Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 45

Search results for: Rayleigh number

45 Mixed Convection Heat Transfer of Copper Oxide-Heat Transfer Oil Nanofluid in Vertical Tube

Authors: Farhad Hekmatipour, M. A. Akhavan-Behabadi, Farzad Hekmatipour

Abstract:

In this paper, experiments were conducted to investigate the heat transfer of Copper Oxide-Heat Transfer Oil (CuO-HTO) nanofluid laminar flow in vertical smooth and microfin tubes as the surface temperature is constant. The effect of adding the nanoparticle to base fluid and Richardson number on the heat transfer enhancement is investigated as Richardson number increases from 0.1 to 0.7. The experimental results demonstrate that the combined forced-natural convection heat transfer rate may be improved significantly with an increment of mass nanoparticle concentration from 0% to 1.5%. In this experiment, a correlation is also proposed to predict the mixed convection heat transfer rate of CuO-HTO nanofluid flow. The maximum deviation of both correlations is less than 14%. Moreover, a correlation is presented to estimate the Nusselt number inside vertical smooth and microfin tubes as Rayleigh number is between 2´105 and 6.8´106 with the maximum deviation of 12%.

Keywords: Nanofluid, heat transfer oil, mixed convection, vertical tube, laminar flow.

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44 Triple Diffusive Convection in a Vertically Oscillating Oldroyd-B Liquid

Authors: Sameena Tarannum, S. Pranesh

Abstract:

The effect of linear stability analysis of triple diffusive convection in a vertically oscillating viscoelastic liquid of Oldroyd-B type is studied. The correction Rayleigh number is obtained by using perturbation method which gives prospect to control the convection. The eigenvalue is obtained by using perturbation method by adopting Venezian approach. From the study, it is observed that gravity modulation advances the onset of triple diffusive convection.

Keywords: Gravity modulation, Oldroyd-B liquid, triple diffusive convection, Venezian approach.

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43 Experimental on Free and Forced Heat Transfer and Pressure Drop of Copper Oxide-Heat Transfer Oil Nanofluid in Horizontal and Inclined Microfin Tube

Authors: F. Hekmatipour, M. A. Akhavan-Behabadi, B. Sajadi

Abstract:

In this paper, the combined free and forced convection heat transfer of the Copper Oxide-Heat Transfer Oil (CuO-HTO) nanofluid flow in horizontal and inclined microfin tubes is studied experimentally. The flow regime is laminar, and pipe surface temperature is constant. The effect of nanoparticle and microfin tube on the heat transfer rate is investigated with the Richardson number which is between 0.1 and 0.7. The results show an increasing nanoparticle concentration between 0% and 1.5% leads to enhance the combined free and forced convection heat transfer rate. According to the results, five correlations are proposed to provide estimating the free and forced heat transfer rate as the increasing Richardson number from 0.1 to 0.7. The maximum deviation of both correlations is less than 16%. Moreover, four correlations are suggested to assess the Nusselt number based on the Rayleigh number in inclined tubes from 1800000 to 7000000. The maximum deviation of the correlation is almost 16%. The Darcy friction factor of the nanofluid flow has been investigated. Furthermore, CuO-HTO nanofluid flows in inclined microfin tubes.

Keywords: Nanofluid; heat transfer oil; mixed convection; inclined tube; laminar flow.

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42 Analyses of Natural Convection Heat Transfer from a Heated Cylinder Mounted in Vertical Duct

Authors: H. Bhowmik, A. Faisal, Ahmed Al Yaarubi, Nabil Al Alawi

Abstract:

Experiments are conducted to analyze the steady-state and the power-on transient natural convection heat transfer from a horizontal cylinder mounted in a vertical up flow circular duct. The heat flux ranges from 177 W/m2 to 2426 W/m2 and the Rayleigh number ranges from 1×104 to 4.35×104. For natural air flow and constant heat flux condition, the effects of heat transfer around the cylinder under steady-state condition are investigated. The steady-state results compare favorably with that of the available data. The effects of transient heat transfer data on different angular position of the thermocouple (0o, 90o, 180o) are also reported. It is observed that the transient heat transfer around the cylinder is strongly affected by the position of thermocouples. In the transient region, the rate of heat transfer obtained at 90o and 180o are higher than that of stagnation point (0o). Finally, the dependence of the average Nusselt number on Rayleigh number for steady and transient natural convection heat transfer are analyzed, and a correlation equation is presented.

