scholarly journals Effects of Mass Suction on MHD Boundary Layer Flow and Heat Transfer over a Porous Shrinking Sheet with Heat Source/Sink

2019 ◽  
Vol 8 (10) ◽  
pp. 263-266 ◽  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Shrinking Sheet ◽  
Dynamic Framework ◽  
Mhd Boundary Layer ◽  
Source Sink

An examination is made to think about the impacts of the mass suction on the steady flow of 2-D magneto-hydrodynamic (MHD) boundary layer flows and heat transfer past on a shrinking sheet with source/sink. In the dynamic framework, an-uniform magnetic field acts perpendicular to the plane of flow. The governing non-dimensional partial differential equations are changed into nonlinear ordinary differential equations (ODE’s) using similarity transformations. The so derived ordinary differential equations are solved numerically by using the MAT LAB solver bvp5c. From the keen examinations it is found that the velocity inside the boundary layer increments with increment of wall mass suction, magnetic field and reportedly the thickness of the momentum layer diminishes. There is a reduction in temperature as increases the Prandtl number. With heat source specifications, Hartmann number, heat sink parameter & the temperature increments are seen. Moreover, for strong heat source heat assimilation at the sheet happens.

scholarly journals Three-dimensional MHD boundary layer flow due to an axisymmetric shrinking sheet with radiation, viscous dissipation and heat source/sink

2016 ◽  
Vol 21 (2) ◽  
pp. 393-406
Author(s):  
M. Madhu ◽  
B. Balaswamy ◽  
N. Kishan
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Heat Source ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Shrinking Sheet ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Source Sink ◽  
Mhd Boundary Layer Flow

AbstractAn analysis is made to study a three dimensional MHD boundary layer flow and heat transfer due to a porous axisymmetric shrinking sheet. The governing partial differential equations of momentum and energy are transformed into self similar non-linear ordinary differential equations by using the suitable similarity transformations. These equations are, then solved by using the variational finite element method. The flow phenomena is characterised by the magnetic parameterM, suction parameterS, porosity parameterKp, heat source/sink parameterQ, Prandtl number Pr, Eckert number Ec and radiation parameterRd. The numerical results of the velocity and temperature profiles are obtained and displayed graphically.

Effects of Non-Uniform Heat Source/Sink and Viscous Dissipation on MHD Boundary Layer Flow of Williamson Nanofluid through Porous Medium

2018 ◽  
Vol 389 ◽  
pp. 110-127 ◽  
Author(s):  
Kharabela Swain ◽  
Sampada Kumar Parida ◽  
G.C. Dash
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Porous Medium ◽  
Heat Source ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Source Sink ◽  
Mhd Boundary Layer Flow

The effects of non-uniform heat source/sink and viscous dissipation on MHD boundary layer flow of Williamson nanofluid through porous medium under convective boundary conditions are studied. Surface transport phenomena such as skin friction, heat flux and mass flux are discussed besides the three boundary layers. The striking results reported as: increase in Williamson parameter exhibiting nanofluidity and external magnetic field lead to thinning of boundary layer, besides usual method of suction and shearing action at the plate, a suggestive way of controlling the boundary layer growth. It is easy to implement to augment the strength of magnetic field by regulating the voltage in the circuit. Also, addition of nano particle to the base fluid serves as an alternative device to control the growth of boundary layer and producing low friction at the wall. The present analysis is an outcome of Runge-Kutta fourth order method with a self corrective procedure i.e. shooting method.

scholarly journals Numerical Solution of MHD Viscoelastic Nanofluid Flow over a Stretching Sheet with Partial Slip and Heat Source/Sink

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Mania Goyal ◽  
Rama Bhargava
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Heat Source ◽  
Uniform Magnetic Field ◽  
Stretching Sheet ◽  
Partial Slip ◽  
Local Similarity ◽  
Source Sink

We analyze the effect of velocity slip boundary condition on the flow and heat transfer of non-Newtonian nanofluid over a stretching sheet with a heat source/sink, under the action of a uniform magnetic field, orientated normally to the plate. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of local similarity transformations. The differential equations are solved by the variational finite element method (FEM). We have examined the effects of different controlling parameters, namely, the Brownian motion parameter, the thermophoresis parameter, uniform magnetic field, viscoelastic parameter, Prandtl number, heat source/sink parameter, Lewis number, and the slip parameter on the flow field and heat transfer characteristics. Graphical display of the numerical examination is performed to illustrate the influence of various flow parameters on the velocity, temperature, concentration, and Nusselt and Sherwood numbers distributions. The present study has many applications in coating and suspensions, cooling of metallic plate, paper production, heat exchangers technology, and materials processing exploiting.

