scholarly journals NUMERICAL SOLUTION OF TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY ON MHD FREE CONVECTION FLOW WITH JOULE HEATING ALONG A VERTICAL WAVY SURFACE

2014 ◽  
Vol 44 (1) ◽  
pp. 43-50 ◽  
Author(s):  
N. Parveen ◽  
M. A. Alim
Keyword(s):  
Thermal Conductivity ◽  
Joule Heating ◽  
Skin Friction Coefficient ◽  
Wavy Surface ◽  
Convection Flow ◽  
Temperature Dependent ◽  
Boundary Layer Equations ◽  
Box Scheme ◽  
Stream Lines ◽  
Temperature Dependent Thermal Conductivity

Temperature dependent thermal conductivity on magnetohydrodynamic (MHD) free convective flow of viscous incompressible fluid with Joule heating along a uniformly heated vertical wavy surface has been investigated numerically. The governing nonlinear boundary layer equations are mapped into a domain of a vertical flat plate and solved by an implicit finite difference method known as Keller-box scheme. The skin friction coefficient, the rate of heat transfer in terms of local Nusselt number, the stream lines and the isotherms are reported for different parameter combinations. DOI: http://dx.doi.org/10.3329/jme.v44i1.19497

scholarly journals Joule heating effect on magnetohydrodynamic natural convection flow along a vertical wavy surface

2012 ◽  
Vol 9 (1) ◽  
pp. 11-24 ◽  
Author(s):  
Nazma Parveen ◽  
M A Alim
Keyword(s):  
Natural Convection ◽  
Joule Heating ◽  
Skin Friction Coefficient ◽  
Wavy Surface ◽  
Convection Flow ◽  
Surface Shear Stress ◽  
Natural Convection Flow ◽  
Surface Shear ◽  
Boundary Layer Equations ◽  
Marine Engineering

In this paper, the effect of Joule heating on magnetohydrodynamic natural convection flow of viscous incompressible fluid along a uniformly heated vertical wavy surface has been investigated. The governing boundary layer equations with associated boundary conditions for this phenomenon are converted to nondimensional form using a suitable transformation. The equations are mapped into the domain of a vertical flat plate and then solved numerically employing the implicit finite difference method, known as the Keller-box scheme. Effects of pertinent parameters, such as the Joule heating parameter (J), Prandtl number (Pr), magnetic parameter (M) and the amplitude of the wavy surface ? on the surface shear stress in terms of the skin friction coefficient (Cfx), the rate of heat transfer in terms of local Nusselt number (Nux), the streamlines and the isotherms are discussed. A comparison with previously published work is performed and the results show excellent agreement. DOI: http://dx.doi.org/10.3329/jname.v9i1.5954 Journal of Naval Architecture and Marine Engineering 9(2012) 11-24

scholarly journals Natural Convection Flow from an Isothermal Sphere with Temperature Dependent Thermal Conductivity

1970 ◽  
Vol 2 (2) ◽  
pp. 53-64 ◽  
Author(s):  
Md Mamun Molla ◽  
Azad Rahman ◽  
Lineeya Tanzin Rahman
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Natural Convection ◽  
Convection Flow ◽  
Temperature Dependent ◽  
Boundary Layer Equations ◽  
Wide Range ◽  
Conductivity Parameter ◽  
Marine Engineering ◽  
Temperature Dependent Thermal Conductivity

Laminar free convection flow from an isothermal sphere immersed in a fluid with thermal conductivity proportional to linear function of temperature has been studied. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations is reduced to local non-similarity equations, which are solved numerically by very efficient implicit finite difference method together with Keller box scheme. Numerical results are presented by velocity and temperature distribution of the fluid as well as heat transfer characteristics, namely the heat transfer rate and the skin-friction coefficients for a wide range of thermal conductivity parameter γ (= 0.0, 0.5, 1.0, 2.0, 3.0, 5.0) and the Prandtl number Pr (= 0.7, 1.0, 3.0, 5.0, 7.0).   Keywords: Natural convection, temperature dependent thermal conductivity, isothermal sphere.    doi:10.3329/jname.v2i2.1872  Journal of Naval Architecture and Marine Engineering 2(2005) 53-64

scholarly journals Combined effects of viscous dissipation and temperature dependent thermal conductivity on MHD free convection flow with conduction and joule heating along a vertical flat plate

