Integral Transform Method for Solving Inhomogeneous Heat Equation with Mixed Boundary Conditions

The inhomogeneous heat equation for a semi-infinite cylindrical solid body with mixed boundary conditions of the first and second kinds on the surface of the cylinder was solved using the Laplace and Hankel integral transforms. The solution of the mixed boundary-value problem was reduced to the dual integral equations which were solved using an appropriate substitution, and their solution was finally reduced to the Fredholm integral equations of the second kind which were solved by the infinite series method.