Effect of Pr on the Development of Upward Laminar Mixed Convection in the Entrance Region of Vertical Quarter Circle Ducts

2007 ◽  
Author(s):  
Yousef M. F. El Hasadi
Keyword(s):  
Boundary Condition ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Friction Factor ◽  
Local Nusselt Number ◽  
Entrance Region ◽  
Wall Friction ◽  
Simpler Algorithm ◽  
Laminar Mixed Convection ◽  
Wide Range

Upward laminar mixed convection in the entrance region for vertical quarter circle ducts is investigated theoretically. The governing momentum and energy equations are solved numerically using a marching technique with finite control volume approach following the SIMPLER algorithm. Results are obtained for the thermal boundary condition of uniform heat input axially with uniform wall temperature circumferentially at any cross section (H1 boundary condition) with Pr = 7.0 and 0.7 which corresponds to water and air respectively, Re = 500 and wide range of Grashof numbers. These results include the velocity and temperature distributions, at different axial locations, axial distribution of local Nusselt number and local average wall friction factor. It is found that the local Nusselt number follows the expected behavior of monotonic decrease along the developing region down to the fully developed region. However, the axial development of the local friction factor follows a different trend than that of local Nusselt number. The effect of Grashof number is to increase the values of local Nusselt number and friction factor in the developing and fully developed regions. The effect of Pr is mainly in the entrance region where the values of Nusselt number and friction factor corresponding to air are higher than those of water; however, the flow in the fully developed region is independent of Pr.

Laminar Mixed Convection in the Entrance Region of Horizontal Semicircular Ducts With the Flat Wall at the Top

2006 ◽  
Vol 129 (9) ◽  
pp. 1203-1211 ◽  
Author(s):  
Y. M. F. El. Hasadi ◽  
A. A. Busedra ◽  
I. M. Rustum
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Friction Factor ◽  
Entrance Region ◽  
Wall Friction ◽  
Flat Wall ◽  
Simpler Algorithm ◽  
Laminar Mixed Convection ◽  
Wide Range ◽  
Semicircular Ducts

Laminar mixed convection in the entrance region for horizontal semicircular ducts with the flat wall on top is investigated theoretically. The governing momentum and energy equations are solved numerically using a marching technique with the finite control volume approach following the SIMPLER algorithm. Results are obtained for the thermal boundary conditions of uniform heat input axially with uniform wall temperature circumferentially at any cross section (H1 boundary condition) with Pr=0.7 and a wide range of Grashof numbers. These results include the velocity and temperature distributions at different axial locations, axial distribution of local Nusselt number, and local average wall friction factor. It is found that Nusselt number values are close to the forced convection values near the entrance region and then decrease to a minimum as the distance from the entrance increases and then rise due to the effect of free convection before reaching constant value (fully developed). As the Grashof number increases the Nusselt number and the average wall friction factor increase in both developing and fully developed regions and the location of the onset of the secondary flow moves upstream.

Developing Forced and Free Convection for Inclined Semicircular Ducts

2008 ◽  
Author(s):  
Yousef M. F. El. Hasadi
Keyword(s):  
Boundary Condition ◽  
Free Convection ◽  
Thermal Boundary Condition ◽  
Entrance Region ◽  
Nusselt Numbers ◽  
Simpler Algorithm ◽  
Laminar Mixed Convection ◽  
Wide Range ◽  
Inclination Angles ◽  
Semicircular Ducts

