Magneto-nanofluid flow with heat transfer past a stretching surface for the new heat flux model using numerical approach

Abstract

Sheet processing of magnetic nanomaterials is emerging as a new branch of smart materials manufacturing. The efficient production of such materials combines many physical phenomena including magnetohydrodynamics (MHD), nanoscale, thermal and mass diffusion effects. To improve understanding of complex inter-disciplinary transport phenomena in such systems, mathematical models provide a robust approach. Motivated by this, herein we develop a mathematical model for steady, laminar, magnetohydrodynamic, incompressible nanofluid flow, heat and mass transfer from a stretching sheet. A uniform constant strength magnetic field is applied transverse to the plane of the stretching flow. The Buonjiornio nanofluid model is employed to represent thermophoretic and Brownian motion effects. A non-Fourier (Cattaneo-Christov) model is deployed to simulate thermal conduction effects of which the Fourier model is a special case when thermal relaxation effects are neglected. The governing conservation equations are rendered dimensionless with suitable scaling transformations. The emerging nonlinear boundary value problem is solved with a fourth order Runge-Kutta algorithm and also shooting quadrature. Validation is achieved with earlier non-magnetic and forced convection flow studies. The influence of key thermophysical parameters e.g. Hartmann magnetic number, thermal Grashof number, thermal relaxation time parameter, Schmidt number, thermophoresis parameter, Prandtl number and Brownian motion number on velocity, skin friction, temperature, Nusselt number, Sherwood number and nano-particle concentration distributions is investigated. A strong elevation in temperature accompanies an increase in Brownian motion parameter whereas increasing magnetic parameter is found to reduce heat transfer rate at the wall (Nusselt number). Nano-particle volume fraction is observed to be strongly suppressed with greater thermal Grashof number, Schmidt number and thermophoresis parameter whereas it is elevated significantly with greater Brownian motion parameter. Higher temperatures are achieved with greater thermal relaxation time values i.e. the non-Fourier model predicts greater values for temperature than the classical Fourier model.

Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

“…Malik et al [33] analyzed the MHD flow of Casson fluid and also found that the temperature decreased using the Cattaneo Christov heat flux model. Very recently, a similar study conducted for nanofluids [24,34] and diverse non-Newtonian fluid models such as Oldroyd B-fluid [35], Eyring Powell [36,37], Carreau fluid [38], viscoelastic fluid [39,40] and second grade fluid [41,42] resulted in the non-Fourier model leading to the reduction of the temperature distribution. Mahmood et al [43] designed the boundary layer flow of Casson nanofluid using Cattaneo-Christov heat flux model while Jamshed and Aziz [44] utilized the Casson hybrid TiO 2 -CuO/EG nanofluid on the stretched flow problem with entropy generation.…”

“…and eliminating q from Equations (1) and (4) will give a non-Fourier energy equation (see Akbar et al [24], Salahuddin et al [31], Kumar and Varma [34] and Khan et al [41])…”

“…Most of the boundary layer flow and heat transfer problems considered the classical Fourier model which represents the thermal conduction heat transfer. On the other hand, the model is not precise for specific situations in real engineering phenomena since it produces a parabolic energy equation [24]. In 1948, Cattaneo [25] modified the Fourier model known as Maxwell-Cattaneo (MC) law by including a thermal relaxation time term to present the thermal inertia.…”

Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non‐Fourier heat flux model

“…The Cattaneo‐Christov model defines the heat flux, q , according to: …”

“…Ai and Li used a discontinuous Galerkin finite element method to simulate ultra‐short pulsed laser thermal processing of thin films with a non‐Fourier heat conduction model, observing significant boundary thermal wave reflection/interactions. Akbar et al used fourth order Runge‐Kutta shooting quadrature to compute the hydromagnetic flow of nanofluids from a stretching surface with the Cattaneo‐Christov heat flux model noting that heat transfer rates are substantially altered with non‐Fourier thermal relaxation effects. Further studies include Bhatti et al who simulated the multimode non‐Fourier heat transfer in electrically conducting viscoelastic boundary layer flow from an extending sheet noting that increasing thermal relaxation decreases the thermal layer boundary layer thickness.…”