A benchmark solution is of great importance in validating algorithms and codes for magnetohydrodynamic(MHD) flows.Hunt and Shercliff's solutions are usually employed as benchmarks for MHD flows in a duct with insu...A benchmark solution is of great importance in validating algorithms and codes for magnetohydrodynamic(MHD) flows.Hunt and Shercliff's solutions are usually employed as benchmarks for MHD flows in a duct with insulated walls or with thin conductive walls,in which wall effects on MHD are represented by the wall conductance ratio.With wall thickness resolved,it is stressed that the solution of Sloan and Smith's and the solution of Butler's can be used to check the error of the thin wall approximation condition used for Hunt's solutions.It is noted that Tao and Ni's solutions can be used as a benchmark for MHD flows in a duct with wall symmetrical or unsymmetrical,thick or thin.When the walls are symmetrical,Tao and Ni's solutions are reduced to Sloan and Smith's solution and Butler's solution,respectively.展开更多
This paper presents two exact explicit solutions for the three dimensional dual-phase lag （DLP） heat conduction equation, during the derivation of which the method of trial and error and the authors＇ previous exper...This paper presents two exact explicit solutions for the three dimensional dual-phase lag （DLP） heat conduction equation, during the derivation of which the method of trial and error and the authors＇ previous experiences are utilized. To the authors＇ knowledge, most solutions of 2D or 3D DPL models available in the literature are obtained by numerical methods, and there are few exact solutions up to now. The exact solutions in this paper can be used as benchmarks to validate numerical solutions and to develop numerical schemes, grid generation methods and so forth. In addition, they are of theoretical significance since they correspond to physically possible situations. The main goal of this paper is to obtain some possible exact explicit solutions of the dual-phase lag heat conduction equation as the benchmark solutions for computational heat transfer, rather than specific solutions for some given initial and boundary conditions. Therefore, the initial and boundary conditions are indeterminate before derivation and can be deduced from the solutions afterwards. Actually, all solutions given in this paper can be easily proven by substituting them into the governing equation.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11125212 and 50936066)the National Magnetic Confinement Fusion Science Program of China (Grant No. 2009GB10401)
文摘A benchmark solution is of great importance in validating algorithms and codes for magnetohydrodynamic(MHD) flows.Hunt and Shercliff's solutions are usually employed as benchmarks for MHD flows in a duct with insulated walls or with thin conductive walls,in which wall effects on MHD are represented by the wall conductance ratio.With wall thickness resolved,it is stressed that the solution of Sloan and Smith's and the solution of Butler's can be used to check the error of the thin wall approximation condition used for Hunt's solutions.It is noted that Tao and Ni's solutions can be used as a benchmark for MHD flows in a duct with wall symmetrical or unsymmetrical,thick or thin.When the walls are symmetrical,Tao and Ni's solutions are reduced to Sloan and Smith's solution and Butler's solution,respectively.
基金supported by the National Natural Science Foundation of China (50576097) the National Defense Basic Research Program of China (DEDP 1003)
文摘This paper presents two exact explicit solutions for the three dimensional dual-phase lag （DLP） heat conduction equation, during the derivation of which the method of trial and error and the authors＇ previous experiences are utilized. To the authors＇ knowledge, most solutions of 2D or 3D DPL models available in the literature are obtained by numerical methods, and there are few exact solutions up to now. The exact solutions in this paper can be used as benchmarks to validate numerical solutions and to develop numerical schemes, grid generation methods and so forth. In addition, they are of theoretical significance since they correspond to physically possible situations. The main goal of this paper is to obtain some possible exact explicit solutions of the dual-phase lag heat conduction equation as the benchmark solutions for computational heat transfer, rather than specific solutions for some given initial and boundary conditions. Therefore, the initial and boundary conditions are indeterminate before derivation and can be deduced from the solutions afterwards. Actually, all solutions given in this paper can be easily proven by substituting them into the governing equation.
