Abstract
In this paper, a new approach of analytical solutions is carried out on the thermal transport phenomena of Casson fluid based on Prabhakar's fractional derivative with generalized Fourier's law. The governing equations are obtained through constitutive relations and analytical solutions obtained via Laplace transform technique. Solutions for temperature and velocity fields were analyzed through graphical description by Mathcad software. The fluid properties revealed various aspects for different flow parameters as well as fractional parameter values and found important results. As a result, it is found that fluid properties can be enhanced by increasing the values of fractional parameters and useful in some experimental data fitting in the heating and cooling phenomena especially electronic devices.