Thermal impedance at the interface of contacting bodies: 1-D example solved by semi-derivatives

Abstract

Simple 1-D semi-infinite heat conduction problems enable to demonstrate the potential of the fractional calculus in determination of transient thermal impedances of two bodies with different initial temperatures contacting at the interface (x = 0) at t = 0. The approach is purely analytic and uses only semi-derivatives (half-time) and semi-integrals in the Riemann-Liouville sense. The example solved clearly reveals that the fractional calculus is more effective in calculation the thermal resistances than the entire domain solutions.