Heat transfer in magnetohydrodynamic free convection flow of generalized ferrofluid with magnetite nanoparticles

Abstract

This article investigates the effects of magnetite $$ {\text{Fe}}_{3}^{{}} {\text{O}}_{4}^{{}} $$ nanoparticles on free convection flow of nanofluid with magnetohydrodynamics. The magnetite $$ {\text{Fe}}_{3}^{{}} {\text{O}}_{4}^{{}} $$ nanoparticles that have been dispersed in water are taken as a conventional base fluid. In order to compare newly fractional derivatives, the governing equations have been fractionalized via Atangana–Baleanu and Caputo–Fabrizio fractional operators. The resulting partial differential equations are solved by employing Laplace transforms. Exact solutions have been investigated for temperature and velocity field via Atangana–Baleanu and Caputo–Fabrizio fractional operators and then expressed in Mittag–Leffler function $$ {\mathbf{M}}_{{\upbeta,\upgamma}}^{\rm{y}} \left( W \right) $$ and M-function $$ {\mathbf{M}}_{\text{q}}^{\rm{p}} \left( W \right) $$ . The enhancement of heat transfer and effects in the natural convection flows are analyzed graphically by Atangana–Baleanu and Caputo–Fabrizio fractional operators. Graphical comparison has been depicted via Atangana–Baleanu and Caputo–Fabrizio derivatives for four types of models, i.e., (1) fractionalized nanofluid with magnetic field, (2) ordinary nanofluid with magnetic field, (3) fractionalized nanofluid without magnetic field and (4) ordinary nanofluid without magnetic field on fluid flows.