## THERMAL SCIENCE

International Scientific Journal

### APPLICATION OF FRACTIONAL CALCULUS IN GROUND HEAT FLUX ESTIMATION

**ABSTRACT**

Ground (soil) heat flux is important physical factor primarily because of its role in surface energy balance, analysis of atmospheric boundary layer and land surface-atmosphere interaction. Direct measurement of this property is often associated with difficulties arising from need for adequate calibration of measuring devices, determination of proper depth for probes, upward water migration and accumulation below measuring plates to lack of understanding of the governing thermal processes occurring at the ground surface. In the following paper approach for inferring heat flux indirectly, from known ground surface temperature time-dependant functions, using previously developed fractional diffusion equation for ground heat conduction is elaborated. Fractional equation is solved for two, most frequently encountered harmonic surface temperature functions. Yielded results were compared with analytic solutions. Validation results indicate that solutions obtained with fractional approach closely correspond to analytic solutions with remark that former are more general, containing the term covering the transitional effect.

**KEYWORDS**

PAPER SUBMITTED: 2011-01-31

PAPER REVISED: 2011-07-12

PAPER ACCEPTED: 2011-07-18

**THERMAL SCIENCE** YEAR

**2012**, VOLUME

**16**, ISSUE

**2**, PAGES [373 - 384]

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