Keywords: Steady-state, transient, natural convection, Rayleigh number, Nusselt number, Fourier Number.

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41 Heat and Mass Transfer of Triple Diffusive Convection in a Rotating Couple Stress Liquid Using Ginzburg-Landau Model

Authors: Sameena Tarannum, S. Pranesh

Abstract:

A nonlinear study of triple diffusive convection in a rotating couple stress liquid has been analysed. It is performed to study the effect of heat and mass transfer by deriving Ginzburg-Landau equation. Heat and mass transfer are quantified in terms of Nusselt number and Sherwood numbers, which are obtained as a function of thermal and solute Rayleigh numbers. The obtained Ginzburg-Landau equation is Bernoulli equation, and it has been elucidated numerically by using Mathematica. The effects of couple stress parameter, solute Rayleigh numbers, and Taylor number on the onset of convection and heat and mass transfer have been examined. It is found that the effects of couple stress parameter and Taylor number are to stabilize the system and to increase the heat and mass transfer.

Keywords: Couple stress liquid, Ginzburg-Landau model, rotation, triple diffusive convection.

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40 Evaluation of Heat Transfer and Entropy Generation by Al2O3-Water Nanofluid

Authors: Houda Jalali, Hassan Abbassi

Abstract:

In this numerical work, natural convection and entropy generation of Al2O3–water nanofluid in square cavity have been studied. A two-dimensional steady laminar natural convection in a differentially heated square cavity of length L, filled with a nanofluid is investigated numerically. The horizontal walls are considered adiabatic. Vertical walls corresponding to x=0 and x=L are respectively maintained at hot temperature, Th and cold temperature, Tc. The resolution is performed by the CFD code "FLUENT" in combination with GAMBIT as mesh generator. These simulations are performed by maintaining the Rayleigh numbers varied as 103 ≤ Ra ≤ 106, while the solid volume fraction varied from 1% to 5%, the particle size is fixed at dp=33 nm and a range of the temperature from 20 to 70 °C. We used models of thermophysical nanofluids properties based on experimental measurements for studying the effect of adding solid particle into water in natural convection heat transfer and entropy generation of nanofluid. Such as models of thermal conductivity and dynamic viscosity which are dependent on solid volume fraction, particle size and temperature. The average Nusselt number is calculated at the hot wall of the cavity in a different solid volume fraction. The most important results is that at low temperatures (less than 40 °C), the addition of nanosolids Al2O3 into water leads to a decrease in heat transfer and entropy generation instead of the expected increase, whereas at high temperature, heat transfer and entropy generation increase with the addition of nanosolids. This behavior is due to the contradictory effects of viscosity and thermal conductivity of the nanofluid. These effects are discussed in this work.

Keywords: Entropy generation, heat transfer, nanofluid, natural convection.

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39 Effects of Roughness Elements on Heat Transfer during Natural Convection

Authors: M. Yousaf, S. Usman

Abstract:

The present study focused on the investigation of the effects of roughness elements on heat transfer during natural convection in a rectangular cavity using numerical technique. Roughness elements were introduced on the bottom hot wall with a normalized amplitude (A*/H) of 0.1. Thermal and hydrodynamic behaviors were studied using computational method based on Lattice Boltzmann method (LBM). Numerical studies were performed for a laminar flow in the range of Rayleigh number (Ra) from 103 to 106 for a rectangular cavity of aspect ratio (L/H) 2.0 with a fluid of Prandtl number (Pr) 1.0. The presence of the sinusoidal roughness elements caused a minimum to maximum decrease in the heat transfer as 7% to 17% respectively compared to smooth enclosure. The results are presented for mean Nusselt number (Nu), isotherms and streamlines.

