A Time- Fractional Model for Brinkman-Type Nanofluid with Variable Heat and Mass Transfer

Abstract

Nanofluids are used in a variety of thermal applications, including heat exchangers, automobiles and solar power generation among others. Nanofluids are the next generation of fluids, with thermal properties that exceed traditional fluids. In order to inticipate the heat transport characteristics of an inclined solar collector using nanofluids under the influence of a transverse magnetic field, a generalised Brinkman-type fluid model was developed. The effects of thermal radiation and concentration are also addressed. Moreover, in this article we apply the idea of Caputo time fractional derivative by using the generalized Fick's and Fourier's Law??™s to convert classical governing equations to fractional PDEs. The equations of energy and concentration are transformed with the help of new productive transform initial and boundary conditions. The Laplace and Fourier sine transforms are applied together and solve the transformed equations. The current study used a variety of nano-sized solid particles, including SWCNTs, MWCNTs, ? and , and found that adding of MWCNTs to the water (working fluid) can increase the rate of heat transfer up to 34.84 percent, improving the working ability of inclined solar collectors by increasing their solar radiation absorbtion power.