Analytical solutions have varied uses. One is to provide solutions that can be used in verification of numerical methods. Another is to provide relatively simple forms of exact solutions that can be used in estimating...Analytical solutions have varied uses. One is to provide solutions that can be used in verification of numerical methods. Another is to provide relatively simple forms of exact solutions that can be used in estimating parameters, thus, it is possible to reduce computation time in comparison with numerical methods. In this paper, an alternative procedure is presented. Here is used a hybrid solution based on Green＇s function and real characteristics （discrete data） of the boundary conditions.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
文摘Analytical solutions have varied uses. One is to provide solutions that can be used in verification of numerical methods. Another is to provide relatively simple forms of exact solutions that can be used in estimating parameters, thus, it is possible to reduce computation time in comparison with numerical methods. In this paper, an alternative procedure is presented. Here is used a hybrid solution based on Green＇s function and real characteristics （discrete data） of the boundary conditions.
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.
