Analytical And Numerical Analysis Of Heat Transfer In Hollow Channeland Circular Channel Filled With Porous Medium

Hollow circular channel and annular channel as the most common channel model,which are applied to electronics,engineering and solar energy fields.Heat transfer in hollow channel has been attracted sustained attention by researcher.In recent years,due to the development of the theory of porous medium,the heat transfer in porous media channels are widely used in many natural systems and engineering practice,such as nuclear waste storage,energy storage,electronics cooling,heat insulation,packed bed heat exchanger,heat pipe,oil,geothermal systems and catalytic reactor.Through the combination of numerical simulation and theoretical analysis the heat transfer in hollow channel and circular channel filled with porous medium are researched,the obtained results has a very important reference value for both engineering practices and scientific researches.Firstly,analytical solutions for temperature field in cross-section of hollow circular channel and annular channel with boundary conditions of circumferentially non-uniform temperature are obtained by the method of separation of variables,then we carry on case study for hollow circular channel and annular channel model and carry out parametric study based on the analytical solutions of case study.Then,for the forced convective heat transfer in circular channel filled with a porous medium under the asymmetric distribution of entrance temperature boundary condition,the solid phase and fluid phase dimensionless temperature distributions are obtained by the method of separation of variables under local thermal non-equilibrium(LTNE)and thermally developing conditions.Subsequently,the analytical solid phase and fluid phase dimensionless temperatures are validate by COMSOL Multiphysics,a good agreement is found between the present analytical solutions and numerical results.Next the parameter analysis is carried on for the dimensionless temperature in circular channel filled with a porous medium,it is found that solid and fluid phase dimensionless temperatures are both decrease by increasing the axial and radical locations,and present periodic variation by angle of circumference,the increase of P_ewill lead to thermally developing region translate to thermally fully develop region,the temperature difference between solid and fluid phase decrease by increasing the B_i,as a limiting case,the LTNE model degenerate to the LTE model when B_iapproaches infinity.Finally,with the help of COMSOL Multiphysics,the corresponding energy equations are solved by considering the fluid phase heat conduction in cross-section of circular channel,the results show that the solid and fluid phases dimensionless temperatures for circular channel filled with a porous medium are lower than those without the fluid phase heat conduction in cross-section of circular channel but the same trend,the difference between two conditions is slight.At the same time,we carry out numerical simulation for forced convective heat transfer in circular channel filled with a porous medium under the consideration of Brinkman momentum equation,the results indicate that the dimensionless velocity and dimensionless temperatures are increase by increasing the Darcy number,and decrease by increasing the effective viscosity of the fluid M,The increase of D_aleads to the extension of thermally developing region,the increase of M presents the opposite trend.