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

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 Slip and Heat Generation/Absorption on MHD Mixed Convection Flow of a Micropolar Fluid over a Heated Stretching Surface

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Mostafa Mahmoud ◽  
Shimaa Waheed
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Mixed Convection ◽  
Skin Friction ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Local Skin ◽  
Local Skin Friction

A theoretical analysis is performed to study the flow and heat transfer characteristics of magnetohydrodynamic mixed convection flow of a micropolar fluid past a stretching surface with slip velocity at the surface and heat generation (absorption). The transformed equations solved numerically using the Chebyshev spectral method. Numerical results for the velocity, the angular velocity, and the temperature for various values of different parameters are illustrated graphically. Also, the effects of various parameters on the local skin-friction coefficient and the local Nusselt number are given in tabular form and discussed. The results show that the mixed convection parameter has the effect of enhancing both the velocity and the local Nusselt number and suppressing both the local skin-friction coefficient and the temperature. It is found that local skin-friction coefficient increases while the local Nusselt number decreases as the magnetic parameter increases. The results show also that increasing the heat generation parameter leads to a rise in both the velocity and the temperature and a fall in the local skin-friction coefficient and the local Nusselt number. Furthermore, it is shown that the local skin-friction coefficient and the local Nusselt number decrease when the slip parameter increases.

scholarly journals Effect of Temperature-Dependent Variable Viscosity on Magnetohydrodynamic Natural Convection Flow along a Vertical Wavy Surface

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Nazma Parveen ◽  
Md. Abdul Alim
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Variable Viscosity ◽  
Skin Friction Coefficient ◽  
Effect Of Temperature ◽  
Convection Flow ◽  
Temperature Dependent ◽  
Natural Convection Flow

The effect of temperature dependent variable viscosity on magnetohydrodynamic (MHD) natural convection flow of viscous incompressible fluid along a uniformly heated vertical wavy surface has been investigated. The governing boundary layer equations are first transformed into a nondimensional 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. 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, the stream lines and the isotherms are shown graphically for a selection of parameters set consisting of viscosity parameter (), magnetic parameter (), and Prandtl number (Pr). Numerical results of the local skin friction coefficient and the rate of heat transfer for different values are also presented in tabular form.

scholarly journals Thermo-micropolar fluid flow along a vertical permeable plate with uniform surface heat flux in the presence of heat generation

2009 ◽  
Vol 13 (1) ◽  
pp. 23-36 ◽  
Author(s):  
Mohammad Rahman ◽  
Ibrahim Eltayeb ◽  
Mohammad Rahman
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Heat Generation ◽  
Surface Heat Flux ◽  
Micropolar Fluid ◽  
Skin Friction Coefficient ◽  
Surface Heat ◽  
Viscous Drag

A two-dimensional steady convective flow of thermo-micropolar fluid past a vertical permeable flat plate in the presence of heat generation with uniform surface heat flux has been analyzed numerically. The local similarity solutions for the flow, microrotation (angular velocity) and heat transfer characteristics are illustrated graphically for various material parameters entering into the problem. The effects of the pertinent parameters on the local skin friction coefficient, plate couple stress, and the rate of heat transfer are also calculated and displayed graphically. The results show that skin friction coefficient (viscous drag) and the rate of heat transfer (Nusselt number) in micropolar fluid are less compared to that of the Newtonian fluid.

scholarly journals COMBINED EFFECTS OF VISCOUS DISSIPATION AND HEAT GENERATION ON NATURAL CONVECTION FLOW ALONG A VERTICAL WAVY SURFACE

2015 ◽  
Vol 45 (1) ◽  
pp. 24-31
Author(s):  
K. H. Kabir ◽  
M. A. Alim ◽  
L. S. Andallah ◽  
Saika Mahjabin
Keyword(s):  
Natural Convection ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Skin Friction Coefficient ◽  
Wavy Surface ◽  
Convection Flow ◽  
Physical Parameters ◽  
Surface Shear Stress ◽  
Natural Convection Flow ◽  
Surface Shear

In this paper, the effects of viscous dissipation on natural convection flow along a uniformly heated vertical wavy surface with heat generation 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 systems of partial differential equations are mapped into the domain of a vertical flat plate and then solved numerically employing the Keller-box method. 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, the velocity as well as the temperature profiles are shown graphically and in tabular form for different values of physical parameters namely, viscous dissipation parameter Vd, heat generation parameter Q and Prandtl number Pr. 

scholarly journals Effects of viscous dissipation on natural convection flow along a sphere with radiation and heat generation

2013 ◽  
Vol 10 (1) ◽  
pp. 13-24 ◽  
Author(s):  
Salina Aktar ◽  
Mahmuda Binte Mostafa Ruma ◽  
M. A. Alim
Keyword(s):  
Friction Coefficient ◽  
Surface Temperature ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Linear Equations ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Temperature Profiles ◽  
Generation Parameter

