Non-linear heat conduction with ramped surface heating ramp surface heating and approximate solution

Abstract

Non-linear heat conduction with a power-law thermal diffusivity and ramped surface temperature has been solved by the double-integration technique of the integral-balance integral method. The case of a semi-infinite medium and infinite ramp of surface temperature has been considered as example demonstrating the versatility of the solution approach. The thermal penetration depth and solution behaviours with finite speeds have been analyzed.

Mathematical fractional modeling of transpot phenomena of viscous fluid-flow between two plates

“…In the last few years, a momentous role has been played by fractional calculus in different fields such as mechanics, electricity, chemistry, biology, and economics, heat transfer, nanotechnology Miller and Ross [1]. The most recent developments of fractional calculus in the application point of view can be seen in the following references [2][3][4][5]. Baleanu, et al [6] introduce a new fractional parameter known as Constant proportional Caputo.…”