Keywords: Natural convection, Rayleigh number, surface roughness, Nusselt number, Lattice Boltzmann Method.

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38 Numerical Study of Mixed Convection Coupled to Radiation in a Square Cavity with a Lid-Driven

Authors: Mohamed Amine Belmiloud, Nord Eddine Sad Chemloul

Abstract:

In this study, we investigated numerically heat transfer by mixed convection coupled to radiation in a square cavity; the upper horizontal wall is movable. The purpose of this study is to see the influence of the emissivity ε and the varying of the Richardson number Ri on the variation of average Nusselt number Nu. The vertical walls of the cavity are differentially heated, the left wall is maintained at a uniform temperature higher than the right wall, and the two horizontal walls are adiabatic. The finite volume method is used for solving the dimensionless Governing Equations. Emissivity values used in this study are ranged between 0 and 1, the Richardson number in the range 0.1 to 10. The Rayleigh number is fixed to Ra=104 and the Prandtl number is maintained constant Pr=0.71. Streamlines, isothermal lines and the average Nusselt number are presented according to the surface emissivity. The results of this study show that the Richardson number Ri and emissivity ε affect the average Nusselt number.

Keywords: Numerical study, mixed convection, square cavity, wall emissivity, lid-driven.

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37 Influence of Internal Heat Source on Thermal Instability in a Horizontal Porous Layer with Mass Flow and Inclined Temperature Gradient

Authors: Anjanna Matta, P. A. L. Narayana

Abstract:

An investigation has been presented to analyze the effect of internal heat source on the onset of Hadley-Prats flow in a horizontal fluid saturated porous medium. We examine a better understanding of the combined influence of the heat source and mass flow effect by using linear stability analysis. The resultant eigenvalue problem is solved by using shooting and Runga-Kutta methods for evaluate critical thermal Rayleigh number with respect to various flow governing parameters. It is identified that the flow is switch from stabilizing to destabilizing as the horizontal thermal Rayleigh number is enhanced. The heat source and mass flow increases resulting a stronger destabilizing effect.

Keywords: Linear stability analysis, heat source, porous medium, mass flow.

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36 Effects of Viscous Dissipation and Concentration Based Internal Heat Source on Convective Instability in a Porous Medium with Throughflow

Authors: N. Deepika, P. A. L. Narayana

Abstract:

Linear stability analysis of double diffusive convection in a horizontal porous layer saturated with fluid is examined by considering the effects of viscous dissipation, concentration based internal heat source and vertical throughflow. The basic steady state solution for Governing equations is derived. Linear stability analysis has been implemented numerically by using shooting and Runge-kutta methods. Critical thermal Rayleigh number Rac is obtained for various values of solutal Rayleigh number Sa, vertical Peclet number Pe, Gebhart number Ge, Lewis number Le and measure of concentration based internal heat source γ. It is observed that Ge has destabilizing effect for upward throughflow and stabilizing effect for downward throughflow. And γ has considerable destabilizing effect for upward throughflow and insignificant destabilizing effect for downward throughflow.

Keywords: Porous medium, concentration based internal heat source, vertical throughflow, viscous dissipation.

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35 Entropy Generation Analyze Due to the Steady Natural Convection of Newtonian Fluid in a Square Enclosure

Authors: T. T. Naas, Y. Lasbet, C. Kezrane

Abstract:

The thermal control in many systems is widely accomplished applying mixed convection process due to its low cost, reliability and easy maintenance. Typical applications include the aircraft electronic equipment, rotating-disc heat exchangers, turbo machinery, and nuclear reactors, etc. Natural convection in an inclined square enclosure heated via wall heater has been studied numerically. Finite volume method is used for solving momentum and energy equations in the form of stream function–vorticity. The right and left walls are kept at a constant temperature, while the other parts are adiabatic. The range of the inclination angle covers a whole revolution. The method is validated for a vertical cavity. A general power law dependence of the Nusselt number with respect to the Rayleigh number with the coefficient and exponent as functions of the inclination angle is presented. For a fixed Rayleigh number, the inclination angle increases or decreases is found.