scholarly journals Unsteady viscous MHD flow over a permeable curved stretching/shrinking sheet

2016 ◽  
Vol 26 (8) ◽  
pp. 2370-2392 ◽  
Author(s):  
Ioan Pop ◽  
Siti Suzilliana Putri Mohamed Isa ◽  
Norihan M. Arifin ◽  
Roslinda Nazar ◽  
Norfifah Bachok ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Flow Characteristics ◽  
Mhd Flow ◽  
Integration Scheme ◽  
Shrinking Sheet ◽  
Content Type

Purpose The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically. Design/methodology/approach The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined. Findings Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter. Originality/value The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible.

Unsteady heat and mass transfer magnetohydrodynamic (MHD) nanofluid flow over a stretching sheet with heat source–sink using quasi-linearization technique

2015 ◽  
Vol 93 (12) ◽  
pp. 1477-1485 ◽  
Author(s):  
R. Ahmad ◽  
Waqar A. Khan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Heat Source ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Numerical Technique ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Source Sink

The current study deals with two-dimensional unsteady incompressible MHD water-based nanofluid flow over a convectively heated stretching sheet by considering Buongiorno’s model. A uniform magnetic field is applied in the direction normal to the stretching sheet. It is assumed that the lower surface of the sheet is heated by convection by a nanofluid at temperature Tf, which generates the heat transfer coefficient, hf. Uniform temperature and nanofluid volume fraction are assumed at the sheet’s surface and the flux of the nanoparticle is taken to be zero. The assumption of zero nanoparticle flux at the sheet’s surface makes the model physically more realistic. The effects of the uniform heat source–sink are included in the energy equation. With the help of similarity transformations, the partial differential equations of momentum, energy, and nanoparticle concentration are reduced to a system of nonlinear ordinary differential equations along with the transformed boundary conditions. The derived equations are solved with the help of the quasi-qinearization technique. The model is solved by considering the realistic values for the Lewis number, thermophoresis, and Brownian motion parameters. The objective of the current study is (i) to provide an efficient numerical technique for solving the boundary layer flow model and (ii) introduction of zero nanoparticle flux on the convectively heated stretching surface. The current study also focuses on the physical relevance and accurate trends of the boundary layer profiles, which are adequate in the laminar boundary layer theory. The dependence of the nanoparticle volume fraction and other pertinent parameters on the dimensionless velocity, temperature, shear stress, and heat transfer rates over the stretching surface are presented in the form of profiles.

scholarly journals Parametric analysis of the heat transfer behavior of the nano-particle ionic-liquid flow between concentric cylinders

2021 ◽  
Vol 13 (6) ◽  
pp. 168781402110240
Author(s):  
Rehan Ali Shah ◽  
Hidayat Ullah ◽  
Muhammad Sohail Khan ◽  
Aamir Khan
Keyword(s):  
Heat Transfer ◽  
Ionic Liquid ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Concentric Cylinders

This paper investigates the enhanced viscous behavior and heat transfer phenomenon of an unsteady two di-mensional, incompressible ionic-nano-liquid squeezing flow between two infinite parallel concentric cylinders. To analyze heat transfer ability, three different type nanoparticles such as Copper, Aluminum [Formula: see text], and Titanium oxide [Formula: see text] of volume fraction ranging from 0.1 to 0.7 nm, are added to the ionic liquid in turns. The Brinkman model of viscosity and Maxwell-Garnets model of thermal conductivity for nano particles are adopted. Further, Heat source [Formula: see text], is applied between the concentric cylinders. The physical phenomenon is transformed into a system of partial differential equations by modified Navier-Stokes equation, Poisson equation, Nernst-Plank equation, and energy equation. The system of nonlinear partial differential equations, is converted to a system of coupled ordinary differential equations by opting suitable transformations. Solution of the system of coupled ordinary differential equations is carried out by parametric continuation (PC) and BVP4c matlab based numerical methods. Effects of squeeze number ( S), volume fraction [Formula: see text], Prandtle number (Pr), Schmidt number [Formula: see text], and heat source [Formula: see text] on nano-ionicliquid flow, ions concentration distribution, heat transfer rate and other physical quantities of interest are tabulated, graphed, and discussed. It is found that [Formula: see text] and Cu as nanosolid, show almost the same enhancement in heat transfer rate for Pr = 0.2, 0.4, 0.6.

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