Numerical-analytical method of solution of a nonlinear unsteady heat-conduction equation

A method of solution of a one-dimensional nonlinear unsteady heat-conduction equation has been proposed. The use of the method of Green’s functions made it possible to transform the resulting equation to a nonlinear Volterra integral equation of the second kind for temperature, which is solved by the quadratic-form method. A system of recurrence relations, which is solved numerically, has been obtained. The influence of the nonlinearity on the temperature profiles has been analyzed. A comparison to the numerical finite-element method has shown that the numerical-analytical technique allows a reduction of more than 103 times in the calculation time.