Analysis of Combined Forced and Free Flow in a Vertical Channel With Viscous Dissipation and Isothermal-Isoflux Boundary Conditions

1999 ◽  
Vol 121 (2) ◽  
pp. 349-356 ◽  
Author(s):  
A. Barletta
Keyword(s):  
Boundary Conditions ◽  
Parallel Plate ◽  
Vertical Channel ◽  
Uniform Heat Flux ◽  
Viscous Heating ◽  
Perturbation Expansions ◽  
Nusselt Numbers ◽  
Buoyancy Parameter ◽  
Laminar Mixed Convection ◽  
Friction Factors

Fully developed and laminar mixed convection in a parallel-plate vertical channel is investigated in the case of non-negligible viscous heating. The channel walls are subjected to asymmetric boundary conditions: One wall experiences a constant and uniform heat flux, while the other is kept at a uniform and constant temperature. The velocity field and the temperature field are evaluated analytically by means of perturbation expansions with respect to a buoyancy parameter, i.e., the ratio between the Grashof number and the Reynolds number. The Nusselt numbers and the friction factors are obtained as functions of the buoyancy parameter.

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.

Experimental Investigation of Natural Convection in an Asymmetrically Heated Vertical Channel with an Asymmetric Chimney

2005 ◽  
Vol 127 (8) ◽  
pp. 888-896 ◽  
Author(s):  
Oronzio Manca ◽  
Marilena Musto ◽  
Vincenzo Naso
Keyword(s):  
Heat Flux ◽  
Experimental Investigation ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Vertical Channel ◽  
Expansion Ratio ◽  
Uniform Heat Flux ◽  
Geometrical Parameters ◽  
Nusselt Numbers ◽  
Lower Maximum

An experimental investigation on air natural convection, in a vertical channel asymmetrically heated at uniform heat flux, with downstream unheated parallel extensions, is carried out. One extension is coplanar to the unheated channel wall and the distance between the extensions is equal to or greater than the channel gap (geometrically asymmetric chimney). Experiments are performed with different values of the wall heat flux, aspect ratio (Lh∕b), extension ratio (L∕Lh) and expansion ratio (B∕b). For the largest value of the aspect ratio (Lh∕b=10), the adiabatic extensions improve the thermal performance in terms of lower maximum wall temperature of the channel. Optimal configurations of the system with asymmetrical chimney are detected. Flow visualization shows a cold inflow in the channel-chimney system that penetrates down below the channel exit section. Maximum wall temperatures and channel Nusselt numbers are correlated to the channel Rayleigh number, Ra*, and to the geometrical parameters, in the ranges 3.0×102⩽Ra*B∕b⩽1.0105, 1.0⩽B∕b⩽3.0 and 1.0⩽L∕Lh⩽4.0 with Lh∕b=5.0 and 10.0.

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.

On Laminar Magnetoconvection Flow in a Vertical Channel in the Presence of Heat Generation and Heat Absorption

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
J. C. Umavathi ◽  
B. Patil Mallikarjun ◽  
S. Narasimha Murthy
Keyword(s):  
Electrical Conductivity ◽  
Boundary Conditions ◽  
Heat Generation ◽  
Vertical Channel ◽  
Perturbation Parameter ◽  
Perturbation Series ◽  
Convection Flow ◽  
Thermal Boundary Conditions ◽  
Laminar Mixed Convection ◽  
Reversal Flow

The problem of hydromagnetic fully developed laminar mixed convection flow in a vertical channel and asymmetric wall heating conditions in the presence of electrical conductivity effect is considered through proper choice of dimensionless variables. The governing with symmetric equations are developed and three types of thermal boundary conditions are presented. These boundary conditions are isothermal–isothermal, isoflux–isothermal, and isothermal–isoflux for the left–right walls of the channel respectively. The velocity field and the temperature field are obtained by perturbation series method which employs a perturbation parameter proportional to the Brinkman number. In addition, closed form expressions for reversal flow conditions at both the left–right channel walls are derived. Selected set of graphical results illustrating the effects of the various parameters involved in the problem including magnetic dissipation, heat generation or absorption, and the electrical conductivity on the velocity and temperature profiles as well as flow reversal situation are presented. The solutions obtained are also compared with that of results obtained by finite difference method.

