Numerical Investigation of a Three-Dimensional Laminar Mixed Convection Flows in Lid-Driven Cavity for Very Small Richardson Numbers

2015 ◽  
Author(s):  
M. M. Abo Elazm ◽  
A. I. Shahata ◽  
A. F. Elsafty ◽  
M. A. Teamah
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Richardson Number ◽  
Three Dimensional ◽  
Lewis Number ◽  
Maximum Error ◽  
Driven Cavity ◽  
Laminar Mixed Convection ◽  
Nusselt Number Distribution ◽  
Volume Method

Laminar mixed convection in a three-dimensional lid driven cavity is numerically investigated. The top lid of the cavity is moving rightwards with a constant speed at a cold temperature. The bottom wall is maintained at an isothermal hot temperature, while the other vertical walls of the cavity are assumed to be insulated. In this study the mass diffusion was not taken into account and the fluid used was air. The flow and heat transfer behavior is studied for various Richardson number ranging from 5 × 10−5 to 3 × 10−4 at a fixed Prandtl number of 0.71 through analyzing the local Nusselt number distribution at different sections inside the cavity. Lewis number Le is assumed to be unity and the buoyancy ratio parameter N is equal to zero. Computations were done using an in-house code based on a finite volume method. The results showed a good agreement with previous two dimensional studies, while the three dimensional study gives different results at different sections inside the cavity. It is observed that, the average Nusselt number “Av Nu” on top and bottom surfaces decreases for all sections inside the cavity with increasing Richardson number. A correlation was formulated for each section on both walls for “Av Nu” as a function of “Ri” with a maximum error of 7.3%.

scholarly journals Mixed Convection and Entropy Generation of an Ag-Water Nanofluid in an Inclined L-Shaped Channel

Energies ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 1150 ◽  
Author(s):  
Taher Armaghani ◽  
Muneer Ismael ◽  
Ali Chamkha ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Entropy Generation ◽  
Richardson Number ◽  
Volume Fraction ◽  
Governing Equations ◽  
Nanoparticles Volume Fraction ◽  
The Mean ◽  
The Right ◽  
Volume Method

This paper investigates the mixed convection and entropy generation of an Ag-water nanofluid in an L-shaped channel fixed at an inclination angle of 30° to the horizontal axis. An isothermal heat source was positioned in the middle of the right inclined wall of the channel while the other walls were kept adiabatic. The finite volume method was used for solving the problem’s governing equations. The numerical results were obtained for a range of pertinent parameters: Reynolds number, Richardson number, aspect ratio, and the nanoparticles volume fraction. These results were Re = 50–200; Ri = 0.1, 1, 10; AR = 0.5–0.8; and φ = 0.0–0.06, respectively. The results showed that both the Reynolds and the Richardson numbers enhanced the mean Nusselt number and minimized the rate of entropy generation. It was also found that when AR. increased, the mean Nusselt number was enhanced, and the rate of entropy generation decreased. The nanoparticles volume fraction was predicted to contribute to increasing both the mean Nusselt number and the rate of entropy generation.

Numerical simulation of water/alumina nanofluid mixed convection in square lid-driven cavity

2019 ◽  
Vol 30 (5) ◽  
pp. 2781-2807
Author(s):  
Davood Toghraie ◽  
Ehsan Shirani
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Richardson Number ◽  
Hartmann Number ◽  
Two Phase ◽  
Content Type ◽  
Driven Cavity

Purpose The purpose of this paper is to investigate the mixed convection of a two-phase water–aluminum oxide nanofluid in a cavity under a uniform magnetic field. Design/methodology/approach The upper wall of the cavity is cold and the lower wall is warm. The effects of different values of Richardson number, Hartmann number, cavitation length and solid nanoparticles concentration on the flow and temperature field and heat transfer rate were evaluated. In this paper, the heat flux was assumed to be constant of 10 (W/m2) and the Reynolds number was assumed to be constant of 300 and the Hartmann number and the volume fraction of solid nanoparticles varied from 0 to 60 and 0 to 0.06, respectively. The Richardson number was considered to be 0.1, 1 and 5. Aspect ratios were 1, 1.5 and 2. Findings Comparison of the results of this paper with the results of the numerical and experimental studies of other researchers showed a good correlation. The results were presented in the form of velocity and temperature profiles, stream and isotherm lines and Nusselt numbers. The results showed that by increasing the Hartmann number, the heat transfer rate decreases. An increase from 0 to 20 in Hartmann number results in a 20 per cent decrease in Nusselt numbers, and by increasing the Hartmann number from 20 to 40, a 16 per cent decrease is observed in Nusselt number. Accordingly, it is inferred that by increasing the Hartmann number, the reduction in the Nusselt number is decreased. As the Richardson number increased, the heat transfer rate and, consequently, the Nusselt number increased. Therefore, an increase in the Richardson number results in an increase of the Nusselt number, that is, an increase in Richardson number from 0.1 to 1 and from 1 to 5 results in 37 and 47 per cent increase in Nusselt number, respectively. Originality/value Even though there have been numerous investigations conducted on convection in cavities under various configurations and boundary conditions, relatively few studies are conducted for the case of nanofluid mixed convection in square lid-driven cavity under the effect of magnetic field using two-phase model.

