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.

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.

Correlations for Laminar Mixed Convection Flows on Vertical, Inclined, and Horizontal Flat Plates

1986 ◽  
Vol 108 (4) ◽  
pp. 835-840 ◽  
Author(s):  
T. S. Chen ◽  
B. F. Armaly ◽  
N. Ramachandran
Keyword(s):  
Free Convection ◽  
Mixed Convection ◽  
Forced Flow ◽  
Flat Plates ◽  
Maximum Increase ◽  
Nusselt Numbers ◽  
Laminar Mixed Convection ◽  
Wide Range ◽  
Flow Configurations ◽  
Prandtl Numbers

Local Nusselt numbers for laminar mixed convection flows along isothermal vertical, inclined, and horizontal flat plates are presented for the entire mixed convection regime for a wide range of Prandtl numbers, 0.1 ≤ Pr ≤ 100. Simple correlation equations for the local and average mixed convection Nusselt numbers are developed, which are found to agree well with the numerically predicted values and available experimental data for both buoyancy assisting and opposing flow conditions. The threshold values of significant buoyancy effects on forced convection and forced flow effects on free convection, as well as the maximum increase in the local mixed convection Nusselt number from the respective pure convection limits, are also presented for all flow configurations. It is found that the buoyancy or forced flow effect can increase the surface heat transfer rate from pure forced or pure free convection by about 20 percent.

scholarly journals Darcy-Brinkman free convection about a wedge and a cone subjected to a mixed thermal boundary condition

1992 ◽  
Vol 15 (4) ◽  
pp. 789-794 ◽  
Author(s):  
G. Ramanaiah ◽  
V. Kumaran
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Porous Medium ◽  
Heat Transfer Coefficient ◽  
Free Convection ◽  
Transformation Group ◽  
Darcy Number ◽  
Thermal Boundary Condition ◽  
High Porosity

The Darcy-Brinkman free convection near a wedge and a cone in a porous medium with high porosity has been considered. The surfaces are subjected to a mixed thermal boundary condition characterized by a parameterm;m=0,1,∞correspond to the cases of prescribed temperature, prescribed heat flux and prescribed heat transfer coefficient respectively. It is shown that the solutions for differentmare dependent and a transformation group has been found, through which one can get solution for anymprovided solution for a particular value ofmis known. The effects of Darcy number on skin friction and rate of heat transfer are analyzed.

Numerical Simulation of Nanofluid-Cooling Enhancement of Three Fins Mounted in a Horizontal Channel

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Moussa Khentoul ◽  
Rachid Bessaïh
Keyword(s):  
Volume Fraction ◽  
Numerical Study ◽  
Solid Volume Fraction ◽  
Horizontal Channel ◽  
Thermal Fields ◽  
Nusselt Numbers ◽  
Simpler Algorithm ◽  
Laminar Mixed Convection ◽  
Cooling Enhancement ◽  
Volume Method

This article presents a numerical study of two-dimensional laminar mixed convection in a horizontal channel. The upper horizontal wall of the channel is insulated. The governing equations were solved by using the finite volume method based on the simpler algorithm. Comparisons with previous results were performed and found to be in excellent agreement. The results were presented in terms of streamlines, isotherms, local and average Nusselt numbers for the Richardson number (0 ≤ Ri ≤ 10), Reynolds number (5 ≤ Re ≤ 100), solid volume fraction of nanoparticles (0 ≤ ϕ ≤ 0.10), and the type of nanofluids (Cu, Ag, Al2O3, and TiO2). The results show that the previous parameters have considerable effects on the flow and thermal fields. It was found that the heat transfer increases with increasing of Ra, Re, and ϕ.

