Abstract
In this paper, investigation is devoted to study the homotopy analysis method to solve numerically the problem of harmonic wave propagation in a nonlinear thermoelasticity under influence of rotation and magnetic field. The problem is solved in one-dimensional thermoelastic half-space model subjected to initially a prescribed harmonic displacement and the temperature of the medium. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution. The displacement and temperature are calculated for the methods for different values of the magnetic field and rotation. The results obtained are displayed graphically to show the influences of the new parameters. Comparison is made with the results obtained in the presence and absence of rotation and magnetic field. The results indicate that the effect of rotation and magnetic field are very pronounced.