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.

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.

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.

Analysis of Mixed Convection in Vertical Convergent Channels

Volume 1 ◽  
2004 ◽  
Author(s):  
Nicola Bianco ◽  
Oronzio Manca ◽  
Alfonso W. Mauro ◽  
Vincenzo Naso
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Free Convection ◽  
Mixed Convection ◽  
Forced Flow ◽  
Uniform Heat Flux ◽  
Turbulent Model ◽  
Flat Plates ◽  
Convergent Channel ◽  
Converging Angle

Air mixed convection in a convergent channel with the two principal flat plates at uniform heat flux is analyzed numerically. In the considered system two parallel adiabatic extensions are placed downstream the convergent channel. The forced flow is obtained by imposing a pressure drop between the inlet and the outlet of the channel. The flow in the channel is assumed to be two-dimensional, turbulent and incompressible. A k-ε turbulent model is employed. Results in terms of dimensionless wall temperature distribution as a function of the walls converging angle, the Grashof number and the pressure drop are presented in the ranges: 0 ≤ ΔP ≤ 2.2·107, 2.8·104 ≤ Gr ≤ 2.1·105. Results show that increasing the angle of converging the Reynolds number increases at the same pressure drop. The larger the pressure drop the smaller the contribution of the free convection to the Reynolds number. Increasing the converging angle only slightly increases the ΔP value for which the effect of free convection is negligible.

Laminar mixed convection in two-dimensional far wakes above heated/cooled bodies: model and experiments

2001 ◽  
Vol 439 ◽  
pp. 165-198 ◽  
Author(s):  
PETER EHRHARD
Keyword(s):  
Mixed Convection ◽  
Vertical Velocity ◽  
Forced Flow ◽  
Horizontal Flow ◽  
Asymptotic Model ◽  
Buoyant Plume ◽  
Velocity Deficit ◽  
Laminar Mixed Convection ◽  
Prandtl Numbers ◽  
Thermal Wake

A heated or cooled body is positioned in a vertically rising forced flow. This develops both a kinematic and a thermal wake, the latter adding buoyant effects to the otherwise forced flow field. An asymptotic model is developed to treat this mixed convection in both plane and axisymmetric geometry. The model holds for laminar flow in the boundary layer approximation and uses a far-wake expansion for weak buoyant forces. For plane geometry the model is validated against both experiments in water and FEM simulations.It is found for a heated wake that buoyant forces accelerate the fluid in the thermal wake such that the vertical velocity deficit in the kinematic wake is reduced. For strong heating this may even lead to vertical velocities larger than the forced flow amplitude. In conjunction the entrainment is intensified in a heated wake. The effects in a cooled wake are opposite in that the vertical velocity deficit is increased within the thermal wake and the horizontal flow into the wake is weakened. In a strongly cooled wake the horizontal flow may even invert, going from the wake centre into the ambient. The Prandtl number controls the width of the thermal wake and, thus, the portion of the kinematic wake which is affected by buoyant forces. Large Prandtl numbers superimpose a narrow buoyant plume, small Prandtl numbers a wide buoyant plume, onto the kinematic wake.

Influence of free convection on the diffusion current to a sphere in a laminar forced flow regime

1985 ◽  
Vol 50 (12) ◽  
pp. 2697-2714
Author(s):  
Arnošt Kimla ◽  
Jiří Míčka
Keyword(s):  
Asymptotic Expansion ◽  
Free Convection ◽  
Boundary Value Problem ◽  
Concentration Gradient ◽  
Empirical Formula ◽  
Convective Diffusion ◽  
Forced Flow ◽  
Diffusion Current ◽  
Wide Range ◽  
Free And Forced Convection

The formulation and solution of a boundary value problem is presented, describing the influence of the free convective diffusion on the forced one to a sphere for a wide range of Rayleigh, Ra, and Peclet, Pe, numbers. It is assumed that both the free and forced convection are oriented in the same sense. Numerical results obtained by the method of finite differences were approximated by an empirical formula based on an analytically derived asymptotic expansion for Pe → ∞. The concentration gradient at the surface and the total diffusion current calculated from the empirical formula agree with those obtained from the numerical solution within the limits of the estimated errors.

Free Convection Through Vertical Plane Layers of Non-Newtonian Power Law Fluids

1971 ◽  
Vol 93 (2) ◽  
pp. 164-171 ◽  
Author(s):  
A. F. Emery ◽  
H. W. Chi ◽  
J. D. Dale
Keyword(s):  
Free Convection ◽  
Vertical Plane ◽  
Constant Heat Flux ◽  
Experimental Measurements ◽  
Temperature Profiles ◽  
Flat Plates ◽  
Constant Heat ◽  
Layer Height ◽  
Power Law Fluids ◽  
Prandtl Numbers

Experimental measurements of the heat transferred from a constant heat flux hot wall across vertical plane layers of several pseudoplastic non-Newtonian fluids with generalized Prandtl numbers of 10–500 are reported for a range of Grashof moduli and layer height to width ratios. The rheological properties of the fluids are discussed and it is shown that the similarity analysis of free convection for constant-temperature vertical flat plates presented by Acrivos for infinite Prandtl numbers can be used to correlate the data. Several temperature profiles are given and compared to those measured in water.

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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