The Lie group method is applied to present an analysis of the magneto hydro-dynamics（MHD） steady laminar flow and the heat transfer from a warm laminar liquid flow to a melting moving surface in the presence of ther...The Lie group method is applied to present an analysis of the magneto hydro-dynamics（MHD） steady laminar flow and the heat transfer from a warm laminar liquid flow to a melting moving surface in the presence of thermal radiation.By using the Lie group method,we have presented the transformation groups for the problem apart from the scaling group.The application of this method reduces the partial differential equations（PDEs） with their boundary conditions governing the flow and heat transfer to a system of nonlinear ordinary differential equations（ODEs） with appropriate boundary conditions.The resulting nonlinear system of ODEs is solved numerically using the implicit finite difference method（FDM）.The local skin-friction coefficients and the local Nusselt numbers for different physical parameters are presented in a table.展开更多
The theoretic transformation group approach is applied to address the problem of unsteady boundary layer flow of a non-Newtonian fluid near a stagnation point with variable viscosity and thermal conductivity. The appl...The theoretic transformation group approach is applied to address the problem of unsteady boundary layer flow of a non-Newtonian fluid near a stagnation point with variable viscosity and thermal conductivity. The application of a two- parameter group method reduces the number of independent variables by two, and consequently the governing partial differential equations with the boundary conditions transformed into a system of ordinary differential equations with the appropriate corresponding conditions. Two systems of ordinary differential equations have been solved numerically using a fourth-order Runge-Kutta algorithm with a shooting technique. The effects of various parameters governing the problem are investigated.展开更多
文摘The Lie group method is applied to present an analysis of the magneto hydro-dynamics（MHD） steady laminar flow and the heat transfer from a warm laminar liquid flow to a melting moving surface in the presence of thermal radiation.By using the Lie group method,we have presented the transformation groups for the problem apart from the scaling group.The application of this method reduces the partial differential equations（PDEs） with their boundary conditions governing the flow and heat transfer to a system of nonlinear ordinary differential equations（ODEs） with appropriate boundary conditions.The resulting nonlinear system of ODEs is solved numerically using the implicit finite difference method（FDM）.The local skin-friction coefficients and the local Nusselt numbers for different physical parameters are presented in a table.
文摘The theoretic transformation group approach is applied to address the problem of unsteady boundary layer flow of a non-Newtonian fluid near a stagnation point with variable viscosity and thermal conductivity. The application of a two- parameter group method reduces the number of independent variables by two, and consequently the governing partial differential equations with the boundary conditions transformed into a system of ordinary differential equations with the appropriate corresponding conditions. Two systems of ordinary differential equations have been solved numerically using a fourth-order Runge-Kutta algorithm with a shooting technique. The effects of various parameters governing the problem are investigated.
