## THERMAL SCIENCE

International Scientific Journal

### 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.

**KEYWORDS**

PAPER SUBMITTED: 2020-06-15

PAPER REVISED: 2020-07-10

PAPER ACCEPTED: 2020-07-15

PUBLISHED ONLINE: 2020-10-25

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**Supplement 1**, PAGES [S377 - S389]

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