Fractional Brinkman type fluid in channel under the effect of MHD with Caputo-Fabrizio fractional derivative

Abstract

The purpose of this paper is to evaluate the exact solution of the unsteady flow of a generalized Brinkman type fluid under the effect of MHD in a channel. The classical Brinkman model reduced to non-dimensional form by using appropriate dimensionless variables. Furthermore, the non-dimensional Brinkman model is transformed to a generalize Brinkman model with Caputo-Fabrizio fractional derivative. The dimensionless Brinkman model has been solved with applicable conditions by integral transforms techniques that is Fourier and Laplace. The effect of different physical parameters and fractional order on fluid velocity and shear stress are illustrated graphically. Moreover, through this recent work, the recovery of classical Brinkman type fluid is possible through graphs.

Keywords

• Caputo-Fabrizio fractional operator
• Brinkman type fluid
• MHD
• Shear stress
• Exact solutions
• Fourier and Laplace transforms