Keywords: Inclined enclosure, natural convection in enclosure, Nusselt number.

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34 Heat and Mass Transfer in a Saturated Porous Medium Confined in Cylindrical Annular Geometry

Authors: A. Ja, J. Belabid, A. Cheddadi

Abstract:

This paper reports the numerical simulation of doublediffusive natural convection flows within a horizontal annular filled with a saturated porous medium. The analysis concerns the influence of the different parameters governing the problem, namely, the Rayleigh number Ra, the Lewis number Le and the buoyancy ratio N, on the heat and mass transfer and on the flow structure, in the case of a fixed radius ratio R = 2. The numerical model used for the discretization of the dimensionless equations governing the problem is based on the finite difference method, using the ADI scheme. The study is focused on steady-state solutions in the cooperation situation.

Keywords: Natural convection, double-diffusion, porous medium, annular geometry, finite differences.

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33 Sinusoidal Roughness Elements in a Square Cavity

Authors: M. Yousaf, S. Usman

Abstract:

Numerical studies were conducted using Lattice Boltzmann Method (LBM) to study the natural convection in a square cavity in the presence of roughness. An algorithm based on a single relaxation time Bhatnagar-Gross-Krook (BGK) model of Lattice Boltzmann Method (LBM) was developed. Roughness was introduced on both the hot and cold walls in the form of sinusoidal roughness elements. The study was conducted for a Newtonian fluid of Prandtl number (Pr) 1.0. The range of Ra number was explored from 10^3 to 10^6 in a laminar region. Thermal and hydrodynamic behavior of fluid was analyzed using a differentially heated square cavity with roughness elements present on both the hot and cold wall. Neumann boundary conditions were introduced on horizontal walls with vertical walls as isothermal. The roughness elements were at the same boundary condition as corresponding walls. Computational algorithm was validated against previous benchmark studies performed with different numerical methods, and a good agreement was found to exist. Results indicate that the maximum reduction in the average heat transfer was 16.66 percent at Ra number 10^5.

Keywords: Lattice Boltzmann Method Natural convection, Nusselt Number Rayleigh number, Roughness.

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32 Investigation of Enhancement of Heat Transfer in Natural Convection Utilizing of Nanofluids

Authors: S. Etaig, R. Hasan, N. Perera

Abstract:

This paper analyses the heat transfer performance and fluid flow using different nanofluids in a square enclosure. The energy equation and Navier-Stokes equation are solved numerically using finite volume scheme. The effect of volume fraction concentration on the enhancement of heat transfer has been studied icorporating the Brownian motion; the influence of effective thermal conductivity on the enhancement was also investigated for a range of volume fraction concentration. The velocity profile for different Rayleigh number. Water-Cu, water AL2O3 and water-TiO2 were tested.

Keywords: Computational fluid Dynamics, Natural convection, Nanofluid and Thermal conductivity.

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31 Unsteady Natural Convection in a Square Cavity Partially Filled with Porous Media Using a Thermal Non-Equilibrium Model

Authors: Ammar Alsabery, Habibis Saleh, Norazam Arbin, Ishak Hashim

Abstract:

Unsteady natural convection and heat transfer in a square cavity partially filled with porous media using a thermal non-equilibrium model is studied in this paper. The left vertical wall is maintained at a constant hot temperature Th and the right vertical wall is maintained at a constant cold temperature Tc, while the horizontal walls are adiabatic. The governing equations are obtained by applying the Darcy model and Boussinesq approximation. COMSOL’s finite element method is used to solve the non-dimensional governing equations together with specified boundary conditions. The governing parameters of this study are the Rayleigh number (Ra = 10^5, and Ra = 10^6 ), Darcy namber (Da = 10^−2, and Da = 10^−3), the modified thermal conductivity ratio (10^−1 ≤ γ ≤ 10^4), the inter-phase heat transfer coefficien (10^−1 ≤ H ≤ 10^3) and the time dependent (0.001 ≤ τ ≤ 0.2). The results presented for values of the governing parameters in terms of streamlines in both fluid/porous-layer, isotherms of fluid in fluid/porous-layer, isotherms of solid in porous layer, and average Nusselt number.