Effect of Driven Sidewalls on Mixed Convection in an Open Trapezoidal Cavity With a Channel

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Muneer A. Ismael ◽  
Ahmed Kadhim Hussein ◽  
Fateh Mebarek-Oudina ◽  
Lioua Kolsi
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Airflow Velocity ◽  
Driven Cavity ◽  
Thermal Fields ◽  
Number Ratio ◽  
The Right

Abstract The mixed convection in an open trapezoidal lid-driven cavity connected with a channel is investigated in the present paper. Four different cases were considered depending on the movement of the cavity sidewalls. For case I, the left sidewall moves downward; for case II, the left sidewall moves downward and the right one moves upward; while for case III, only the right sidewall moves upward. A comparative case (case 0) is accounted when both sidewalls are assumed stationary. The base of the cavity is subjected to a localized heat source of constant temperature Th. The effects of Richardson number Ri and Reynolds number ratio Rer on the flow and thermal fields have been investigated. The results indicated that for cases I and II, the average Nusselt number increases with the increase of the Richardson number and Reynolds number ratio. Moreover, it was found that the maximum average Nusselt number occurs with case I. When the lid-driven speed is three times that of the inlet airflow velocity, the augmentations of the average Nusselt number compared with stationary walls are 163%, 158%, and 96% for cases I, II, and III, respectively.

Mixed Convection From a Heated Square Cylinder to Newtonian and Power-Law Fluids

2006 ◽  
Vol 129 (4) ◽  
pp. 506-513 ◽  
Author(s):  
A. K. Dhiman ◽  
N. Anjaiah ◽  
R. P. Chhabra ◽  
V. Eswaran
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Power Law ◽  
Richardson Number ◽  
Square Cylinder ◽  
Laminar Mixed Convection ◽  
Power Law Fluids ◽  
Power Law Index

Steady laminar mixed convection flow and heat transfer to Newtonian and power-law fluids from a heated square cylinder has been analyzed numerically. The full momentum and energy equations along with the Boussinesq approximation to simulate the buoyancy effects have been solved. A semi-explicit finite volume method with nonuniform grid has been used for the range of conditions as: Reynolds number 1–30, power-law index: 0.8–1.5, Prandtl number 0.7–100 (Pe⩽3000) for Richardson number 0–0.5 in an unbounded configuration. The drag coefficient and the Nusselt number have been reported for a range of values of the Reynolds number, Prandtl number, and Richardson number for Newtonian, shear-thickening (n>1) and shear-thinning (n<1) fluids. In addition, detailed streamline and isotherm contours are also presented to show the complex flow field, especially in the rear of the cylinder. The effects of Prandtl number and of power-law index on the Nusselt number are found to be more pronounced than that of buoyancy parameter (Ri⩽0.5) for a fixed Reynolds number in the steady cross-flow regime (Re⩽30).

