On one variational principle of Hamilton's type for nonlinear heat transfer problem

Abstract In this paper a new Lagrangian for nonlinear heat conduction problem is constructed. Using the concept of penetration depth a computational procedure for solving the nonlinear heat equation is given. Problem with nonlinear boundary conditions (surface radiation) is also discussed. Applying the method of Yang [33–35], it is shown that the solutions can be improved. Also, the method of choosing the best trial polynomial for the description of the temperature distribution is discussed. In the light of Yang's theory the solutions obtained by means of the variational principle have some degree of optimality in comparison to other approximative solutions.

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