The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of soli...The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.展开更多
In this study, the e?ect of the lower boundary position selection for the Fourier equation on heat transfer and energy balance in soil is evaluated. A detailed numerical study shows that the proper position of the l...In this study, the e?ect of the lower boundary position selection for the Fourier equation on heat transfer and energy balance in soil is evaluated. A detailed numerical study shows that the proper position of the lower boundary is critical when solving the Fourier equation by using zero heat ?ux as the lower boundary condition. Since the position de?nes the capacity of soil as a heat sink or source, which absorbs and stores radiation energy from the sky in summer and then releases the energy to the atmosphere in winter, and regulates the deep soil temperature distribution, the depth of the position greatly in?uences the heat balance within the soil as well as the interaction between the soil and the atmosphere. Based on physical reasoning and the results of numerical simulation, the proper depth of the position should be equal to approximately 3 times of the annual heat wave damping depth. For most soils, the proper lower boundary depth for the Fourier equation should be around 8 m to 15 m, depending on soil texture.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 51305080
文摘The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.
基金National Natural Science Founda-tion of China under Grant Nos.40233034 , 40075019KZCX2-SW-210National Natural Science Foun-dation of China under Grant No.40305011.
文摘In this study, the e?ect of the lower boundary position selection for the Fourier equation on heat transfer and energy balance in soil is evaluated. A detailed numerical study shows that the proper position of the lower boundary is critical when solving the Fourier equation by using zero heat ?ux as the lower boundary condition. Since the position de?nes the capacity of soil as a heat sink or source, which absorbs and stores radiation energy from the sky in summer and then releases the energy to the atmosphere in winter, and regulates the deep soil temperature distribution, the depth of the position greatly in?uences the heat balance within the soil as well as the interaction between the soil and the atmosphere. Based on physical reasoning and the results of numerical simulation, the proper depth of the position should be equal to approximately 3 times of the annual heat wave damping depth. For most soils, the proper lower boundary depth for the Fourier equation should be around 8 m to 15 m, depending on soil texture.
