Mathematical modeling of ( Cu − A l 2 O 3 ) water based Maxwell hybrid nanofluids with Caputo-Fabrizio fractional derivative

In this article, a free convection flow of Cu − A l 2 O 3 − H 2 O hybrid Maxwell nanofluids through a channel formed by two infinite vertical plates have been studied. Together with the the energy balance and heat source, a fractional model of Maxwell fluid is considered. To develop an analytical exact solution for velocity field, only the Caputo-Fabrizio definition of non-integral derivative together with application of Laplace transform method has been used. Some graphical presentation and discussion are made to see the effects of hybrid nanofluids and non-dimensional parameters on velocity boundary layer. As a result, a dual behavior of velocity was exposed due to fractional parameter for large and small times. A comparison between two kind of non-Newtonian fluids has been made and found that Brinkman fluid is more viscous than Maxwell fluid. Also, by letting Brinkman and Maxwell parameters zero, they coincides and the results obtained for Newtonian fluid showed graphically. The obtained results are realistic from the fractional model as by adjusting the values of fractional parameter can be compared with some experimental data.