A generalized perspective of Fourier and Fick’s laws: Magnetized effects of Cattaneo-Christov models on transient nanofluid flow between two parallel plates with Brownian motion and thermophoresis

Abstract

<jats:title>Abstract</jats:title><jats:p>Present research article reports the magnetized impacts of Cattaneo-Christov double diffusion models on heat and mass transfer behaviour of viscous incompressible, time-dependent, two-dimensional Casson nanofluid flow through the channel with Joule heating and viscous dissipation effects numerically. The classical transport models such as Fourier and Fick’s laws of heat and mass diffusions are generalized in terms of Cattaneo-Christov double diffusion models by accounting the thermal and concentration relaxation times. The present physical problem is examined in the presence of Lorentz forces to investigate the effects of magnetic field on double diffusion process along with Joule heating. The non-Newtonian Casson nanofluid flow between two parallel plates gives the system of time-dependent, highly nonlinear, coupled partial differential equations and is solved by utilizing RK-SM and bvp4c schemes. Present results show that, the temperature and concentration distributions are fewer in case of Cattaneo-Christov heat and mass flux models when compared to the Fourier’s and Fick’s laws of heat and mass diffusions. The concentration field is a diminishing function of thermophoresis parameter and it is an increasing function of Brownian motion parameter. Finally, an excellent comparison between the present solutions and previously published results show the accuracy of the results and methods used to achieve the objective of the present work.</jats:p>

Thermally fully developed CNTs suspended nano fluid flow through annular sector duct

“…Viscous dissipation, free convection and axial heat conduction are ignored. Classical Fourier’s law of conduction will become accordingly 26 in the absence of Cattaneo-Christov modelswhere q is the heat flux and κ nf the effective thermal conductivity of nano fluid. Since we have carried out the fully developed fluid flow, 24 so, we have…”

“…Viscous dissipation, free convection and axial heat conduction are ignored. Classical Fourier's law of conduction will become accordingly 26 in the absence of Cattaneo-Christov models…”

A Non-Fourier’s and Non-Fick’s Approach to Study MHD Mixed Convective Copper Water Nanofluid Flow over Flat Plate Subjected to Convective Heating and Zero Wall Mass Flux Condition

“…The relations for heat flux q and mass flux j with their respective relaxation factor according to Cattaneo-Christov theory are given as (see Refs. [28,[30][31][32]):…”

“…They announced that thermal boundary layer thickness of Carreau liquid with C-C double diffusion is smaller in contrast to Carreau liquid implementing the Fourier's law. Literature search revealed that recently many other researchers [28][29][30][31][32] have also used Cattaneo-Christov model to inspect heat and mass movement.…”

Effect of magnetized variable thermal conductivity on flow and heat transfer characteristics of unsteady Williamson fluid

“…It is noticed from their analysis that, the Blasius ow gives the thicker temperature boundary layer when compared to the Sakiadis ow. Usha et al [45] numerically analyzed the impacts of Cattaneo-Christov double di usion heat and mass ux models on the transient nano uid ow between two parallel plates with Joule heating and chemical reaction. It is remarked from their study that, the concentration pro le is a decaying function of thermophoresis parameter and increasing function of Brownian motion parameter.…”