An MHD couple stress fluid due to a perforated sheet undergoing linear stretching with heat transfer

We investigate an MHD couple stress liquid due to a perforated sheet undergoing linear stretching withradiation. The liquid is initially at rest with its activity is restricted by pulling the two sheet ends withparallel and identical forces. The consequential movement of the or else quiescent fluid is consequently generated exclusively by the stirring plate that develops a linearly varied speed with the distance from the slit. In addition to fluid flow, heat transfer with two cases of different boundary conditions from the sheet is considered, the first with prescribed surface temperature and, the second with prescribed heat flux. The arising set of non-linear coupled nonlinear partial differential equations is rehabilitated into non-linear ordinary differential equations and then exact expressions are derived for velocity and by means of a power series method with Kummer’s confluent hypergeometric functions for temperature

Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet

This paper numerically investigates radiative magnetohydrodynamic mixed convection boundary layer flow of nanofluids over a nonlinear inclined stretching/shrinking sheet in the presence of heat source/sink and viscous dissipation. The Rosseland approximation is adopted for thermal radiation effects and the Maxwell-Garnetts and Brinkman models are used for the effective thermal conductivity and dynamic viscosity of the nanofluids respectively. The governing coupled nonlinear momentum and thermal boundary layer equations are rendered into a system of ordinary differential equations via local similarity transformations with appropriate boundary conditions. The non-dimensional, nonlinear, well-posed boundary value problem is then solved with the Keller box implicit finite difference scheme. The emerging thermo-physical dimensionless parameters governing the flow are the magnetic field parameter, volume fraction parameter, power-law stretching parameter, Richardson number, suction/injection parameter, Eckert number and heat source/sink parameter. A detailed study of the influence of these parameters on velocity and temperature distributions is conducted. Additionally the evolution of skin friction coefficient and Nusselt number values with selected parameters is presented. Verification of numerical solutions is achieved via benchmarking with some limiting cases documented in previously reported results, and generally very good correlation is demonstrated. This investigation is relevant to fabrication of magnetic nanomaterials and high temperature treatment of magnetic nano-polymers

Application of differential transform method to unsteady free convective heat transfer of a couple stress fluid over a stretching sheet

In the present article, the transient rheological boundary layer flow over a stretching sheet with heat transfer is investigated, a topic of relevance to non-Newtonian thermal materials processing. Stokes couple stress model is deployed to simulate non-Newtonian characteristics. Similarity transformations are utilized to convert the governing partial differential equations into nonlinear ordinary differential equations with appropriate wall and free stream boundary conditions. The non-dimensional boundary value problem emerging is shown to be controlled by a number of key thermophysical and rheological parameters, namely the rheological couple stress parameter, unsteadiness parameter, Prandtl number (Pr), buoyancy parameter. The semi-analytical Differential Transform Method (DTM) is used to solve the reduced nonlinear coupled ordinary differential boundary value problem. A numerical solution is also obtained via the MATLAB built in solver ‘bvp4c’ to validate the results. Further validation with published results from the literature is included. Fluid velocity is enhanced with increasing couple stress parameter whereas it is decreased with unsteadiness parameter. Temperature is elevated with couple stress parameter whereas it is initially reduced with unsteadiness parameter. The flow is accelerated with increasing positive buoyancy parameter (for heating of the fluid) whereas it is decelerated with increasing negative buoyancy parameter (cooling of the fluid). Temperature and thermal boundary layer thickness are boosted with increasing positive values of buoyancy parameter. Increasing Prandtl number decelerates the flow, reduces temperatures, increases momentum boundary layer thickness and decreases thermal boundary layer thickness. Excellent accuracy is achieved with the DTM approach

Energy conversion under conjugate conduction, magneto-convection, diffusion and nonlinear radiation over a non-linearly stretching sheet with slip and multiple convective boundary conditions

Energy conversion under conduction, convection, diffusion and radiation has been studied for MHD free convection heat transfer of a steady laminar boundary-layer flow past a moving permeable non-linearly extrusion stretching sheet. The nonlinear Rosseland thermal radiation flux model, velocity slip, thermal and mass convective boundary conditions are considered to obtain a model with fundamental applications to real world energy systems. The Navier slip, thermal and mass convective boundary conditions are taken into account. Similarity differential equations with corresponding boundary conditions for the flow problem, are derived, using a scaling group of transformation. The transformed model is shown to be controlled by magnetic field, conduction-convection, convection-diffusion, suction/injection, radiation-conduction, temperature ratio, Prandtl number, Lewis number, buoyancy ratio and velocity slip parameters. The transformed non-dimensional boundary value problem comprises a system of nonlinear ordinary differential equations and physically realistic boundary conditions, and is solved numerically using the efficient Runge-Kutta-Fehlberg fourth fifth order numerical method, available in Maple17 symbolic software. Validation of results is achieved with previous simulations available in the published literature. The obtained results are displayed both in graphical and tabular form to exhibit the effect of the controlling parameters on the dimensionless velocity, temperature and concentration distributions. The current study has applications in high temperature materials processing utilizing magnetohydrodynamics, improved performance of MHD energy generator wall flows and also magnetic-microscale fluid devices

Flow of a viscoelastic fluid over a stretching sheet

This paper presents a study of the flow of an incompressible second-order fluid past a stretching sheet. The problem has a bearing on some polymer processing application such as the continuous extrusion of a polymer sheet from a die.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47204/1/397_2005_Article_BF01332078.pd

A numerical study of magnetohydrodynamic transport of nanofluids from a vertical stretching sheet with exponential temperature-dependent viscosity and buoyancy effects

In this paper, a mathematical study is conducted of steady incompressible flow of a temperature-dependent viscous nanofluid from a vertical stretching sheet under applied external magnetic field and gravitational body force effects. The Reynolds exponential viscosity model is deployed. Electrically-conducting nanofluids are considered which comprise a suspension of uniform dimension nanoparticles suspended in viscous base fluid. The nanofluid sheet is extended with a linear velocity in the axial direction. The Buonjiornio model is utilized which features Brownian motion and thermophoresis effects. The partial differential equations for mass, momentum, energy and species (nano-particle concentration) are formulated with magnetic body force term. Viscous and Joule dissipation effects are neglected. The emerging nonlinear, coupled, boundary value problem is solved numerically using the Runge–Kutta fourth order method along with a shooting technique. Graphical solutions for velocity, temperature, concentration field, skin friction and Nusselt number are presented. Furthermore stream function plots are also included. Validation with Nakamura’s finite difference algorithm is included. Increasing nanofluid viscosity is observed to enhance temperatures and concentrations but to reduce velocity magnitudes. Nusselt number is enhanced with both thermal and species Grashof numbers whereas it is reduced with increasing thermophoresis parameter and Schmidt number. The model is applicable in nano-material manufacturing processes involving extruding sheets