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Sathiyamoorthy M.,SSN College of Engineering | Chamkha A.,Public Authority for Applied Education and Training
International Journal of Thermal Sciences | Year: 2010

A numerical study is presented for natural convection flow of electrically conducting liquid gallium in a square cavity. In the cavity, the bottom wall is uniformly heated and the left vertical wall is linearly heated whereas the right vertical wall is linearly heated or cooled while the top wall kept thermally insulated. A uniform magnetic field inclined at an angle φ with respect to horizontal plane is externally imposed. Penalty finite element method with bi-quadratic rectangular elements is used to solve the non-dimensional governing equations. Numerical results are presented for wide range of Hartmann number (Ha = 0-100) with inclined angles (φ=0,π/2) for high Rayleigh number Ra = 105 in terms of stream functions and isotherm contours, local and average Nusselt number. The results shows that the magnetic field with inclined angle has effects on the flow and heat transfer rates in the cavity. It is also found that the average Nusselt number decreases non-linearly by increasing Hartmann number for any inclined angle. © 2010 Elsevier Masson SAS. All rights reserved.


Magyari E.,ETH Zurich | Chamkha A.J.,Public Authority for Applied Education and Training
International Journal of Thermal Sciences | Year: 2010

In a recent paper by Damseh et al. (Int. J. Thermal Sci. 48, 1658-1663, 2009), the title problem for an infinite vertical plate has been investigated numerically using the fourth-order Runge-Kutta method. In the present paper the full analytical solution is given. Several new features emerging from this approach are discussed in detail. © 2010 Elsevier Masson SAS. All rights reserved.


Chamkha A.J.,Public Authority for Applied Education and Training | Ismael M.A.,University of Basrah
International Journal of Thermal Sciences | Year: 2013

The conjugate natural convection-conduction heat transfer in a square domain composed of nanofluids filled porous cavity heated by a triangular solid wall is studied under steady-state conditions. The vertical and horizontal walls of the triangular solid wall are kept isothermal and at the same hot temperature Th. The other boundaries surrounding the porous cavity are kept adiabatic except the right vertical wall where it is kept isothermally at the lower temperature Tc. Equations governing the heat transfer in the triangular wall and heat and nanofluid flow, based on the Darcy model, in the nanofluid-saturated porous medium together with the derived relation of the interface temperature are solved numerically using the over-successive relaxation finite-difference method. A temperature independent nanofluids properties model is adopted. Three nanoparticle types dispersed in one base fluid (water) are investigated. The investigated parameters are the nanoparticles volume fraction φ (0-0.2), Rayleigh number Ra (10-1000), solid wall to base-fluid saturated porous medium thermal conductivity ratio K ro (0.44, 1, 23.8), and the triangular wall thickness D (0.1-1). The results are presented in the conventional form; contours of streamlines and isotherms and the local and average Nusselt numbers. At a very low Rayleigh number Ra = 10, a significant enhancement in heat transfer within the porous cavity with φ is observed. Otherwise, the heat transfer may be enhanced or deteriorated with φ depending on the wall thickness D and the Rayleigh number Ra. At high Rayleigh numbers and low conductivity ratios, critical values of D, regardless of φ, are observed and accounted. © 2012 Elsevier Masson SAS. All rights reserved.


Parvin S.,Bangladesh University of Engineering and Technology | Chamkha A.J.,Public Authority for Applied Education and Training
International Communications in Heat and Mass Transfer | Year: 2014

A study of natural convective flow, heat transfer and entropy generation in an odd-shaped geometry is presented here. The geometry considered is a combination of the horizontal and vertical enclosure shapes. The cavity is filled with Cu-water nanofluid. The numerical study focuses specifically on the effect of natural convection parameter and solid volume fraction of nanoparticle on the average Nusselt number, total entropy generation and Bejan number. Also isotherms, stream function and entropy generation due to heat transfer are presented for various Rayleigh number and solid volume fraction. The governing equations are solved by using penalty finite element method with Galerkins weighted residual technique. The results reveal that increasing Rayleigh number causes increase of the average Nusselt number as well as the heat transfer term of entropy generation and decrease of the viscous term. The proper choice of Rayleigh number could be able to maximize heat transfer rate simultaneously minimizing entropy generation. © 2014 Elsevier Ltd.


