| Thermal-magnetohydrodynamics(T-MHD)is a study of exploring thermal and hydrodynamic properties of electrically conducting fluid in the presence of magnetic field,which is of great importance considering the number of technological industrial applications involved,such as electromagnetic casting,high quality crystal production,cooling of fusion reactors,etc.The T-MHD problems in the above fields usually occur in high temperature environments,where radiative heat transfer plays an important role in re-distributing energy and further influencing fluid flow,heat and mass transfer,and even flow instability.Ignoring thermal radiation in such environments could result in a considerable deviation,and consequently,radiative-magnetohydrodynamics(R-MHD)has been gradually developed into an important branch of T-MHD.The configuration of T-MHD and R-MHD flows in the annular space is encountered in the above engineering applications,and the physical problem itself also contains abundant natural phenomena.Geometric parameters of the annulus,physical properties of the fluid and Hartmann number have significant impacts on the flow pattern,temperature distribution and heat transfer,which further influences the quality of product and energy consumption.Hence,it stimulate us to examine the coupled phenomena of T-MHD and R-MHD flows in an annulus.Due to the limitation of current experimental technology,including the manufacture of a strong and uniform magnetic field with cavity,the measurement of velocity and temperature fields and the visualization of the flow,numerical simulation is still the most commonly used technique to investigate T-MHD and R-MHD problems.The objective of present work is to use numerical technique to investigate the fluid flow and heat transfer of electrically conducting fluid with consideration of magnetic field and thermal radiation in a concentric annulus,mainly focusing on the analyses of the effects of various parameters on thermal and hydrodynamic behaviors.The detailed contents are as follows:(1)Based on some reasonable assumptions and simplifications,the mathematical models for fluid flow and heat transfer of incompressible viscous electrically conducting fluid with or without consideration of thermal radiation have been proposed.(2)Specific solving procedures and introduction of boundary conditions are presented.Both the artificial compressibility algorithm based on finite volume method(AC-FVM)and the improved projection algorithm based on collocation spectral method(IP-CSM)are applied to solving continuity,momentum,energy,and electric potential equations.Besides,the discrete ordinates method(DOM)is adopted to solve radiative transfer equation(RTE).(3)Three-dimensional(3D)numerical simulation of laminar steady natural convection of electrically conducting fluid under the influence of an uniform axial magnetic field in a horizontal cylindrical annulus has been performed.The governing equations are solved using the AC-FVM with uniform staggered grid.The results show that a typical 3D steady spiral flow exists and transverse convective rolls produced by thermal instabilities form in the vertical upper section of the annulus under a weak magnetic field.Furthermore,the flow field,temperature distribution,the distribution of Nusselt number on the isothermal walls and transverse cells(2 cells)of electrically conducting fluid of Pr=0.8 are symmetric with respect to the vertical mid-plane.However,this symmetry is broken for the electrically conducting fluid of Pr<0.8,due to the intensive transverse spiral flow in the upper part of annulus.Eventually,the present flow possesses an odd number of transverse cells(1 cell).As the Hartmann number is increased,the transverse flow is distinctly suppressed,and the transverse convective rolls finally disappear.The flow patterns and isotherms of electrically conducting fluid of Pr<0.8 become symmetric with respect to the vertical mid-plane as well.Finally,both the flow field and temperature distribution reflect the two-dimensional nature.In addition,Prandtl number has weak effects on the fluid flow and heat transfer under the strong magnetic field.(4)Furthermore,with consideration of the coupled effects of thermal radiation and magnetic field,laminar convective flows in horizontal and vertical cylindrical annulus filled with radiatively participating and electrically conducting fluid have been numerically studied.The influences of the Hartmann number,convection-radiation parameter,radiative properties of fluid and wall on the flow structure,temperature distribution and local Nusselt numbers are mainly discussed.The results indicate that both the flow field and temperature distribution exhibit significant changes for different Hartmann numbers.Convective heat transfer can be effectively reduced by the magnetic field,but its suppression effect on radiative heat transfer would be rather small.Actually,the impact of magnetic field on overall heat transfer is slight,especially for the case of strong radiation.With the increase of convection-radiation parameter,natural convection effect gets weaker,and the temperature distribution is gradually dominated by the diffusive radiative transport.The increase in optical thickness of the fluid enhances the circulating flow,and improves the average temperature of the fluid,but suppresses the heat transfer between the hot wall and the fluid.The emissivity of walls plays a major role in fluid flow and temperature distribution near the hot wall.Compared with other parameters,the influence of scattering albedo is slight.Highlights of present work:(1)By introducing the magnetic field,the spiral motion in the upper part of the annular space is reduced significantly at first,and then the crescent-shaped circulating flow lies in the vertical section of the annulus is suppressed.Under the strong magnetic field,Prandtl number has weak effects on the fluid flow and heat transfer.(2)Both the flow structure and temperature distribution exhibit significant changes for different Hartmann numbers.The applied magnetic field could effectively weaken fluid flow and convective heat transfer,but its suppression effect on radiative heat transfer would be rather small.Radiative properties of fluid and wall have different influences on the fluid flow and heat transfer.(3)Realizing the real coupling of thermal radiation and MHD by solving the radiative transfer equation(RTE),instead of using the Rosseland approximation and other simplifications. |
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