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

Abstract

A two-dimensional mathematical model of magnetized unsteady incompressible Williamson fluid flow over a sensor surface with variable thermal conductivity and exterior squeezing with viscous dissipation effect is investigated, numerically. Present flow model is developed based on the considered flow geometry. Effect of Lorentz forces on flow behaviour is described in terms of magnetic field and which is accounted in momentum equation. Influence of variable thermal conductivity on heat transfer is considered in the energy equation. Present investigated problem gives the highly complicated nonlinear, unsteady governing flow equations and which are coupled in nature. Owing to the failure of analytical/direct techniques, the considered physical problem is solved by using Runge-Kutta scheme (RK-4) via similarity transformations approach. Graphs and tables are presented to describe the physical behaviour of various control parameters on flow phenomenon. Temperature boundary layer thickens for the amplifying value of Weissenberg parameter and permeable velocity parameter. Velocity profile decreased for the increasing squeezed flow index and permeable velocity parameter. Increasing magnetic number increases the velocity profile. Magnifying squeezed flow index magnifies the magnitude of Nusselt number. Also, RK-4 efficiently solves the highly complicated nonlinear complex equations that are arising in the fluid flow problems. The present results in this article are significantly matching with the published results in the literature.

Dissipative Lorentz force influence on mass flow over a micro‐cantilever sensor sheet under magnetic Ohmic heating

“…The guarantee of the implemented BVP4C Matlab numerical code is validated by comparing produced similar results with former solutions stated by Khaled and Vafai [28] and Usha et al [42] under squeezing regime for different parameters namely squeezed flow index and Prandtl number for temperature field with absence of magnetic force field. However, Table 1 clearly explores this comparison and this documentation furnishes the higher order confidence in the produced similar results in this investigation.…”

“…Additionally, the 𝑥 − 𝑦 coordinate system is deployed and in which 𝑥-axis is taken along the axial flow direction. Consequently, under the aforementioned closed channel and boundary layer flow predictions and by deploying the suitable equations from the non-Newtonian second-grade fluid model as depicted in Section 2, the governing flow, thermal and mass distributive Navier-Stokes conservative expressions for the flow of magnetic second-grade fluid under suspended channel regime are shown by generalizing the existing studies [28,29,36,[38][39][40]42].…”

“…Validation of current solutions with Khaled and Vafai [28] and Usha et al [42] for 𝜃(0) with 𝑀 = 𝛼 = 𝑆 = 𝐸𝑐 = 0 for Newtonian fluid case.…”

“…Naduvinamani and Usha [41] illustrated the action of Soret and Dufour effects on the viscous Casson liquid motion between parallel sheets. Recently, Usha et al [42] further enhanced the documented work of Khaled and Vafai [28] by including the mutable thermal diffusion and viscous dissipation parameters in the laminar magnetic Williamson liquid motion of about a sensing surface by deploying RK scheme. Their discussion documented that, the thermal distribution significantly decreased with increasing thermal diffusion number and heat transmission enhanced with response to magnetic number.…”

Casson Fluid Flow Due to Stretching Sheet With Magnetic Effect and Variable Thermal Conductivity

“…Reddy et al (2020) reported the effect of heat absorption/ generation on MHD Cu-water nanofluid stream above a non-linear shrinking/ stretching sheet. The influence of magnetized variable thermal conductivity on the flow and heat transfer characteristics of an unstable Williamson fluid was studied by Shankar et al (2020). Shateyi and Muzara (2020) studied the unsteady MHD Blasius and Sakiadis flows with variable thermal conductivity in the presence of thermal radiation and viscous dissipation.…”