Chamkha A.J.,Public Authority for Applied Education and Training | Ismael M.A.,University of Basrah
Numerical Heat Transfer; Part A: Applications | Year: 2013

The conjugate natural convection-conduction heat transfer in a square domain composed of a cavity heated by a triangular solid wall is studied under steady state condition. The vertical and horizontal walls of the triangular solid are kept isothermal and at the same hot temperature Th. The other boundaries surrounding the porous cavity are kept adiabatic except the right vertical wall, where it is kept isothermally at the lower temperature Tc. Equations governing the heat transfer in the triangular wall and heat and fluid flow, based on the Darcy model, in the fluid-saturated porous medium together with the derived relation of the interface temperature are solved numerically using the second order central differences finite difference scheme with the successive over relaxation (SOR) method. The investigated parameters are the Rayleigh number Ra (100-1000), solid to fluid saturated porous medium thermal conductivity ratio Kr (0.1-10), and the triangular wall thickness D (0.05-1). The results are presented in the conventional form; contours of streamlines and isotherms and the local and average Nusselt numbers. An uncommon behavior of the heat transfer in the porous medium with the triangular wall thickness D is observed and accounted. © 2013 Copyright Taylor and Francis Group, LLC.


Chamkha A.J.,Public Authority for Applied Education and Training | Ismael M.A.,University of Basrah
Numerical Heat Transfer; Part A: Applications | Year: 2014

Natural convection heat transfer in a differentially heated and vertically partially layered porous cavity filled with a nanofluid is studied numerically based on double-domain formulation. The left wall, which is adjacent to the porous layer, is isothermally heated, while the right wall is isothermally cooled. The top and bottom walls of the cavity are thermally insulated. Impermeable cavity walls are considered except the interface between the porous layer and the nanofluid layer. The Darcy-Brinkman model is invoked for the porous layer which is saturated with the same nanofluid. Equations govern the conservation of mass, momentum, and energy with the entity of nanoparticles in the fluid filling the cavity and that are saturated in the porous layer are modeled and solved numerically using under successive relaxation upwind finite difference scheme. The contribution of five parameters are studied, these are; nanoparticle volume fraction φ (0-0.1), porous layer thickness Xp(0-0.9), Darcy number Da (10-7-1), aspect ratio A (1, 2, 4), and Rayleigh number Ra (103-106). The nanofluid is considered to be composed of copper nanoparticles and water as a base fluid. The results have shown that with the aid of a nanofluid, the convective heat transfer can be enhanced even at a low permeable porous medium. It is found that when Ra ≤ 105, there is a critical porous layer thickness Xp at which the Nusselt number is maximum. Otherwise, the Nusselt number Nu decreases rapidly with Xp. Correlations of Nu with the other parameters are established and tested for A = 2. © 2014 Taylor & Francis Group, LLC.


Basak T.,Indian Institute of Technology Madras | Chamkha A.J.,Public Authority for Applied Education and Training
International Journal of Heat and Mass Transfer | Year: 2012

Natural convection of nanofluids in presence of hot and cold side walls (case 1) or uniform or non-uniform heating of bottom wall with cold side walls (case 2) have been investigated based on visualization of heat flow via heatfunctions or heatlines. Galerkin finite element method has been employed to solve momentum and energy balance as well as post processing streamfunctions and heatfunctions. Various nanofluids are considered as Copper-Water, TiO2-Water and Alumina-Water. Enhancement of heat transfer with respect to base fluid (water) has been observed for all ranges of Rayleigh number (Ra). Dominance of viscous force or buoyancy force are found to play significant roles to characterize the heat transfer rates and temperature patterns which are also established based on heatlines. In general, convective closed loop heatlines are present even at low Rayleigh number (Ra=10 3) within base fluid, but all nanofluids exhibit dominant conductive heat transport as the flow is also found to be weak due to dominance of viscous force for case 1. On the other hand, convective heat transport at the core of a circulation cell, typically represented by closed loop heatlines, is more intense for nanofluids compared to base fluid (water) for case 2 at Ra = 10 5. It is also found that heatlines with larger heatfunctions values for nanofluids coincide with heatlines with smaller heatfunction values for water at walls. Consequently, Nusselt number which is also correlated with heatfunctions show larger values of nanofluids for all ranges of Ra. Average Nusselt numbers show that larger enhancement of heat transfer rates for all nanofluids at Ra=10 5 and Alumina-Water and Copper-Water exhibit larger enhancement of heat transfer rates. © 2012 Elsevier Ltd. All rights reserved.