A Numerical Investigation of Laminar Mixed Convection Flow and Heat Transfer in a Lid Driven Cavity with Two Cylinders

2015 ◽  
Vol 789-790 ◽  
pp. 282-286 ◽  
Author(s):  
Khalil Khanafer ◽  
M. El Haj Assad
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Driven Cavity ◽  
Flow And Heat Transfer ◽  
The Impact

Mixed convection flow and heat transfer characteristics in a lid-driven cavity with two isothermally heated circular cylinders inside are studied numerically using a finite element formulation based on the Galerkin method of weighted residuals. The top lid of the cavity is moving rightwards with a constant speed. The two cylinders are maintained at an isothermal hot temperature, while the walls of the cavity are maintained at a cold temperature. Comparisons of streamlines, isotherms and average Nusselt number are presented to show the impact of the Richardson number, non-dimensional radius of the cylinder, and the location of the cylinders on the transport phenomena within the cavity. The results of this investigation show that the presence of the cylinders results in an increase in the average Nusselt number compared with a case with no cylinder. The average Nusselt number increases with an increase in the Richardson number for all non-dimensional radius of the cylinder studied in this work. It is seen that changing the boundary condition on one of the cylinders from isothermal to adiabatic has minimal effect on the average Nusselt number around the walls of the cavity.

Laminar Mixed Convective Heat Transfer in a Shallow Inclined Lid-Driven Cavity Filled With Nanofluid

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Habib Salahi ◽  
Muhammad A. R. Sharif ◽  
Saeid Rasouli
Keyword(s):  
Nusselt Number ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Pure Water ◽  
Nanoparticle Concentration ◽  
Fluid Medium ◽  
Driven Cavity ◽  
Laminar Mixed Convection ◽  
Increasing Trend ◽  
Convection Dominated

Laminar mixed convection in a two-dimensional shallow inclined lid-driven cavity is investigated numerically. The moving cavity lid at the top is isothermally hot and the bottom is isothermally cold while the two sidewalls are insulated. The cavity aspect ratio is taken as 10. The fluid medium consists of a mixture of pure water and copper nanoparticles with volumetric concentrations of 5% and 8%. The flow Richardson number is varied from 0.1 to 10, and the cavity inclination is varied from 0 deg to 30 deg. It is found that, at any specific nanoparticle concentration, the average Nusselt number increases mildly with cavity inclination for the forced convection dominated case (Ri = 0.1) while it increases much more rapidly with inclination for natural convection dominated case (Ri = 10). Also the average Nusselt number has significant increasing trend with increasing concentration of the nanoparticles.

scholarly journals Magnetohydrodynamics Mixed Convection Around a Heat Conducting Horizontal Circular Cylinder in a Rectangular Lid-driven Cavity with Joule Heating

2009 ◽  
Vol 1 (3) ◽  
pp. 461-472 ◽  
Author(s):  
M. M. Rahman ◽  
M. A. Alim ◽  
M. K. Chowdhury
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Hartmann Number ◽  
Heat Conducting ◽  
Fluid Temperature ◽  
Driven Cavity ◽  
Horizontal Circular Cylinder

In the present paper, a study of magnetohydrodynamic (MHD) mixed convection around a heat conducting horizontal circular cylinder placed at the center of a rectangular cavity along with joule heating has been carried out. Steady state heat transfer by laminar mixed convection has been studied numerically by solving the equations of mass, momentum and energy to determine the fluid flow and heat transfer characteristics in the cavity as a function of Richardson number, Hartmann number and the cavity aspect ratio. The results are presented in the form of average Nusselt number at the heated surface; average fluid temperature in the cavity and temperature at the cylinder center for the range of Richardson number, Hartmann number and aspect ratio. The streamlines and isotherms are also presented. It is found that the streamlines, isotherms, average Nusselt number, average fluid temperature and dimensionless temperature at the cylinder center strongly depend on the Richardson number, Hartmann number and the cavity aspect ratio.Keywords: Mixed convection; Finite element method; Cylinder diameter; Lid-driven cavity; Hartmann number. © 2009 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v1i3.2597               J. Sci. Res. 1 (3), 461-472 (2009) 

scholarly journals Numerical study of mixed convection heat transfer in lid-driven cavity utilizing nanofluid: Effect of type and model of nanofluid

2015 ◽  
Vol 19 (5) ◽  
pp. 1575-1590 ◽  
Author(s):  
Nader Pourmahmoud ◽  
Ashkan Ghafouri ◽  
Iraj Mirzaee
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Volume Fraction ◽  
Numerical Study ◽  
Published Data ◽  
Driven Cavity ◽  
Laminar Mixed Convection ◽  
Special Cases

