Analytical solutions of governing equations of various phenomena have their irre-placeable theoretical meanings. In addition, they can also be the benchmark solu-tions to verify the outcomes and codes of numerical sol...Analytical solutions of governing equations of various phenomena have their irre-placeable theoretical meanings. In addition, they can also be the benchmark solu-tions to verify the outcomes and codes of numerical solutions, and even to develop various numerical methods such as their differencing schemes and grid generation skills as well. A hybrid method of separating variables for simultaneous partial differential equation sets is presented. It is proposed that different methods of separating variables for different independent variables in the simultaneous equa-tion set may be used to improve the solution derivation procedure, for example, using the ordinary separating method for some variables and using extraordinary methods of separating variables, such as the separating variables with addition promoted by the first author, for some other variables. In order to prove the ability of the above-mentioned hybrid method, a lot of analytical exact solutions of two-buoyancy convection in porous media are successfully derived with such a method. The physical features of these solutions are given.展开更多
An algebraically explicit analytical solution with heat wave effect is derived for the non-Fourier bioheat transfer Chen-Holmes model. Besides its important theoreti-cal meaning (for example, to expand the understandi...An algebraically explicit analytical solution with heat wave effect is derived for the non-Fourier bioheat transfer Chen-Holmes model. Besides its important theoreti-cal meaning (for example, to expand the understanding of heat wave phenomena in living tissues), this analytical solu-tion is also valuable as the benchmark solution to check the numerical calculation and to develop various numerical computational approaches.展开更多
Reasonable unsteady three-dimensional explicit analytical solutions are derived with different methods for the widely used bio-heat transfer equation–Pennes equation.The condition to decide temperature oscillation is...Reasonable unsteady three-dimensional explicit analytical solutions are derived with different methods for the widely used bio-heat transfer equation–Pennes equation.The condition to decide temperature oscillation is obtained in this paper.In other cases the temperature would vary monotonously along geometric coordinates as time goes by.There have been very few open reports of explicit unsteady multidimensional exact analytical solutions published in literature.Besides its irreplaceable theoretical value,the analytical solution can also serve as standard solution to check numerical calculation,and therefore promote the development of numerical method of computational heat transfer.In addition,some new special methods have been given originally and deserved further attention.展开更多
基金the National Natural Science Foundation of China (Grant No. 50576097)the National Basic Research Development Program of China (Grant No. 2007CB206902)
文摘Analytical solutions of governing equations of various phenomena have their irre-placeable theoretical meanings. In addition, they can also be the benchmark solu-tions to verify the outcomes and codes of numerical solutions, and even to develop various numerical methods such as their differencing schemes and grid generation skills as well. A hybrid method of separating variables for simultaneous partial differential equation sets is presented. It is proposed that different methods of separating variables for different independent variables in the simultaneous equa-tion set may be used to improve the solution derivation procedure, for example, using the ordinary separating method for some variables and using extraordinary methods of separating variables, such as the separating variables with addition promoted by the first author, for some other variables. In order to prove the ability of the above-mentioned hybrid method, a lot of analytical exact solutions of two-buoyancy convection in porous media are successfully derived with such a method. The physical features of these solutions are given.
基金This work was supported by the National Natural Science Foundation of China(Grant No.50246003 and its succeeding foundation)the Major State Basic Research Development Program of China(Grant No.G20000263).
文摘An algebraically explicit analytical solution with heat wave effect is derived for the non-Fourier bioheat transfer Chen-Holmes model. Besides its important theoreti-cal meaning (for example, to expand the understanding of heat wave phenomena in living tissues), this analytical solu-tion is also valuable as the benchmark solution to check the numerical calculation and to develop various numerical computational approaches.
基金supported by the National Natural Science Foundation of China(Grant No.50876106)
文摘Reasonable unsteady three-dimensional explicit analytical solutions are derived with different methods for the widely used bio-heat transfer equation–Pennes equation.The condition to decide temperature oscillation is obtained in this paper.In other cases the temperature would vary monotonously along geometric coordinates as time goes by.There have been very few open reports of explicit unsteady multidimensional exact analytical solutions published in literature.Besides its irreplaceable theoretical value,the analytical solution can also serve as standard solution to check numerical calculation,and therefore promote the development of numerical method of computational heat transfer.In addition,some new special methods have been given originally and deserved further attention.
