A numerical study has been carried out to investigate the temperature distribution and the natural convection heat transfer in axisymmetric two-dimensional vertical saturated porous cylinder with steady state laminar ...A numerical study has been carried out to investigate the temperature distribution and the natural convection heat transfer in axisymmetric two-dimensional vertical saturated porous cylinder with steady state laminar flow. A comparison between two situations is done under the effect of MHD （magnetohydrodynamics） and radiation. In the two situations, the vertical walls of the cylinder are cooled with constant wall temperature and a constant heat generation subjected along the centerline of the cylinder. The first case for cylinder with insulated upper surface and cooled bottom surface while the second case for cylinder with cooled upper surface and insulated bottom surface. The governing equations used are continuity, momentum and energy equations which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 programming. The parameters affected the system are Rayleigh number ranging within （102≤ Ra ≤104）, radiation parameter （0≤ Rd ≤ 2） and magnetohydrodynamics MHD （Mn） （0 ≤ Mn≤ 2）.The results show that the temperature of Case 1 is more than that in Case 2 at constant Ra, Mn and Rd while the value of the stream in Case 2 is greater than that in Case 1. Nu increase with the increase of Rd and increasing Mn caused the temperature to increase and the streamline dropped while Nu decreased. A correlation has been set up to give the average Nusselt number variation with Ra, Rd and Mn for which the results are found to be in good agreement with previously published researches.展开更多
文摘A numerical study has been carried out to investigate the temperature distribution and the natural convection heat transfer in axisymmetric two-dimensional vertical saturated porous cylinder with steady state laminar flow. A comparison between two situations is done under the effect of MHD （magnetohydrodynamics） and radiation. In the two situations, the vertical walls of the cylinder are cooled with constant wall temperature and a constant heat generation subjected along the centerline of the cylinder. The first case for cylinder with insulated upper surface and cooled bottom surface while the second case for cylinder with cooled upper surface and insulated bottom surface. The governing equations used are continuity, momentum and energy equations which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 programming. The parameters affected the system are Rayleigh number ranging within （102≤ Ra ≤104）, radiation parameter （0≤ Rd ≤ 2） and magnetohydrodynamics MHD （Mn） （0 ≤ Mn≤ 2）.The results show that the temperature of Case 1 is more than that in Case 2 at constant Ra, Mn and Rd while the value of the stream in Case 2 is greater than that in Case 1. Nu increase with the increase of Rd and increasing Mn caused the temperature to increase and the streamline dropped while Nu decreased. A correlation has been set up to give the average Nusselt number variation with Ra, Rd and Mn for which the results are found to be in good agreement with previously published researches.
