An alternative integral-balance solutions to transient diffusion of heat (mass) by time-fractional semi-derivatives and semi-integrals: Fixed boundary conditions

A new approach to integral-balance solutions of the diffusion equation of heat (mass) with constant transport properties by applying time-fractional semi-derivatives and semi-integrals of Riemann-Liouville sense has been developed. The time-fractional semiderivatives and semiintegrals replace the surface gradient (temperature) which in the classical Heat-balance integral method (HBIM) of Goodman and the Double-integration method (DIM) should be expressed through the assumed profile. The application of semiderivatives and semiintegrals reduces the approximation errors to levels less than the ones exhibited by the classical HBIM and DIM. The method is exemplified by solutions of Dirichlet and Neumann boundary condition problems.