Keywords: Unsteady natural convection, Thermal non-equilibrium model, Darcy model.

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30 Mixed Convective Heat Transfer in Water-Based Al2O3 Nanofluid in Horizontal Rectangular Duct

Authors: Nur Irmawati, H.A. Mohammed

Abstract:

In the present study, mixed convection in a horizontal rectangular duct using Al2O3 is numerically investigated. The effects of different Rayleigh number, Reynolds number and radiation on flow and heat transfer characteristics are studied in detail. This study covers Rayleigh number in the range of 2 × 10^6 ≤ Ra ≤ 2 × 10^7 and Reynolds number in the range of 100 ≤ Re ≤ 1100. Results reveal that the Nusselt number increases as Reynolds and Rayleigh numbers increase. It is also found that the dimensionless temperature distribution increases as Rayleigh number increases.

Keywords: Numerical simulation, Mixed convection, Horizontal rectangular duct, Nanofluids.

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29 Entropy Generation and Heat Transfer of Cu–Water Nanofluid Mixed Convection in a Cavity

Authors: Mliki Bouchmel, Belgacem Nabil, Abbassi Mohamed Ammar, Geudri Kamel, Omri Ahmed

Abstract:

In this numerical work, mixed convection and entropy generation of Cu–water nanofluid in a lid-driven square cavity have been investigated numerically using the Lattice Boltzmann Method. Horizontal walls of the cavity are adiabatic and vertical walls have constant temperature but different values. The top wall has been considered as moving from left to right at a constant speed, U0. The effects of different parameters such as nanoparticle volume concentration (0–0.05), Rayleigh number (104–106) and Reynolds numbers (1, 10 and 100) on the entropy generation, flow and temperature fields are studied. The results have shown that addition of nanoparticles to the base fluid affects the entropy generation, flow pattern and thermal behavior especially at higher Rayleigh and low Reynolds numbers. For pure fluid as well as nanofluid, the increase of Reynolds number increases the average Nusselt number and the total entropy generation, linearly. The maximum entropy generation occurs in nanofluid at low Rayleigh number and at high Reynolds number. The minimum entropy generation occurs in pure fluid at low Rayleigh and Reynolds numbers. Also at higher Reynolds number, the effect of Cu nanoparticles on enhancement of heat transfer was decreased because the effect of lid-driven cavity was increased. The present results are validated by favorable comparisons with previously published results. The results of the problem are presented in graphical and tabular forms and discussed.

Keywords: Entropy generation, mixed convection, nanofluid, lattice Boltzmann method.

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28 Natural Convection in Wavy-Wall Cavities Filled with Power-Law Fluid

Authors: Cha’o-Kuang Chen, Ching-Chang Cho

Abstract:

This paper investigates the natural convection heat transfer performance in a complex-wavy-wall cavity filled with power-law fluid. In performing the simulations, the continuity, Cauchy momentum and energy equations are solved subject to the Boussinesq approximation using a finite volume method. The simulations focus specifically on the effects of the flow behavior index in the power-law model and the Rayleigh number on the flow streamlines, isothermal contours and mean Nusselt number within the cavity. The results show that pseudoplastic fluids have a better heat transfer performance than Newtonian or dilatant fluids. Moreover, it is shown that for Rayleigh numbers greater than Ra=103, the mean Nusselt number has a significantly increase as the flow behavior index is decreased.

Keywords: Non-Newtonian fluid, Power-law fluid, Natural convection, Heat transfer enhancement, Cavity, Wavy wall.