Measurements and Predictions of Laminar Mixed Convection Flow Adjacent to a Vertical Surface

1985 ◽  
Vol 107 (3) ◽  
pp. 636-641 ◽  
Author(s):  
N. Ramachandran ◽  
B. F. Armaly ◽  
T. S. Chen
Keyword(s):  
Free Convection ◽  
Mixed Convection ◽  
Flat Surface ◽  
Vertical Surface ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Nusselt Numbers ◽  
Buoyancy Parameter ◽  
Laminar Mixed Convection ◽  
Good Agreement

Measurements and predictions of laminar mixed forced and free convection air flow adjacent to an isothermally heated vertical flat surface are reported. Local Nusselt numbers and the velocity and temperature distributions are presented for both the buoyancy assisting and opposing flow cases over the entire mixed convection regime, from the pure forced convection limit (buoyancy parameter ξ = Grx/Rex2 = 0) to the pure free convection limit (ξ = ∞). The measurements are in very good agreement with predictions and deviate from the pure forced and free convection regimes for buoyancy assisting flow in the region of 0.01 ≤ ξ ≤ 10 and for opposing flow in the region of 0.01<ξ< 0.2. The local Nusselt number increases for buoyancy assisting flow and decreases for opposing flow with increasing value of the buoyancy parameter. The mixed convection Nusselt numbers are larger than the corresponding pure forced and pure free convection limits for buoyancy assisting flow and are smaller than these limits for opposing flow. For buoyancy assisting flow, the velocity overshoot and wall shear stress increase, whereas the temperature decreases but the temperature gradient at the wall increases as the buoyancy parameter increases. The reverse trend is observed for the opposing flow. Flow reversal near the wall was detected for the buoyancy opposing flow case at a buoyancy parameter of about ξ = 0.20.

Laminar Mixed Convection in a Shrouded Fin Array

1981 ◽  
Vol 103 (3) ◽  
pp. 559-565 ◽  
Author(s):  
S. Acharya ◽  
S. V. Patankar
Keyword(s):  
Secondary Flow ◽  
Forced Convection ◽  
Tip Clearance ◽  
Base Surface ◽  
Nusselt Numbers ◽  
Laminar Mixed Convection ◽  
Friction Factors ◽  
Wide Range ◽  
Laminar Forced Convection ◽  
The Heat Transfer Coefficient

An analytical study is made to investigate the effect of buoyancy on laminar forced convection in a shrouded fin array. Two heating conditions are considered; in one, the fins and the base surface are hotter than the fluid, and in the other, they are colder. The results are obtained numerically for a wide range of the governing buoyancy parameter. It is found that with a hot fin and base, the secondary flow pattern is mostly made up of a single eddy. The influence of buoyancy is significant and leads to Nusselt numbers and friction factors which are much higher than for pure forced convection. With a cold fin and base, the presence of a tip clearance between the fins and the shroud generates a multiple eddy pattern. The resulting stratification is responsible for the existence of high axial velocity and temperature in the clearance region relative to that in the inter-fin space. Compared to the hot fin case, the secondary flow is weaker, and therefore a relatively smaller increase in the friction factor is obtained. The Nusselt number is found to increase only in the absence of tip clearance. The distribution of the heat transfer coefficient along the fin and the base for both heating situations is found to be highly nonuniform.

Experimental Investigation of Free Convection in a Vertical Rod Bundle—A General Correlation for Nusselt Numbers

1985 ◽  
Vol 107 (3) ◽  
pp. 611-623 ◽  
Author(s):  
M. Keyhani ◽  
F. A. Kulacki ◽  
R. N. Christensen
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Free Convection ◽  
Power Dissipation ◽  
Unit Length ◽  
Outer Cylinder ◽  
Working Fluid ◽  
Curvature Effects ◽  
Nusselt Numbers ◽  
Wide Range

Free convection in two vertical, enclosed rod bundles has been experimentally investigated for a wide range of Rayleigh numbers. A uniform power dissipation per unit length is supplied to each rod, and the enclosing outer cylinder is maintained at constant temperature. Nusselt numbers for each rod, as well as an overall value for each bundle, have been obtained as a function of Rayleigh number. Comparison of the results for air and water as the working fluid indicate that, for a fixed Rayleigh number, an increase in the Prandtl number produces a reduction in the Nusselt number. This is contrary to what has been reported for vertical cavities and is attributed to curvature effects. Furthermore, the data reveal the interesting fact that it is quite possible for the individual rods in the bundle to exchange energy with the working fluid via different but coexisting regimes at a given power dissipation. Also, as the Rayleigh number is increased, the rods each tend to assume nearly the same heat transfer coefficient. Finally, a correlation for the overall convective Nusselt number is developed in terms of Rayleigh number and geometric parameters.

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