Numerical investigation of the laminar mixed convection in two-dimensional lid driven cavity filled with water-Al2O3, water-Cu or water-TiO2 nanofluids is done in this work. In the present study, the top and bottom horizontal walls are thermally insulated while the vertical walls are kept at constant but different temperatures. The governing equations are given in term of the stream function-vorticity formulation in the non-dimensionalized form and then solved numerically by second-order central difference scheme. The thermal conductivity and effective viscosity of nanofluid have been calculated by Maxwell-Garnett and Brinkman models, respectively. An excellent agreement between the current work and previously published data on the basis of special cases are found. The governing parameters are Rayleigh number 103 ? Ra ? 106 and solid concentration 0 ? ? ?0.2 at constant Reynolds and Prandtl numbers. An increase in mean Nusselt number is found as the volume fraction of nanoparticles increases for the whole range of Rayleigh numbers. In addition, it is found that significant heat transfer enhancement can be obtained by increasing thermal conductivity coefficient of additive particles. At Ra=1.75?105, the Nusselt number increases by about 21% for TiO2-Water, and almost 25% for Al2O3-Water, and finally around 40% for Cu-Water nanofluid. Therefore, the highest values are obtained when using Cu nanoparticles. The result obtained using variable thermal conductivity and variable viscosity models are also compared to the results acquired by the Maxwell-Garnett and the Brinkman model.

Numerical Analysis of Laminar Mixed Convection in a Lid Driven Square Cavity With an Isothermally Heated Square Internal Blockage

2012 ◽  
Author(s):  
Akand W. Islam ◽  
Muhammad A. R. Sharif ◽  
Eric S. Carlson
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Blockage Ratio ◽  
Square Cavity ◽  
Ansys Fluent ◽  
Laminar Mixed Convection

Laminar mixed convection characteristics in a square cavity with an isothermally heated square blockage inside have been investigated numerically using the finite volume method of the ANSYS FLUENT commercial CFD code. Various different blockage sizes and concentric and eccentric placement of the blockage inside the cavity have been considered. The blockage is maintained at a hot temperature, Th, and four surfaces of the cavity (including the lid) are maintained at a cold temperature, Tc, under all circumstances. The physical problem is represented mathematically by sets of governing conservation equations of mass, momentum, and energy. The geometrical and flow parameters for the problem are the blockage ratio (B), the blockage placement eccentricities (εx and εy), the Reynolds number (Re), the Grashof number (Gr), and the Richardson number (Ri). The flow and heat transfer behavior in the cavity for a range of Richardson number (0.01–100) at a fixed Reynolds number (100) and Prandtl number (0.71) is examined comprehensively. The variations of the average and local Nusselt number at the blockage surface at various Richardson numbers for different blockage sizes and placement eccentricities are presented. From the analysis of the mixed convection process, it is found that for any size of the blockage placed anywhere in the cavity, the average Nusselt number does not change significantly with increasing Richardson number until it approaches the value of the order of 1 beyond which the average Nusselt number increases rapidly with the Richardson number. For the central placement of the blockage at any fixed Richardson number, the average Nusselt number decreases with increasing blockage ratio and reaches a minimum at around a blockage ratio of slightly larger than 1/2. For further increase of the blockage ratio, the average Nusselt number increases again and becomes independent of the Richardson number. The most preferable heat transfer (based on the average Nusselt number) is obtained when the blockage is placed around the top left and the bottom right corners of the cavity.

scholarly journals Mixed Convection of Heat Transfer in a Square Lid-Driven Cavity

2015 ◽  
Vol 55 ◽  
pp. 180-186 ◽  
Author(s):  
Noura Ben Mansour ◽  
Nader Ben Cheikh ◽  
Brahim Ben Beya ◽  
Taieb Lili
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Richardson Number ◽  
Three Dimensional ◽  
Governing Equations ◽  
Driven Cavity ◽  
Flow And Heat Transfer ◽  
Parametric Studies ◽  
Vertical Walls ◽  
Cubical Cavity

Three dimensional steady state mixed convection in a lid driven cubical cavity heating from below has been investigated numerically. Two sided walls are maintained at a constant ambient temperature Ttop > Tbottom, while the vertical walls are thermally insulated. Governing equations expressing in a dimensionless form are solved by using finite element method. The Reynolds number is fixed at Re=100, while the Richardson number is varied from 0.001 to 10. Parametric studies focusing on the effect of the Richardson number on the fluid flow and heat transfer have been performed. The flow and heat transfer characteristics, expressed in terms of streamlines, isotherms and average wall Nusselt number are presented for the entire range of Richardson number considered. Multiple correlations in terms of the heat transfer rate and Richardson number has been established.

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