A numerical study has been carried out to investigate heat transfer by free convection under the effect of MHD （magnetohydrodynamic） for steady state three-dimensional laminar flow in horizontal and vertical cylindr...A numerical study has been carried out to investigate heat transfer by free convection under the effect of MHD （magnetohydrodynamic） for steady state three-dimensional laminar flow in horizontal and vertical cylindrical annulus filled with saturated porous media （sand silica） with fins attached to the inner cylinder. A single electric coil placed around the inner cylinder to generate a magnetic field. The governing equations which used are continuity, momentum （using Darcy＇s law） and energy equations which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using Fortran 90 program. The parameters affected on the system are Rayleigh number ranging within （102 ~ Ra＊ 〈 104）, and MHD （Mn） （0 〈_ Mn 〈_ 100） and radius ratio Rr （0.225, 0.338 and 0.435）. The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that heat transfer decrease with the increase of magnetohydrodynamic. It was found that the average Nusselt number increase with Ra＊ and decrease with H~ Mn and Rr. A correlation for the average Nusselt number in terms of Ra＊ and Mn, has been developed for the inner cylinder.展开更多
文摘A numerical study has been carried out to investigate heat transfer by free convection under the effect of MHD （magnetohydrodynamic） for steady state three-dimensional laminar flow in horizontal and vertical cylindrical annulus filled with saturated porous media （sand silica） with fins attached to the inner cylinder. A single electric coil placed around the inner cylinder to generate a magnetic field. The governing equations which used are continuity, momentum （using Darcy＇s law） and energy equations which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using Fortran 90 program. The parameters affected on the system are Rayleigh number ranging within （102 ~ Ra＊ 〈 104）, and MHD （Mn） （0 〈_ Mn 〈_ 100） and radius ratio Rr （0.225, 0.338 and 0.435）. The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that heat transfer decrease with the increase of magnetohydrodynamic. It was found that the average Nusselt number increase with Ra＊ and decrease with H~ Mn and Rr. A correlation for the average Nusselt number in terms of Ra＊ and Mn, has been developed for the inner cylinder.
