In this paper, thermal-fluid modeling of nonporous/porous thermal coil filled by alumina nanofluid is discussed considering constant/variable solar heat fluxes. The fluxes are calculated for a parabolic concentrator at the solar paths for the city with a longitude of 59.20 deg and latitude of 32.87 deg in the clear sky at spring season. The governing equations are included as continuity, momentum, and energy conservations with considering variable solar flux by shadow effects of the coil on the parabolic concentrator. The numerical model is based on the finite element method by LU algorithm using the mumps solver. The results show that, in a porous medium, that the normalized temperature of the presented model has an acceptable agreement with experimental data with maximum errors of 3%. The existence of porosity significantly increases heat transfer parameters that improve transferred solar heat from the wall of the coil to nanofluid. The variable solar heat flux increases the temperature in the length of the coil rather than constant heat fluxes because of increasing exchanged heat to nanofluid.

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