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.

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.

A Parametric Study of Laminar Mixed Convection in a Square Cavity Using Numerical Simulation Techniques

2012 ◽  
Author(s):  
K. Hallenbeck ◽  
K. M. Akyuzlu
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Parametric Study ◽  
Numerical Experiments ◽  
Working Fluid ◽  
Two Dimensional ◽  
Square Cavity ◽  
Laminar Mixed Convection ◽  
Prandtl Numbers ◽  
Nusselt Number Correlation

A parametric study is conducted using numerical experimentation to construct an empirical Nusselt number correlation in terms of Richardson and Prandtl numbers for laminar mixed convection in a square cavity. The square cavity under study is assumed to be filled with a compressible fluid. The bottom of the cavity is insulated and stationary where as the top of the cavity (the lid) is pulled at constant speed. The vertical walls of the cavity are kept at constant but unequal temperatures. A two-dimensional, mathematical model is adopted to predict the momentum and heat transfer inside this rectangular cavity. This physics based mathematical model consists of conservation of mass, momentum (two-dimensional, unsteady Navier-Stokes equations for compressible flows) and energy equations for the enclosed fluid subjected to appropriate boundary and initial conditions. The compressibility of the working fluid is represented by an ideal gas relation. The thermodynamic and transport properties of the working fluid are assumed to be constant. The governing equations are discretized using second order accurate central differencing for spatial derivatives and second order finite differencing (based on Taylor expansion) for the time derivatives. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns of the problem. Grid independence and time convergence studies were carried to determine the accuracy of the square mesh adopted for the present study. Two benchmark cases (driven cavity and rectangular channel flows) were studied to verify the accuracy of the CMSIP. Numerical experiments were then carried out to simulate the heat transfer characteristics of mixed convection flow for different Richardson numbers in the range of 0.036<Ri<1.00 where the Reynolds number is kept less than 2000 to ensure laminar flow conditions inside the cavity. The velocity vector field maps (circulation patterns) and temperature contours, and temperature profiles along the horizontal axes were generated for different Prandtl numbers ranging from 0.3 to 1. Wall heat fluxes and Nusselt numbers were determined for each parametric study. The collected data from the numerical experiments were then used to construct an empirical Nusselt number correlation in terms of Richardson and Prandtl numbers.

Combined gas radiation and laminar mixed convection in vertical concentric annuli

2002 ◽  
Author(s):  
Ezeddine Sediki ◽  
Anouar Soufiani ◽  
Mohamed Salah Sifaoui
Keyword(s):  
Mixed Convection ◽  
Gas Radiation ◽  
Laminar Mixed Convection

Coupled Thermal Radiation and Mixed Convection Step Flow of Nongray Gas

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
M. Atashafrooz ◽  
S. A. Gandjalikhan Nassab ◽  
K. Lari
Keyword(s):  
Mixed Convection ◽  
Radiative Transfer Equation ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Discrete Ordinate ◽  
Full Spectrum ◽  
Step Flow ◽  
Laminar Mixed Convection ◽  
Gray Medium ◽  
Hydrodynamic Behaviors

The main goal of this paper is to analyze the thermal and hydrodynamic behaviors of laminar mixed convection flow of a nongray radiating gas over an inclined step in an inclined duct. The fluid is considered an air mixture with 10% CO2 and 20% H2O mole fractions, which is treated as homogeneous, absorbing, emitting, and nonscattering medium. The full-spectrum k-distribution (FSK) method is used to handle the nongray part of the problem, while the radiative transfer equation (RTE) is solved using the discrete ordinate method (DOM). In addition, the results are obtained for different medium assumptions such as pure mixed convection and gray medium to compare with the nongray calculations as a real case. The results show that in many cases, neglecting the radiation part in computations and also use of gray simulations are not acceptable and lead to considerable errors, especially at high values of the Grashof number in mixed convection flow.

MIXED CONVECTION IN AN INCLINED AND LID-DRIVEN RECTANGULAR ENCLOSURE HEATED AND COOLED ON ADJACENT WALLS

2008 ◽  
Vol 32 (2) ◽  
pp. 213-226 ◽  
Author(s):  
Elif Büyük Öğüt
Keyword(s):  
Mixed Convection ◽  
Differential Quadrature Method ◽  
Side Wall ◽  
Temperature Fields ◽  
Convection Flow ◽  
Rectangular Enclosure ◽  
Aspect Ratios ◽  
Laminar Mixed Convection ◽  
Inclination Angles ◽  
Steady Laminar

Steady, laminar, mixed convection flow was considered in an inclined lid-driven rectangular enclosure heated from one side moving with a constant speed and cooled from the stationary adjacent side while the other sides are kept stationary and adiabatic. The governing equations were solved numerically for the stream function, vorticity, and temperature ratio using the differential quadrature method for various Reynolds, Grashof, and Richardson numbers as well as different aspect ratios and inclination angles for the enclosure. The results show that the motion of the side wall, the aspect ratio, and the inclination angle of the enclosure had significant effects on the flow and temperature fields.

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