2010 ◽  
Vol 6 (1) ◽  
pp. 30-40 ◽  
Author(s):  
R. Nasrin ◽  
M. A. Alim
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Convection Flow ◽  
Combined Effects ◽  
Temperature Dependent ◽  
Free Convection Flow ◽  
Temperature Dependent Thermal Conductivity ◽  
Vertical Flat Plate

Combined effects of viscous dissipation and temperature dependent thermal conductivity on MHD free convection flow with heat conduction and Joule heating along a vertical flat plate have been described in the present work. The governing boundary layer equations with associated boundary conditions for this phenomenon are converted to non-dimensional form using a suitable transformation. The resulting non-linear partial differential equations are then solved using the implicit finite difference method with Keller-box scheme. The numerical results in terms of the skin friction coefficient, the surface temperature, the velocity and the temperature profiles over the whole boundary layer are shown graphically for different values of the Prandtl number Pr, the magnetic parameter M, the thermal conductivity variation parameter γ, viscous dissipation parameter N and the Joule heating parameter J. Numerical results of the local skin friction co-efficient and the surface temperature profile for different values of N are presented in tabular form.Keywords: Joule heating; MHD; conduction; temperature dependent thermal conductivity; viscous dissipation;natural convection.DOI: 10.3329/jname.v5i2.2648Journal of Naval Architecture and Marine Engineering 6(1)(2009) 30-40 

scholarly journals Joule heating and MHD free convection flow along a vertical wavy surface with viscosity and thermal conductivity dependent on temperature

2013 ◽  
Vol 10 (2) ◽  
pp. 81-98 ◽  
Author(s):  
Nazma Parveen ◽  
Md. Abdul Alim
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Friction Coefficient ◽  
Free Convection ◽  
Skin Friction ◽  
Joule Heating ◽  
Skin Friction Coefficient ◽  
Wavy Surface ◽  
Convection Flow ◽  
Free Convection Flow

A numerical study is conducted to analyze the effect of Joule heating and MHD (magnetohydrodynamic) free convection flow and heat transfer along a uniformly heated vertical wavy surface with temperature dependent variable viscosity and thermal conductivity. The governing boundary layer equations with associated boundary conditions for phenomenon are converted to non-dimensional form using the appropriate transformations. The resulting nonlinear system of partial differential equations are mapped into the domain of a vertical flat plate and solved numerically by employing implicit finite difference method, known as the Keller-box scheme. The behavior of the fluid in the ranges of Joule heating parameter (0.0–2.0), viscosity parameter (0.0–20.0) and thermal conductivity parameter (0.0 –10.0) are explained in details. It is found that the flow and temperature fields are strongly dependent on the above stated parameters for the ranges considered. The skin friction coefficient and the rate of heat transfer are also presented. The skin friction coefficient and the heat transfer for different values of Prandtl number Pr are compared with previously published work and are found to be in excellent agreement.DOI: http://dx.doi.org/10.3329/jname.v10i2.11707

scholarly journals Effects of Temperature Dependent Thermal Conductivity on Magnetohydrodynamic (MHD) Free Convection Flow along a Vertical Flat Plate with Heat Conduction

2008 ◽  
Vol 13 (4) ◽  
pp. 513-524 ◽  
Author(s):  
M. M. Rahman ◽  
A. A. Mamun ◽  
M. A. Azim ◽  
M. A. Alim
Keyword(s):  
Thermal Conductivity ◽  
Flat Plate ◽  
Linear Equations ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Temperature Dependent ◽  
Electrically Conducting ◽  
Conjugate Conduction ◽  
Temperature Dependent Thermal Conductivity ◽  
Vertical Flat Plate

MHD natural convection flow of an electrically conducting fluid along a vertical flat plate with temperature dependent thermal conductivity and conduction effects is analyzed. The governing equations with associated boundary conditions for this phenomenon are converted to dimensionless forms using a suitable transformation. The transformed non-linear equations are then solved using the implicit finite difference method with Keller-box scheme. Numerical results of the velocity, temperature, skin friction coefficient and surface temperature for different values of the magnetic parameter, thermal conductivity variation parameter, Prandtl number and conjugate conduction parameter are presented graphically. Detailed discussion is given for the effects of the aforementioned parameters.