Laminar mixed convection in the entrance region for inclined semicircular ducts with the flat wall in the vertical position has been investigated numerically. The governing momentum and energy equations were solved numerically using a marching technique with finite control volume approach following the SIMPLER algorithm. Results were obtained for the thermal boundary condition of uniform heat input axially and uniform wall temperature circumferentially (H1 thermal boundary condition), with Pr = 7.0 (i. e. water), Reynolds number equals 500, inclination angles 0°, 20°, 40°, 60°, 80°, and a wide range of Grashof numbers. These results include velocity, and temperature distributions, at different axial locations, as well as, the axial development of the Nusselt numbers, and the wall friction factor a long the duct length. It was found that the Nusselt numbers were close to the forced convection values near the entrance region and then decreases to a minimum as the distance from the entrance increases and than rises up due to the effect of free convection before reaching a constant value (fully developed value). It is observed that at inclination angles 0° and 20° the values of Nusselt number are higher in the developing and fully developed regions, than those corresponding to 40°, 60°, and 80° at the same Grashof number, however, it was found that at the same Grshof number the values of friction factors increases in the developing and fully developed regions with the increase of the inclination angle.

Developing Flow With Combined Forced and Free Convection of Nanofluids for Horizontal Semicircular Ducts With the Flat Wall at the Vertical Position

2008 ◽  
Author(s):  
Yousef M. F. El Hasadi
Keyword(s):  
Boundary Condition ◽  
Nusselt Number ◽  
Friction Factor ◽  
Volume Concentration ◽  
Pure Water ◽  
Wall Friction ◽  
Vertical Position ◽  
Flow Conditions ◽  
Grashof Number ◽  
Flat Wall

This study is concerned with the numerical investigation of the developing laminar mixed convection of a nanofluid which consists of water- γAl2O3 in a horizontal semicircular duct with the flat wall at a vertical position. The governing momentum and energy equations are solved numerically using a marching technique with the finite control volume approach following the SIMPLER algorithm. The properties of the nanofluid have been simulated by using a well known models and correlations from the literature. Results are obtained for the thermal boundary condition of uniform heat input axially with uniform wall temperature circumferentially, at any cross section (H1 boundary condition), different values of particles volume concentration and for two values of Grashof number 104 and 106. These results include the velocity and temperature distributions at different axial locations, axial distributions of local Nusselt number, and local average wall friction factor. It was observed that increasing the nanoparticles concentrations at low Gr, has a negligible effect on the developing of Nusselt number and friction factor. However, at high Gr it was found that increasing the particle volume concentration increases the Nusselt number in the developing and fully developed regions and reduces the friction factor at the developing and fully developed regions, if it is compared to the results obtained from the results obtained from the pure water at the same flow conditions. As an example for the case of Grashof number equals to 106 and particles volume concentration equals to 0.1, the enhancement of the Nusselt number and the reduction of wall friction factor at the fully developed region, are 17.5% and 6.4% respectively, if it is compared to that of the base fluid (water), at the same flow conditions.

Laminar Mixed Convection in Horizontal Concentric Annuli With Four Porous Blocks Attached on the Outside of the Inner Cylinder

2010 ◽  
Author(s):  
Yacine Ould-Amer
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Friction Factor ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Darcy Number ◽  
Conductivity Ratio ◽  
Laminar Mixed Convection ◽  
Porous Blocks

A numerical study is performed to investigate the performance of an innovative thermal system to improve the heat transfer in horizontal annulus. With attached four porous blocks on the inner cylinder, steady laminar mixed convection is presented for the fully developed region of horizontal concentric annuli. Results are presented for a range of the values of the Grashoff number, the Darcy number and the conductivity ratio between the porous medium and the fluid. Results are presented in the form of contours plots of the streamlines and for the temperature isotherms, and in terms of the overall heat transfer coefficients and friction factor. The average Nusselt number increases significantly with an increase of the conductivity ratio and the Grashoff number. With the use of the four porous blocks, the friction factor is consequently increased compared with the situation without porous blocks. The decrease of the Darcy number leads to an increase of the friction factor. If the fully fluid case is taken as a reference, the use of porous blocks is justified only when the ratio of the average Nusselt number to the friction factor is enhanced. The enhancement occurs for the Darcy number higher than 10−3 and for the higher conductivity ratio.