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27 Numerical Study of Laminar Mixed Convection Heat Transfer of a Nanofluid in a Concentric Annular Tube Using Two-Phase Mixture Model

Authors: Roghayyeh Motallebzadeh, Shahin Hajizadeh, Mohammad Reza Ghasemi

Abstract:

Laminar mixed Convection heat transfer of a nanofluid with prescribed constant heat flux on the inner wall of horizontal annular tube has been studied numerically based on two-phase mixture model in different Rayleigh Numbers and Azimuth angles. Effects of applying of different volume fractions of Al2O3 nanoparticles in water as a base fluid on hydrodynamic and thermal behaviors of the fluid flow such as axial velocity, secondary flow, temperature, heat transfer coefficient and friction coefficient at the inner and outer wall region, has been investigated. Conservation equations in elliptical form has been utilized and solved in three dimensions for a steady flow. It is observed that, there is a good agreement between results in this work and previously published experimental and numerical works on mixed convection in horizontal annulus. These particles cause to increase convection heat transfer coefficient of the fluid, meanwhile there is no considerable effect on friction coefficient.

Keywords: Buoyancy force, Laminar mixed convection, Mixture model, Nanofluid, Two-phase.

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26 Effect of Hartmann Number on Free Convective Flow in a Square Cavity with Different Positions of Heated Square Block

Authors: Abdul Halim Bhuiyan, M. A. Alim, Md. Nasir Uddin

Abstract:

This paper is concerned with the effect of Hartmann number on the free convective flow in a square cavity with different positions of heated square block. The two-dimensional Physical and mathematical model have been developed, and mathematical model includes the system of governing mass, momentum and energy equations are solved by the finite element method. The calculations have been computed for Prandtl number Pr = 0.71, the Rayleigh number Ra = 1000 and the different values of Hartmann number. The results are illustrated with the streamlines, isotherms, velocity and temperature fields as well as local Nusselt number.

Keywords: Finite element method, free convection, Hartmann number, square cavity.

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25 Lattice Boltzmann Simulation of MHD Natural Convection in a Nanofluid-Filled Enclosure with Non-Uniform Heating on Both Side Walls

Authors: Imen Mejri, Ahmed Mahmoudi, Mohamed A. Abbassi, Ahmed Omri

Abstract:

This paper examines the natural convection in a square enclosure filled with a water-Al2O3 nanofluid and is subjected to a magnetic field. The side walls of the cavity have spatially varying sinusoidal temperature distributions. The horizontal walls are adiabatic. Lattice Boltzmann method (LBM) is applied to solve the coupled equations of flow and temperature fields. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number of the base fluid, Ra=103 to 106, Hartmann number varied from Ha=0 to 90, phase deviation (γ=0, π/4, π/2, 3π/4 and π) and the solid volume fraction of the nanoparticles between Ø = 0 and 6%. The results show that the heat transfer rate increases with an increase of the Rayleigh number but it decreases with an increase of the Hartmann number. For γ=π/2 and Ra=105 the magnetic field augments the effect of nanoparticles. At Ha=0, the greatest effects of nanoparticles are obtained at γ = 0 and π/4 for Ra=104 and 105 respectively.

 

Keywords: Lattice Boltzmann Method, magnetic field, Natural convection, nanofluid, Sinusoidal temperature distribution.

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24 Study of Natural Convection in a Triangular Cavity Filled with Water: Application of the Lattice Boltzmann Method

Authors: Imen Mejri, Ahmed Mahmoudi, Mohamed A. Abbassi, Ahmed Omri

Abstract:

The Lattice Boltzmann Method (LBM) with double populations is applied to solve the steady-state laminar natural convective heat transfer in a triangular cavity filled with water. The bottom wall is heated, the vertical wall is cooled, and the inclined wall is kept adiabatic. The buoyancy effect was modeled by applying the Boussinesq approximation to the momentum equation. The fluid velocity is determined by D2Q9 LBM and the energy equation is discritized by D2Q4 LBM to compute the temperature field. Comparisons with previously published work are performed and found to be in excellent agreement. Numerical results are obtained for a wide range of parameters: the Rayleigh number from  to  and the inclination angle from 0° to 360°. Flow and thermal fields were exhibited by means of streamlines and isotherms. It is observed that inclination angle can be used as a relevant parameter to control heat transfer in right-angled triangular enclosures.

 

Keywords: Heat transfer, inclination angle, Lattice Boltzmann Method, Nusselt number, Natural convection, Rayleigh number.

