In this paper, the modification of double Laplace decomposition method is pro- posed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples ar...In this paper, the modification of double Laplace decomposition method is pro- posed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples are given to support our presented method. In addition, we prove the convergence of double Laplace transform decomposition method applied to our problems.展开更多
The heat transfer equation is used to determine the heat flow by conduction through a composite material along the real axis.An analytical dimensionless analysis is implemented in the framework of a separation of vari...The heat transfer equation is used to determine the heat flow by conduction through a composite material along the real axis.An analytical dimensionless analysis is implemented in the framework of a separation of variables method(SVM).This approach leads to an Eigenvalues problem that is solved by the Newton’s method.Two types of dynamics are found:An unsteady condition(in the form of jumps or drops in temperatures depending on the considered case),and a permanent equilibrium(tending to the ambient temperature).The validity and effectiveness of the proposed approach for any number of adjacent layers is also discussed.It is shown that,as expected,the diffusion of the temperature is linked to the ratio of the thermo-physical properties of the considered layers and their number.展开更多
文摘In this paper, the modification of double Laplace decomposition method is pro- posed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples are given to support our presented method. In addition, we prove the convergence of double Laplace transform decomposition method applied to our problems.
文摘The heat transfer equation is used to determine the heat flow by conduction through a composite material along the real axis.An analytical dimensionless analysis is implemented in the framework of a separation of variables method(SVM).This approach leads to an Eigenvalues problem that is solved by the Newton’s method.Two types of dynamics are found:An unsteady condition(in the form of jumps or drops in temperatures depending on the considered case),and a permanent equilibrium(tending to the ambient temperature).The validity and effectiveness of the proposed approach for any number of adjacent layers is also discussed.It is shown that,as expected,the diffusion of the temperature is linked to the ratio of the thermo-physical properties of the considered layers and their number.
