Convective Heat Transfer and MHD Viscoelastic Nanofluid Flow Induced by a Stretching Sheet (original) (raw)
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Journal of Magnetism and Magnetic Materials, 2015
The MHD laminar boundary layer flow with heat and mass transfer of an electrically conducting waterbased nanofluid over a nonlinear stretching sheet with viscous dissipation effect is investigated numerically. This is the extension of the previous study on flow and heat transfer of a nanofluid over nonlinear stretching sheet (Rana and Bhargava, Commun. Nonlinear Sci. Numer. Simul. 17 (2012) 212-226). The governing equations are reduced to nonlinear ordinary differential equations using suitable similarity transformation. The effects of the governing parameters on dimensionless quantities like velocity, temperature, nanoparticle concentration, friction factor, local Nusselt, and Sherwood numbers are explored. It is found that the dimensionless velocity decreases and temperature increases with magnetic parameter, and the thermal boundary layer thickness increases with Brownian motion and thermophoresis parameters.
Challenges in Nano and Micro Scale Science and Technology, 2016
Laminar boundary layer flow and heat transfer of Newtonian nanofluid over a stretching sheet with the sheet velocity distribution of the form (UW=cXβ) and the wall temperature distribution of the form (TW=T∞+aXr ) for the steady magnetohydrodynamic (MHD) is studied numerically. The governing momentum and energy equations are transformed to the local non-similarity equations using the appropriate transformations. The set of ODEs are solved using Keller–Box implicit finite-difference method. The effects of several parameters, such as magnetic parameter, volume fraction of different nanoparticles (Ag, Cu, CuO, Al2O3 and TiO2), velocity parameter, Prandtl number and temperature parameter on the velocity and temperature distributions, local Nusselt number and skin friction coefficient are examined. The analysis reveals that the temperature profile increases with increasing magnetic parameter and volume fraction of nanofluid. Furthermore, it is found that the thermal boundary layer increases and momentum boundary layer decreases with the use of water based nanofluids as compared to pure water. At constant volume fraction of nanoparticles, it is also illustrated that the role of magnetic parameter on dimensionless temperature becomes more effective in lower value.
The boundary-layer flow and heat transfer over a non-isothermal stretching sheet in a nanofluid with the effect of magnetic field and thermal radiation have been investigated. The transport equations used for the analysis include the effect of Brownian motion and thermophoresis. The solution for the temperature and nanoparticle concentration depends on six parameters, viz., thermal radiation parameter R, Prandtl number Pr, Lewis number Le, Brownian motion Nb, and the thermophoresis parameter Nt. Similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher order nonlinear ordinary differential equations. These equations were numerically solved using a fourth-order Runge-Kutta method with shooting technique. The analysis has been carried out for two different cases, namely prescribed surface temperature (PST) and prescribed heat flux (PHF) to see the effects of governing parameters for various physical conditions. Numerical results are obtained for distribution of velocity, temperature and concentration, for both cases i.e., prescribed surface temperature and prescribed heat flux, as well as local Nusselt number and Sherwood number. The results indicate that the local Nusselt number decreases with an increase in both Brownian motion parameter Nb and thermophoresis parameter Nt. However, the local Sherwood number increases with an increase in both thermophoresis parameter Nt and Lewis number Le. Besides, it is found that the surface temperature increases with an increase in the Lewis number Le for prescribed heat flux case. A comparison with the previous studies available in the literature has been done and we found an excellent agreement with it.
Canadian Journal of Physics, 2015
The current study deals with the two dimensional unsteady incompressible MHD water-based nanofluid flow over a convectively heated stretching sheet by considering the 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 T f which generates the heat transfer coefficient h f. 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 non-linear ordinary differential equations along with the transformed boundary conditions. The derived equations are solved with the help of the Quasi-Linearization 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 (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.
Symmetry
In this study, the heat and mass transfer characteristics of nanofluid flow over a nonlinearly stretching sheet are investigated. The important effects of axisymmetric of thermal conductivity and viscous dissipation have been included in the model of nanofluids. The Buongiorno model is considered to solve the nanofluid boundary layer problem. The governing nonlinear partial differential equations have been transformed into a system of ordinary differential equations and are solved numerically via the shooting technique. The validity of this method was verified by comparison with previous work performed for nanofluids without the effects of the magnetic field and viscous dissipation. The analytical investigation is carried out for different governing parameters, namely, the Brownian motion parameter, thermophoresis parameter, magnetic parameter, Biot number, and Eckert number. The results indicate that the skin friction coefficient has a direct relationship with the Brownian motion n...
Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: A numerical study
Communications in Nonlinear Science and Numerical Simulation, 2012
Steady, laminar boundary fluid flow which results from the non-linear stretching of a flat surface in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The resulting non-linear governing equations with associated boundary conditions are solved using variational finite element method (FEM) with a local non-similar transformation. The influence of Brownian motion number (Nb), thermophoresis number (Nt), stretching parameter (n) and Lewis ...
The boundary layer flow created due to a linearly stretching sheet in a nanofluid is studied numerically. The boundary value problem consisting of nonlinear partial differential equations are converted into nonlinear ordinary differential equations, using similarity transformation and are solved numerically using Runge-Kutta Fourth order method, with shooting technique. The transport equations include the effects of Brownian motion and thermophoresis. Unlike the commonly employed thermal conditions of constant temperature or constant heat flux, the present study uses a convective heating boundary conditions. The solutions for the temperature and nanoparticle concentration distribution depend on six parameters, Prandtl number, Lewis number, Brownian motion parameter, thermophoresis parameter, convective Biot number and magnetic field parameter. Numerical results are presented both in tabular and graphical forms illustrating the effects of these parameters on thermal and concentration boundary layers. The thermal boundary layer thickness increases, with a rise in the local temperature as the Brownian motion, thermophoresis and convective heating, each intensify. The effect of Lewis number on the temperature distribution is insignificant. With the other parameters unchanging, the local concentration of nanoparticle increases as the convective Biot number increases but decreases as the Lewis number increases. As both reduced Nusselt number, and the reduced Sherwood number increases, when, Brownian motion and thermophoresis effects become stronger.
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.
The aim of the paper is to analyze the effect of velocity slip boundary condition on the flow and heat transfer of non-Newtonian nanofluid over a stretching sheet. 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 group theory transformations. The obtained ordinary differential equations are solved by variational finite element method (FEM). The effects of different controlling parameters, namely, the Brownian motion parameter, the thermophoresis parameter, viscoelastic parameter, Prandtl number, Lewis number and the slip parameter on the flow field and heat transfer characteristics are examined. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically. The present study is of great interest in the fields of coatings and suspensions, cooling of metallic plates, oils and grease, paper production, coal water or coal-oil slurries, heat exchangers' technology, and materials' processing and exploiting.
Frontiers in Heat and Mass Transfer
In this work, the steady natural convective boundary layer flow of nanofluid and heat transfer over a stretching sheet in the presence of a uniform transverse magnetic field is investigated. We consider two different base fluids and three different nanoparticles were examined as nanofluid. A new model was used in the simulation of nanofluid. Similarity transformations are used to obtain a system of nonlinear ordinary differential equations. The resulting equations are solved numerically by shooting method with Runge-Kutta fourth order scheme (MATLAB package). The effects of various parameters describing the transport in the presence of thermal radiation, buoyancy parameter, magnetic parameter and heat source/sink and nanoparticle volume concentration on the nanofluid velocity, temperature, the heat transfer coefficient and skin-friction coefficient are studied through graphs and table. Furthermore, comparisons with published results are in very good agreement.