Chamkha A.J.,Public Authority for Applied Education and Training | Abu-Nada E.,King Faisal University | Abu-Nada E.,Hashemite University
European Journal of Mechanics, B/Fluids | Year: 2012

This work is focused on the numerical modeling of steady laminar mixed convection flow in single and double-lid square cavities filled with a water-Al 2O 3 nanofluid. Two viscosity models are used to approximate nanofluid viscosity, namely, the Brinkman model and the Pak and Cho correlation. The developed equations are given in terms of the stream function-vorticity formulation and are non-dimensionalized and then solved numerically by a second-order accurate finite-volume method. Comparisons with previously published work are performed and found to be in good agreement. A parametric study is conducted and a selective set of graphical results is presented and discussed to illustrate the effects of the presence of nanoparticles and the Richardson number on the flow and heat transfer characteristics in both cavity configurations and to compare the predictions obtained by the two different nanofluid models. It is found that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by increasing the nanoparticle volume fractions at moderate and large Richardson numbers using both nanofluid models for both single- and double-lid cavity configurations. However, for small Richardson number, the Pak and Cho model predicts that the presence of nanoparticle causes reductions in the average Nusselt number in the single-lid cavity configuration. © 2012 Elsevier Masson SAS. All rights reserved.


Abu-Nada E.,King Faisal University | Chamkha A.J.,Public Authority for Applied Education and Training
International Journal of Thermal Sciences | Year: 2010

This work focuses on the study of natural convection heat transfer characteristics in a differentially-heated enclosure filled with a CuO-EG-Water nanofluid for different published variable thermal conductivity and variable viscosity models. The problem is given in terms of the vorticity-stream function formulation and the resulting governing equations are solved numerically using an efficient finite-volume method. Comparisons with previously published work are performed and the results are found to be in good agreement. Various results for the streamline and isotherm contours as well as the local and average Nusselt numbers are presented for a wide range of Rayleigh numbers (Ra = 10 3-105), volume fractions of nanoparticles (0 ≤ φ ≤ 6%), and enclosure aspect ratios ( ≤ A ≤ 2). Different behaviors (enhancement or deterioration) are predicted in the average Nusselt number as the volume fraction of nanoparticles increases depending on the combination of CuO-EG-Water variable thermal conductivity and viscosity models employed. In general, the effects the viscosity models are predicted to be more predominant on the behavior of the average Nusselt number than the influence of the thermal conductivity models. The enclosure aspect ratio is predicted to have significant effects on the behavior of the average Nusselt number which decreases as the enclosure aspect ratio increases. © 2010 Elsevier Masson SAS. All rights reserved.


Gorla R.S.R.,Cleveland State University | Chamkha A.,Public Authority for Applied Education and Training
Nanoscale and Microscale Thermophysical Engineering | Year: 2011

Nanofluid refers to a liquid containing a dispersion of submicronic solid particles or nanoparticles. Nanofluids display a thermal conductivity enhancement. This phenomenon suggests the possibility of using nanofluids in electronic cooling and advanced nuclear systems. In this article, a boundary layer analysis is presented for the natural convection past a nonisothermal vertical plate in a porous medium saturated with a nanofluid. Numerical results for friction factor, surface heat transfer rate, and mass transfer rate are presented for parametric variations of the buoyancy ratio parameter, N r; Brownian motion parameter, N b; thermophoresis parameter, N t; Lewis number, Le; and the power law exponent,γ. The dependency of the friction factor, surface heat transfer rate (Nusselt number), and mass transfer rate on these parameters is discussed. Copyright © Taylor & Francis Group, LLC.

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