Transient Heat Conduction in a Semi-Infinite Domain with a Memory Effect: Analytical Solutions with a Robin Boundary Condition

Abstract

The Robin boundary condition initial value problem for transient heat conduction with the time-fractional Caputo derivative in a semi-infinite domain with a convective heat transfer (Newton’s law) at the boundary has been solved and analyzed by two analytical approaches. The uniqueness and the stability of the solution on the half-axis have been analyzed. The problem solutions by application of the operational method (Laplace transform in the time domain) and the integral-balance method (double integration technique) have been developed analytically.

Keywords

• transient heat conduction
• Robin boundary condition
• analytical solution
• Caputo derivative