Threshold for the generalized Non-Fourier heat flux model: Universal closed form analytic solution

Jafarimoghaddam A., TÜRKYILMAZOĞLU M., Pop I.

INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER, vol.123, 2021 (SCI-Expanded) identifier identifier


The Magnetohydrodynamics (MHD) flow of second grade and viscoelastic fluids due to a linearly stretching sheet in a Darcy porous medium considering Cattaneo-Christov heat flux model (with the thermal relaxation time playing a significant role) is tackled analytically. Closed form analytic solution is presented for the energy equation employing the properties of Appell hypergeometric function of two variables presumably for the 1st time in the literature. It is shown that the associated energy equation yields closed form solution only iff ''(0)(2) > a lambda Pr; in particular, being a structural constraint for the existence of thermal solutions under the studied model. Here, f ''(0) is the normalized shear stress at the wall, lambda is the relaxation time parameter in Cattaneo-Christov model, Pris Prandtl number and ais the positive stretching ratio.