The effects of viscous dissipation on free convection flow along a sphere with radiation and heat generation have been investigated in this paper. 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. Numerical results of the velocity and temperature profiles, skin friction coefficient and surface temperature profiles for different values of the of viscous dissipation parameter Vd ( 0.0 to 4.0), radiation parameter Rd (0.0 to 1.0), the Prandlt number Pr (0.72 to7.0)and the heat generation parameter Q (0.2 to 0.6) are presented graphically. Detailed discussion is given for the effects of the aforementioned parameters. Significant effect is found in the velocity and temperature profiles, skin friction coefficient and surface temperature distribution for the Prandtl number, heat generation and radiation parameters. DOI: http://dx.doi.org/10.3329/jname.v10i1.12809

Numerical Analysis on Nanofluid Forced Convection in Ducts With Triangular Cross Sections

2011 ◽  
Author(s):  
O. Manca ◽  
S. Nardini ◽  
D. Ricci ◽  
S. Tamburrino
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Forced Convection ◽  
Cross Sections ◽  
Fluid Dynamic ◽  
Pure Water ◽  
Convection Flow ◽  
Uniform Heat Flux ◽  
Surface Shear Stress ◽  
Surface Shear

Heat transfer of fluids is very important to many industrial heating or cooling equipments. Convective heat transfer can be enhanced passively by changing flow geometry, boundary conditions or by enhancing the thermal conductivity of the working fluids. An innovative way of improving the fluid thermal conductivity is to introduce suspended small solid nanoparticles in the base fluids. In this paper a numerical investigation on laminar forced convection flow of a water–Al2O3 nanofluid in a duct having an equilateral triangular cross section is performed. The hydraulic diameter is set equal to 1.0×10−2 m. A constant and uniform heat flux on the external surfaces has been applied and the single-phase model approach has been employed. The analysis has been run in steady state regime for a nanoparticle size equal to 38 nm, considering different volume particle concentrations. The CFD code Fluent has been employed in order to solve the tri-dimensional numerical model. Results are presented in terms of temperature and velocity distributions, surface shear stress and heat transfer convective coefficient, Nusselt number and required pumping power profiles. Comparison with results related to the fluid dynamic and thermal behaviors in pure water are carried out in order to evaluate the enhancement due to the presence of nanoparticles in terms of volumetric concentration.

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

Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

2019 ◽  
Vol 29 (9) ◽  
pp. 3110-3127 ◽  
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

PurposeThis paper aims to investigate the steady flow and heat transfer of a Cu-Al2O3/water hybrid nanofluid over a nonlinear permeable stretching/shrinking surface with radiation effects. The surface velocity condition is assumed to be of the power-law form with an exponent of 1/3. The governing equations of the problem are converted into a system of similarity equations by using a similarity transformation.Design/methodology/approachThe problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The results of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented through graphs and tables for several values of the parameters. The effects of these parameters on the flow and heat transfer characteristics are examined and discussed.FindingsResults found that dual solutions exist for a certain range of the stretching/shrinking and suction parameters. The increment of the skin friction coefficient and reduction of the local Nusselt number on the shrinking sheet is observed with the increasing of copper (Cu) nanoparticle volume fractions for the upper branch. The skin friction coefficient and the local Nusselt number increase when suction parameter is increased for the upper branch. Meanwhile, the temperature increases in the presence of the radiation parameter for both branches.Originality/valueThe problem of Cu-Al2O3/water hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface with radiation effects is the important originality of the present study where the dual solutions for the flow reversals are obtained.

Non-uniform mass transfer in MHD mixed convection flow of water over a sphere with variable viscosity and Prandtl number

2016 ◽  
Vol 26 (7) ◽  
pp. 2235-2251 ◽  
Author(s):  
J. Rajakumar ◽  
P. Saikrishnan ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mixed Convection ◽  
Skin Friction ◽  
Variable Viscosity ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Content Type ◽  
Slot Suction

Purpose The purpose of this paper is to consider axisymmetric mixed convection flow of water over a sphere with variable viscosity and Prandtl number and an applied magnetic field. Design/methodology/approach The non-similar solutions have been obtained from the origin of the streamwise co-ordinate to the point of zero skin friction using quasilinearization technique with an implicit finite-difference scheme. Findings The effect of M is not notable on the temperature and heat transfer coefficient when λ is large. The skin friction coefficient and velocity profile are enhance with the increase of MHD parameter M when λ is small. Viscous dissipation has no significant on the skin friction coefficient under MHD effect. For M=1, the movement of the slot or slot suction or slot injection do not cause any effect on flow separation. The slot suction and the movement of the slot in downstream direction delay the point of zero skin friction for M=0. Originality/value The present results are original and new for water boundary-layer flow over sphere in mixed convection flow with MHD effect and non-uniform mass transfer. So this study would be useful in analysing the skin friction and heat transfer coefficient on sphere of mixed convection flow of water boundary layer with MHD effect.

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