MHD Flow of a Newtonian Fluid in Symmetric Channel with ABC Fractional Model Containing Hybrid Nanoparticles

Abstract

Introduction: The nanofluid is the novelty of nanotechnology to overcome the difficulties of heat transfer in several manufacturing and engineering areas. Fractional calculus has many applications in nearly all fields of science and engineering, which include electrochemistry, dispersion and viscoelasticity.

Objectives: This paper focused on the heat transfer of a hybrid nanofluid in two vertical parallel plates and presented a comparison between fractional operators.

Methods: In this paper, the fractional viscous fluid model is considered along with physical initial and boundary conditions for the movement occurrences. The analytical solutions have been obtained via the Laplace transform method for the concentration, temperature and velocity fields. After that, we have presented a comparison between Atangana-Baleanu (ABC), Caputo (C) and Caputo-Fabrizio (CF) fractional operators.

Results: The comparison of different base fluids (Water, kerosene, Engine Oil) is discussed graphically with respect to temperature and velocity. The results show that due to the high thermal conductivity of water, temperature and velocity are high. While engine oil has maximum viscosity than water and kerosene, thus temperature and velocity are very low. However, due to the improvement in the thermal conductivity with the enrichment of hybrid nanoparticles, the temperature increased, and since the viscosity also increased, the velocity got reduced.

Conclusion: Atangana-Baleanu (ABC) fractional operator provided better memory effect of concentration, temperature and velocity fields than Caputo (C) and Caputo-Fabrizio (CF). Temperature and velocity of water with hybridized nanoparticles were high in comparison to kerosene and engine oil.

Keywords: Hybrid nanofluid; M-function; MHD flow; fractional derivative; heat generation; newtonian fluid model.