Abstract
A nonlocal fractional model of Brinkman type fluid (BTF) containing a hybrid nanostructure was examined. The magnetohydrodynamic (MHD) flow of the hybrid nanofluid was studied using the fractional calculus approach. Hybridized silver (Ag) and Titanium dioxide (TiO2) nanoparticles were dissolved in base fluid water (H2O) to form a hybrid nanofluid. The MHD free convection flow of the nanofluid (Ag-TiO2-H2O) was considered in a microchannel (flow with a bounded domain). The BTF model was generalized using a nonlocal Caputo-Fabrizio fractional operator (CFFO) without a singular kernel of order α with effective thermophysical properties. The governing equations of the model were subjected to physical initial and boundary conditions. The exact solutions for the nonlocal fractional model without a singular kernel were developed via the fractional Laplace transform technique. The fractional solutions were reduced to local solutions by limiting α → 1 . To understand the rheological behavior of the fluid, the obtained solutions were numerically computed and plotted on various graphs. Finally, the influence of pertinent parameters was physically studied. It was found that the solutions were general, reliable, realistic and fixable. For the fractional parameter, the velocity and temperature profiles showed a decreasing trend for a constant time. By setting the values of the fractional parameter, excellent agreement between the theoretical and experimental results could be attained.
Highlights
In thermal transport systems, the poor thermophysical properties of various working fluids can be improved by the addition of nanometer-sized particles
The Ag − TiO2 − H2 O hybrid nanofluid was characterized by fractional rheological analysis
To analyze the rheological behavior of the hybrid nanofluid, the fractional model was solved via the Laplace transform technique
Summary
The poor thermophysical properties of various working fluids can be improved by the addition of nanometer-sized particles. They focused on recent advancements in the literature, with a detailed explanation of the thermophysical properties, modeling and simulation of heat transport in the flow of nanofluids They highlighted the main challenges which still exist in this field. The kernel of ABFO is a nonlocal and nonsingular Mittag-Leffler function [31] This new operator satisfies all the properties of a fractional derivate except index law. The electromagnetic force Fem is incorporated into the momentum equation of the natural convection flow of an incompressible Ag − TiO2 − H2 O hybrid nanofluid in the absence of a pressure gradient and a transverse magnetic field is applied, taking the following form [35]. Dynamic viscosity, electrical conductivity, magnetic field, thermal expansion, specific heat, temperature and thermal conductivity, respectively
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