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23 Laminar Free Convection of Nanofluid Flow in Horizontal Porous Annulus

Authors: Manal H. Saleh

Abstract:

A numerical study has been carried out to investigate the heat transfer by natural convection of nanofluid taking Cu as nanoparticles and the water as based fluid in a three dimensional annulus enclosure filled with porous media (silica sand) between two horizontal concentric cylinders with 12 annular fins of 2.4mm thickness attached to the inner cylinder under steady state conditions. The governing equations which used are continuity, momentum and energy equations under an assumptions used Darcy law and Boussinesq-s approximation which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7. The parameters affected on the system are modified Rayleigh number (10 ≤Ra*≤ 1000), fin length Hf (3, 7 and 11mm), radius ratio Rr (0.293, 0.365 and 0.435) and the volume fraction(0 ≤ ¤ò ≤ 0 .35). It was found that the average Nusselt number depends on (Ra*, Hf, Rr and φ). The results show that, increasing of fin length decreases the heat transfer rate and for low values of Ra*, decreasing Rr cause to decrease Nu while for Ra* greater than 100, decreasing Rr cause to increase Nu and adding Cu nanoparticles with 0.35 volume fraction cause 27.9% enhancement in heat transfer. A correlation for Nu in terms of Ra*, Hf and φ, has been developed for inner hot cylinder.

Keywords: Annular fins, laminar free convection, nanofluid, porous media, three dimensions horizontal annulus.

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22 Magnetohydrodynamic Free Convection in a Square Cavity Heated from Below and Cooled from Other Walls

Authors: S. Jani, M. Mahmoodi, M. Amini

Abstract:

Magnetohydrodynamic free convection fluid flow and heat transfer in a square cavity filled with an electric conductive fluid with Prandtl number of 0.7 has been investigated numerically. The horizontal bottom wall of the cavity was kept at Th while the side and the top walls of the cavity were maintained at a constant temperature Tc with Th>Tc. The governing equations written in terms of the primitive variables were solved numerically using the finite volume method while the SIMPLER algorithm was used to couple the velocity and pressure fields. Using the developed code, a parametric study was performed, and the effects of the Rayleigh number and the Hartman number on the fluid flow and heat transfer inside the cavity were investigated. The obtained results showed that temperature distribution and flow pattern inside the cavity depended on both strength of the magnetic field and Rayleigh number. For all cases two counter rotating eddies were formed inside the cavity. The magnetic field decreased the intensity of free convection and flow velocity. Also it was found that for higher Rayleigh numbers a relatively stronger magnetic field was needed to decrease the heat transfer through free convection.

Keywords: Free Convection, Magnetic Field, Square Cavity, Numerical Simulation.

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21 Uniform Solution on the Effect of Internal Heat Generation on Rayleigh-Benard Convection in Micropolar Fluid

Authors: Izzati K. Khalid, Nor Fadzillah M. Mokhtar, Norihan Md. Arifin

Abstract:

The effect of internal heat generation is applied to the Rayleigh-Benard convection in a horizontal micropolar fluid layer. The bounding surfaces of the liquids are considered to be rigid-free, rigid-rigid and free-free with the combination of isothermal on the spin-vanishing boundaries. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. It is shown that the critical Rayleigh number decreases as the value of internal heat generation increase and hence destabilize the system.

Keywords: Internal heat generation, micropolar fluid, rayleighbenard convection.

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20 Effect of Gravity Modulation on Weakly Non-Linear Stability of Stationary Convection in a Dielectric Liquid

Authors: P. G. Siddheshwar, B. R. Revathi

Abstract:

The effect of time-periodic oscillations of the Rayleigh- Benard system on the heat transport in dielectric liquids is investigated by weakly nonlinear analysis. We focus on stationary convection using the slow time scale and arrive at the real Ginzburg- Landau equation. Classical fourth order Runge-kutta method is used to solve the Ginzburg-Landau equation which gives the amplitude of convection and this helps in quantifying the heat transfer in dielectric liquids in terms of the Nusselt number. The effect of electrical Rayleigh number and the amplitude of modulation on heat transport is studied.

