CAPUTO TIME FRACTIONAL MODEL BASED ON GENERALIZED FOURIER’S AND FICK’S LAWS FOR BRINKMAN-TYPE FLUID: EXACT SOLUTION VIA INTEGRAL TRANSFORM
Abstract
This paper proposes a new method for the development of the Caputo time fractional model. The method relies on generalized Fourier’s and Fick’ laws to describe the flow behavior of Brinkman-type fluids. An analysis of the free convection flow through a channel is carried out using a new transformation method. This transformation affects fluid energy and concentration equations. The specific governing equations are solved using a Laplace transform and Fourier sine transform. We obtain the solutions of the governing partial differential equations (PDEs) in terms of the Mittag–Leffler function. Mathematical software has been used for both graphical and numerical computation in order to examine the effects of embedded parameters. From graphical and tabular analysis, fractional-order solution provides more than one layer for fluid behavior, thermal, and concentration distribution in the channel. Experimentalists and engineers can choose from many best-fitted layers to compare their data and results. A deviation in the velocity profile’s behavior is also seen for larger values of the Brinkman parameter.
