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.

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.

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.

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.

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.

Combined Buoyancy Effects of Thermal and Mass Diffusion on Laminar Mixed Convection in Vertical and Horizontal Semicircular Ducts

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
A. Budabous ◽  
A. A. Busedra
Keyword(s):  
Mass Transfer ◽  
Mixed Convection ◽  
Heat And Mass Transfer ◽  
Convection Boundary Layer ◽  
Input Concentration ◽  
Transfer Rates ◽  
Thermal Boundary Conditions ◽  
Laminar Mixed Convection ◽  
Boundary Layer Development ◽  
Semicircular Ducts

The development of laminar mixed convection with heat and mass transfer in vertical and horizontal semicircular ducts has been investigated for the case of thermal boundary conditions of uniform heat input, concentration at the fluid–solid interface axially, and uniform peripheral wall temperature at any axial station. The governing equations were solved numerically over the following conditions: Pr = 0.7, Le = 1, Re = 500, Grt = 1.66 × 105, and Grc = 1.66 × 105. The combined effects of solutal and thermal Grashof numbers on the flow and thermal fields were observed in terms of the axial velocity, temperature, and concentration distributions, as well as, friction factor, Nusselt number, and Sherwood number. Further, the development of velocity, temperature, and concentration at different axial stations was found to be influenced by the solutal and thermal Grashof numbers. The results also showed that the forced-convection boundary layer development dominates very close to the duct inlet, while further downstream, the heat and mass transfer rates are enhanced due to the effect of solutal buoyancy.

Heat Transfer by Mixed Convection Opposing Laminar Flow From the Inside Surface of Uniformly Heated Inclined Circular Tube

2006 ◽  
Author(s):  
H. Mohammed ◽  
T. Yusaf
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Flow Direction ◽  
Convection Heat Transfer ◽  
Heat Transfer Process ◽  
Secondary Flows ◽  
Opposed Flow ◽  
Wide Range

This paper aims to investigate the effect of the flow pattern on the mixed convection heat transfer. A 28 thermocouples wire were installed along a 900mm copper tube to measure the temperature distribution. Three insulation layers of fiber glass, asbestos and gypsum were used to minimize to heat lost to the surrounding. A forced convection at the entrance region of a fully developed opposing laminar air flow was investigated to evaluate the flow direction effect on the Nusselt number. The investigation covered a wide range of Reynolds number from 410 to 1600 and heat flux varied from 63W/m2 to 1260W/m2, with different angles of tube inclination of 30°, 45°, 60°, and 90°. It was found that the surface temperature variation along the tube for opposed flow higher than the assisted flow but lower than the horizontal orientation. The Reynolds number has a significant effect on Nusselt number in opposed flow while the effect of Reynolds number was found to be small in the case of assisted flow. The Nusselt number values were lower for opposed flow than the assisted flow. The temperature profiles results have revealed that the secondary flows created by natural convection have a significant effect on the heat transfer process. The obtained average Nusselt number values were correlated by dimensionless groups as Log Nu against Log Ra/Re.

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