scholarly journals Forced and mixed convection experiments in a confined vertical backward facing step at low-Prandtl number

2021 ◽  
Vol 63 (1) ◽  
Author(s):  
Thomas Schaub ◽  
Frederik Arbeiter ◽  
Wolfgang Hering ◽  
Robert Stieglitz
Keyword(s):  
Boundary Condition ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Permanent Magnet ◽  
Local Nusselt Number ◽  
Velocity Profiles ◽  
Thermal Boundary Condition ◽  
Backward Facing Step ◽  
Heating Plate

Abstract In this paper, we present experimental results for a non-isothermal vertical confined backward facing step conducted with a low-Prandtl number fluid. The eutectic alloy gallium–indium–tin is used as the working fluid. We conducted experiments for different Reynolds and Richardson numbers covering both forced and mixed convection regimes. Time-averaged velocity profiles were measured at six streamwise positions along the test section center-plane with so-called permanent magnet probes. The local Nusselt number was measured in streamwise and spanwise directions along the heating plate mounted right after the step. We further ran RANS simulations of the experiment to study the qualitative influence of assuming a constant specific heat flux thermal boundary condition for the experiment heating plate. The measured velocity profiles show the expected behavior for both studied convection regimes, while the measured streamwise local Nusselt number profiles do not. This is explained by how the heating plate thermal boundary condition is defined. We performed an order of magnitude estimate to estimate the forced- to mixed convection transition onset. The estimate shows good agreement with the experimental data, although further measurements are needed to further validate the estimated transition threshold. The measurement of fluctuating quantities remains an open task to be addressed in future experiments, since the permanent magnet probe measurement equation needs further adjustments. Graphical Abstract

Laminar Mixed Convection Nanofluids Flow in a Elliptic Duct Using Two Phase Approach

2011 ◽  
Author(s):  
A. Akbarinia ◽  
M. Shariat ◽  
R. Laur
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Friction Factor ◽  
Skin Friction ◽  
Volume Fraction ◽  
Nanofluid Flow ◽  
Two Phase ◽  
Local Skin ◽  
Laminar Mixed Convection ◽  
Mean Diameter

Laminar mixed convection Al2O3-Water nanofluid flow in elliptic ducts with constant heat flux boundary condition has been simulated employing two phase mixture model. Three-dimensional Navier-Stokes, energy and volume fraction equations have been discretized using the Finite Volume Method (FVM). The Brownian motions of nanoparticles have been considered to determine the thermal conductivity and dynamics viscosity of Al2O3-Water nanofluid, which vary with temperature. Simulation effects of solid volume fraction and nanoparticles mean diameter on thermal and hydraulics behaviors of nanofluid flow in elliptic ducts have been presented and discussed. The calculated results show good agreement with the previous numerical data. Results show that in a given Reynolds number (Re) and Richardson number (Ri), increasing solid nanoparticles volume fraction increases the Nusselt number (Nu) while the skin friction factor decreases. Increasing nanoparticles mean diameter augments the local skin friction factor whereas it causes the Nusselt number to reduce. But these effects are significant for nanoparticles diameter equal to 13nm especially.

Measurements of Laminar Mixed Convection Flow Adjacent to an Inclined Surface

1987 ◽  
Vol 109 (1) ◽  
pp. 146-150 ◽  
Author(s):  
N. Ramachandran ◽  
B. F. Armaly ◽  
T. S. Chen
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Local Nusselt Number ◽  
Convection Flow ◽  
Nusselt Numbers ◽  
Buoyancy Parameter ◽  
Laminar Mixed Convection ◽  
Inclined Surfaces ◽  
Inclined Surface ◽  
Good Agreement

