include the following aspects:(1)The Chebyshev CSM is applied to investigate the problems of radiation-MHD in enclosed cavities on the same grid system.(2)The inclination angle of the magnetic field effects on fluid flow and heat transfer of participating MHD is investigated in two-dimensional enclosed square cavity.(3)Comparative study of fluid flow and heat transfer of participating MHD in three-dimensional enclosed cubical cavity is conducted,with and without thermal radiation,respectively.It is found that Hartmann number and thermal radiation play significant roles on fluid flow and heat transfer of participating MHD.(4)The effects of the optical thickness and the conduction-radiation interaction parameter on fluid flow and heat transfer of participating MHD in three-dimensional enclosed cubical cavity are investigated.