Numerical Research On Fluid Flow And Heat Transfer Of Radiatively Participating MHD In A Cubic Enclosure Using The Collocation Spectral Method

Magnetofluid is a new type of functional material.Due to a number of special magnetic,optical and electrical characteristics,magnetofluid possesses important application prospect.Many applications of magnetohydrodynamics(MHD)in the industrial field make the MHD being wildly focused in recent years.However,we need to understand the effects of thermal radiation on MHD in thermonuclear reaction device,aerospace equipment,missiles,nuclear power plants and MHD accelerator and so on.Therefore,the radiation MHD(R-MHD)has become an important research direction.The investigation of the fluid flow in a square cavity is a typical case in the fluid dynamics.If the fluid was magnetofluid and was placed in a magnetic field together with thermal radiation,it will imply special natures for fluid flow and heat transfer.The collocation spectral method(CSM)has high accuracy and exponential convergence,and can be implemented with easy.So in this thesis,we adopt the CSM to investigate the effects of thermal radiation on the fluid flow and heat transfer in a three-dimensional enclosed cubic cavity.The main contents and results of this thesis are as follows:1)First,after the reasonable assumptions for the physical problem,a three-dimensional mathematical model is presented in Cartesian coordinate system.Then,the governing equations are transformed into dimensionless forms for the purpose of generality.To ensure numerical stability and further applications to unsteady flow in the future,the steady flow is treated as unsteady one.The radiative heat flux,which appears in the energy equation as a source term,is obtained by the Rosseland approximation.The temporal discretizations are carried out by the combination of Adams-Bashforth and backward Euler schemes,which give the second-order accuracy and semi-implicit scheme in total.The collocation points are used for the spatial discretization.The improved projection scheme(IPS)is applied to deal with the coupling of the velocity and the pressure in the N-S equations.2)The Matlab computer language is used to design the codes and further to solve the discretized governing equations.The grid independence test is conducted to validate the codes,and the codes are proved to be reliable and accurate.After that,the effects of different parameters,say,the Ra number,the Ha number and the radiative parameter R,on fluid flow and heat transfer of radiative magnetofluid are investigated with both the Dirichlet and Neumann boundary conditions.When one parameter is considered,all other parameters are fixed.The results indicate that:(1)with the increase of Ra number,the flow intensity goes up at beginning and drops gradually,the flow structures changed obviously;(2)the increase of Ha number can suppress the fluid flow and heat transfer remarkably;(3)when the radiative parameter R number is small,radiation heat transfer is the main way of heat transfer.The effect of thermal radiation will be weakened with the increase of R number,and the effect of thermal radiation can even be ignored when the R number is greater than some critical value.The main innovations are as followings:1)The accurate CSM is adopted to investigate the effects of magnetic field and thermal radiation on MHD fluid flow and heat transfer in a cubic enclosure.2)The Rosseland approximation is adopted to solve the MHD problem concerned with thermal radiation in the three-dimensional cubic enclosure.