Laminar Mixed Convection Pressure Drop in Vertical Ducts

2010 ◽  
Author(s):  
Carl-Olof Olsson
Keyword(s):  
Reynolds Number ◽  
Rayleigh Number ◽  
Mixed Convection ◽  
Friction Factor ◽  
Parallel Plate ◽  
Width Ratio ◽  
Uniform Heat Flux ◽  
Laminar Mixed Convection ◽  
Transformer Oils ◽  
Rayleigh Numbers

The friction factor at laminar flow in vertical parallel plate ducts with uniform heat flux has been determined as function of Reynolds number and Rayleigh number using a numerical model. The velocity field and the wall shear stress are modified as compared to forced convection due to buoyancy effects when the Rayleigh number is increased, and for sufficiently large Rayleigh numbers the friction factor becomes increased. The duct height to width ratio has been 10, 20, and 50, and combinations of Reynolds number and Rayleigh number have been chosen in order to study mixed convection situations when the Reynolds number is larger as well as smaller as compared to free convection. The Prandtl number has been set to 0.72 corresponding to e.g. air and to 70 which is typical for e.g. some transformer oils, which are fluids that are frequently applied in buoyancy driven cooling applications.

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.

A Nondimensional Analysis of Boiling Dry a Vertical Channel with a Uniform Heat Flux

1981 ◽  
Vol 103 (4) ◽  
pp. 667-672 ◽  
Author(s):  
K. H. Sun ◽  
R. B. Duffey ◽  
C. Lin
Keyword(s):  
Heat Flux ◽  
Nuclear Power ◽  
Closed Form Solution ◽  
Vertical Channel ◽  
Form Solution ◽  
Uniform Heat Flux ◽  
Two Phase ◽  
Drift Flux ◽  
Rod Bundle ◽  
Uniform Heat

A thermal-hydraulic model has been developed for describing the phenomenon of hydrodynamically-controlled dryout, or the boil-off phenomenon, in a vertical channel with a spatially-averaged or uniform heat flux. The use of the drift flux correlation for the void fraction profile, along with mass and energy balances for the system, leads to a dimensionless closed-form solution for the predictions of two-phase mixture levels and collapsed liquid levels. The physical significance of the governing dimensionless parameters are discussed. Comparisons with data from single-tube experiments, a 3 × 3 rod bundle experiment, and the Three Mile Island nuclear power plant show good agreement.

Mixed convection flow of an electrically conducting fluid in a vertical channel with boundary conditions of the third kind

2014 ◽  
Vol 92 (11) ◽  
pp. 1387-1396 ◽  
Author(s):  
J.C. Umavathi ◽  
A.J. Chamkha
Keyword(s):  
Mixed Convection ◽  
Average Velocity ◽  
Vertical Channel ◽  
Perturbation Parameter ◽  
Conducting Fluid ◽  
Integration Scheme ◽  
Electrically Conducting ◽  
Nusselt Numbers ◽  
Electrically Conducting Fluid ◽  
External Fluid

In this study, the effects of viscous and Ohmic dissipation in steady, laminar, mixed, convection heat transfer for an electrically conducting fluid flowing through a vertical channel is investigated in both aiding and opposing buoyancy situations. The plates exchange heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. First, the simpler cases of either negligible Brinkman number or negligible Grashof number are addressed with the help of analytical solutions. The combined effects of buoyancy forces and viscous dissipation are analyzed using a perturbation series method valid for small values of the perturbation parameter. To relax the conditions on the perturbation parameter, the governing equations are also evaluated numerically by a shooting technique that uses the classical explicit Runge–Kutta method of four slopes as an integration scheme and the Newton–Raphson method as a correction scheme. In the examined cases of velocity and temperature fields, the Nusselt numbers at both the walls and the average velocity are explored. It is found that the velocity profiles for an open circuit (E > 0 or E < 0) lie in between the short circuit (E = 0). The graphical results illustrating the effects of various parameters on the flow as well as the average velocity and Nusselt numbers are presented for open and short circuits. In the absence of electric field load parameter and Hartmann number, the results agree with Zanchini (Int. J. Heat Mass Transfer, 41, 3949 (1998)). Further, the analytical and numerical solutions agree very well for small values of the perturbation parameter.

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