This work concerns with the nonlocal problems and the main theme of it can be divide into three categories, which can be listed as follows: First: Some analytical methods namely, the separation of variables and the eigenfunction expansion method to solve some types of linear partial differential equations with nonlocal conditions, are presented. Second: The varaitional iteration method is used to solve special types of the nonhomogenous partial differential equations and linear nonhomogenous parabolic integro-differential equations with nonlocal conditions. Third : Some real life applications for the nonlocal problems arising in thermoelasticity problems and its solutions via the separation of variables, the eigenfunction expansion method and the varaitional iteration method with its convergence, are introduced.