Keywords: Dielectric liquid, Nusselt number, amplitude equation.

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19 Effect of Time-Periodic Boundary Temperature on the Onset of Nanofluid Convection in a Layer of a Saturated Porous Medium

Authors: J.C. Umavathi

Abstract:

The linear stability of nanofluid convection in a horizontal porous layer is examined theoretically when the walls of the porous layer are subjected to time-periodic temperature modulation. The model used for the nanofluid incorporates the effects of Brownian motion and thermopherosis, while the Darcy model is used for the porous medium. The analysis revels that for a typical nanofluid (with large Lewis number) the prime effect of the nanofluids is via a buoyancy effect coupled with the conservation of nanoparticles. The contribution of nanoparticles to the thermal energy equation being a second-order effect. It is found that the critical thermal Rayleigh number can be found reduced or decreased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy or bottom-heavy. Oscillatory instability is possible in the case of a bottom-heavy nanoparticle distribution, phase angle and frequency of modulation.

Keywords: Brownian motion and thermophoresis, Porous medium, Nanofluid, Natural convection, Thermal modulation.

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18 Free Convective Heat Transfer in an Enclosure Filled with Porous Media with and without Insulated Moving Wall

Authors: Laith Jaafer Habeeb

Abstract:

The present work is concerned with the free convective two dimensional flow and heat transfer, in isotropic fluid filled porous rectangular enclosure with differentially heated walls for steady state incompressible flow have been investigated for non- Darcy flow model. Effects of Darcy number (0.0001 £Da£ 10), Rayleigh number (10 £Ra£ 5000), and aspect ratio (0.25 £AR£ 4), for a range of porosity (0.4 £e£ 0.9) with and without moving lower wall have been studied. The cavity was insulated at the lower and upper surfaces. The right and left heated surfaces allows convective transport through the porous medium, generating a thermal stratification and flow circulations. It was found that the Darcy number, Rayleigh number, aspect ratio, and porosity considerably influenced characteristics of flow and heat transfer mechanisms. The results obtained are discussed in terms of the Nusselt number, vectors, contours, and isotherms.

Keywords: Numerical study, moving-wall cavity flow, saturated porous medium, different Darcy and Rayleigh numbers.

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17 Simulation of Natural Convection in Concentric Annuli between an Outer Inclined Square Enclosure and an Inner Horizontal Cylinder

Authors: Sattar Al-Jabair, Laith J. Habeeb

Abstract:

In this work, the natural convection in a concentric annulus between a cold outer inclined square enclosure and heated inner circular cylinder is simulated for two-dimensional steady state. The Boussinesq approximation was applied to model the buoyancy-driven effect and the governing equations were solved using the time marching approach staggered by body fitted coordinates. The coordinate transformation from the physical domain to the computational domain is set up by an analytical expression. Numerical results for Rayleigh numbers 103 , 104 , 105 and 106, aspect ratios 1.5 , 3.0 and 4.5 for seven different inclination angles for the outer square enclosure 0o , -30o , -45o , -60o , -90o , -135o , -180o are presented as well. The computed flow and temperature fields were demonstrated in the form of streamlines, isotherms and Nusselt numbers variation. It is found that both the aspect ratio and the Rayleigh number are critical to the patterns of flow and thermal fields. At all Rayleigh numbers angle of inclination has nominal effect on heat transfer.

Keywords: natural convection, concentric annulus, square inclined enclosure

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16 Fourth Order Accurate Free Convective Heat Transfer Solutions from a Circular Cylinder

Authors: T. V. S. Sekhar, B. Hema Sundar Raju

Abstract:

Laminar natural-convective heat transfer from a horizontal cylinder is studied by solving the Navier-Stokes and energy equations using higher order compact scheme in cylindrical polar coordinates. Results are obtained for Rayleigh numbers of 1, 10, 100 and 1000 for a Prandtl number of 0.7. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results. Streamlines, vorticity - lines and isotherms are plotted.

Keywords: Higher order compact scheme, Navier-Stokes equations, Energy equation, Natural convection, Boussinesq's approximation and Mean Nusselt number.

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