scholarly journals Viscous Dissipation Effects on MHD Natural Convection Flow Over a Sphere in the Presence of Heat Generation

2007 ◽  
Vol 12 (4) ◽  
pp. 447-459 ◽  
Author(s):  
Md. M. Alam ◽  
M. A. Alim ◽  
Md. M. K. Chowdhury
Keyword(s):  
Natural Convection ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Surface Shear Stress ◽  
Natural Convection Flow ◽  
Surface Shear ◽  
Boundary Layer Equations ◽  
Box Scheme

In this paper, the viscous dissipation effects on magnetohydrodynamic natural convection flow over a sphere in the presence of heat generation have been described. The governing boundary layer equations are first transformed into a nondimensional form and the resulting nonlinear system of partial differential equations are then solved numerically using finite-difference method together with Keller-box scheme. The numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, velocity as well as temperature profiles are shown graphically and tabular form for a selection of parameters set consisting of heat generation parameter Q, magnetic parameter M, viscous dissipation parameter N and the Prandlt number Pr.

Computational exploration for radiative flow of Sutterby nanofluid with variable temperature-dependent thermal conductivity and diffusion coefficient

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1073-1083
Author(s):  
Muhammad Sohail ◽  
Umar Nazir ◽  
Yu-Ming Chu ◽  
Hussam Alrabaiah ◽  
Wael Al-Kouz ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Differential Equations ◽  
Variable Temperature ◽  
Variable Thermal Conductivity ◽  
Skin Friction Coefficient ◽  
Temperature Dependent ◽  
Similarity Transformations ◽  
Rate Dependent ◽  
And Diffusion ◽  
Temperature Dependent Thermal Conductivity

Abstract This article addresses the effects of thermal radiation, stratification, and Joule heating for the flow of magnetohydrodynamics Sutterby nanofluid past over a stretching cylinder. The transport phenomenon of heat and mass are modeled under temperature-dependent thermal conductivity and diffusion coefficients, respectively. Moreover, traditional Fourier and Fick’s laws have been implemented in thermal and mass transport expressions. The governing model that consists of a set of coupled partial differential equations is converted into system of nonlinear coupled ordinary differential equations via suitable similarity transformations. The resulting set of expressions is analytically treated through an optimal homotopy scheme. The effects of different dimensionless flow parameters on the velocity, temperature, and concentration fields are illustrated through graphs. The patterns of skin friction coefficient, local Nusselt, and Sherwood numbers are examined via bar charts. The major outcome of the proposed study is that variable thermal conductivity decays the temperature and radiation raises the temperature of the system. Stratification parameters show the reverse behavior for temperature and concentration boundary layers. Shear rate-dependent rheology in view of Sutterby liquid has the ability to reduce the flow of fluid. Therefore, the ability of flow in rheology of Sutterby liquid becomes reduced. Consequently, layer of momentum boundary has increased with respect to parameter of Sutterby liquid.

scholarly journals Conjugate effects of temperature sensitive viscosity and thermal conductivity on free convection flow along a wavy surface with heat generation

2013 ◽  
Vol 10 (2) ◽  
pp. 139-148 ◽  
Author(s):  
Md. Abdul Alim ◽  
M. Miraj Akand ◽  
M. Rezaul Karim
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Heat Generation ◽  
Skin Friction Coefficient ◽  
Numerical Results ◽  
Wavy Surface ◽  
Convection Flow ◽  
Surface Shear Stress

The effects of internal heat generation on natural convection flow with temperature dependent variable viscosity along a uniformly heated vertical wavy surface have been investigated. The governing boundary layer equations are first transformed into a non-dimensional form using suitable set of dimensionless variables. The resulting nonlinear system of partial differential equations are mapped into the domain of a vertical flat plate and then solved numerically employing the implicit finite difference method, known as Keller-box scheme. Numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, the stream lines as well as the isotherms are shown graphically for a selection of parameters set consisting of viscosity variation parameter e, thermal conductivity parameter g, heat generation parameter Q and Prandtl number Pr. Numerical results of the local skin friction coefficient and the rate of heat transfer for different values are presented in tabular form and graphically.DOI: http://dx.doi.org/10.3329/jname.v10i2.9450

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