Measurements of laminar mixed forced and free convection air flow adjacent to an upward and a downward facing, isothermal, heated inclined surface (at 45 deg) are reported. Local Nusselt number and the velocity and temperature distributions are presented for both the buoyancy assisting and the buoyancy opposing flow cases for a range of buoyancy parameter 0 ≤ ξ ≤ 5 (ξ = Grx/Rex2). The measurements are in good agreement with predictions which define a laminar mixed convection regime for buoyancy assisting flow as 0.1 ≤ ξ ≤ 7, and for buoyancy opposing flows as 0.06 ≤ ξ ≤ 0.25 for this inclination angle of 45 deg. Simple mixed convection correlations for the local and average Nusselt numbers for inclined surfaces are also presented and they agree very well with predicted results. As expected, the local Nusselt number increases with increasing buoyancy parameter for assisting flows and decreases for opposing flows. For a given buoyancy parameter and Reynolds number, a downward facing surface provides essentially the same Nusselt number as the upward facing surface for the conditions examined in the experiment.

Effect of Nanofluid on Heat Transfer Enhancement for Mixed Convection Flow Over a Corrugated Surface

2020 ◽  
Vol 45 (4) ◽  
pp. 373-383
Author(s):  
Nepal Chandra Roy ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Local Nusselt Number ◽  
Richardson Number ◽  
Thermal Boundary Layer ◽  
Volume Fraction ◽  
Convection Flow ◽  
Mixed Convection Flow

AbstractA mathematical model for mixed convection flow of a nanofluid along a vertical wavy surface has been studied. Numerical results reveal the effects of the volume fraction of nanoparticles, the axial distribution, the Richardson number, and the amplitude/wavelength ratio on the heat transfer of Al2O3-water nanofluid. By increasing the volume fraction of nanoparticles, the local Nusselt number and the thermal boundary layer increases significantly. In case of \mathrm{Ri}=1.0, the inclusion of 2 % and 5 % nanoparticles in the pure fluid augments the local Nusselt number, measured at the axial position 6.0, by 6.6 % and 16.3 % for a flat plate and by 5.9 % and 14.5 %, and 5.4 % and 13.3 % for the wavy surfaces with an amplitude/wavelength ratio of 0.1 and 0.2, respectively. However, when the Richardson number is increased, the local Nusselt number is found to increase but the thermal boundary layer decreases. For small values of the amplitude/wavelength ratio, the two harmonics pattern of the energy field cannot be detected by the local Nusselt number curve, however the isotherms clearly demonstrate this characteristic. The pressure leads to the first harmonic, and the buoyancy, diffusion, and inertia forces produce the second harmonic.

scholarly journals Performance of Air-Cooled Heat Exchanger with Laminar, Transitional, and Turbulent Tube Flow

2018 ◽  
Vol 240 ◽  
pp. 02012
Author(s):  
Dawid Taler
Keyword(s):  
Nusselt Number ◽  
Heat Exchanger ◽  
Heat Flow ◽  
Friction Factor ◽  
Flow Rate ◽  
Empirical Relationship ◽  
Heat Flow Rate ◽  
Transition Flow ◽  
Water Side ◽  
Wide Range

Some air-cooled heat exchangers, especially in air conditioning and heating installations, heat pumps, as well as car radiators, work in a wide range of loads when the liquid flow in the tubes can be laminar, transitional or turbulent. In this paper, a semi-empirical and empirical relationship for the Nusselt number on the liquid-side in the transitional and turbulent range was derived. The friction factor in the transition flow range Rew,trb ≤ Rew ≤ Rew,tre was calculated by linear interpolation between the values of the friction factor for Rew,trb =2,100 and Rew,tre =3,000. Based on experimental data for a car radiator, empirical heat transfer relationships for the air and water-side were found by using the least squares method. The water temperature at the outlet of the heat exchanger was calculated using P-NTU (effectiveness-number of transfer units) method. The heat flow rate from water to air was calculated as a function of the water flow rate to compare it with the experimental results. The theoretical and empirical correlation for the water-side Nusselt number developed in the paper were used when determining the heat flow rate. The calculation results agree very well with the results of the measurements.

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