scholarly journals Finite Prandtl number convection with nearly insulating boundaries

1981 ◽  
Vol 24 (3) ◽  
pp. 339-347
Author(s):  
N. Riahi
Keyword(s):  
Heat Flux ◽  
Prandtl Number ◽  
Maximum Amount ◽  
Two Dimensional ◽  
Thermal Conductivities

Arbitrary Prandtl number convection in a layer with nearly insulating boundaries is investigated. For B1/3 > 3.95P (P is the Prandtl number and B being the ratio between the thermal conductivities of the boundary and of the fluid) two-dimensional rolls are stable. The heat transported by the stable rolls reaches its peak at a critical P = B1/3/5.77 beyond which the heat flux decreases with increasing P. For B1/3 = 3.95P rolls become unstable to disturbances in the form of rolls oriented at a right angle to the original rolls. For B1/3 > 3.95P square pattern convection represents the preferred stable convection. The stable square pattern transports the maximum amount of heat at a critical P = B1/3/3.7.

Numerical calculations of two-dimensional large Prandtl number convection in a box

2013 ◽  
Vol 729 ◽  
pp. 584-602 ◽  
Author(s):  
J. A. Whitehead ◽  
A. Cotel ◽  
S. Hart ◽  
C. Lithgow-Bertelloni ◽  
W. Newsome
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Heat Source ◽  
Prandtl Number ◽  
Steady Flow ◽  
Maximum Velocity ◽  
Numerical Calculations ◽  
Two Dimensional ◽  
Long Time ◽  
Constant Viscosity

AbstractConvection from an isolated heat source in a chamber has been previously studied numerically, experimentally and analytically. These have not covered long time spans for wide ranges of Rayleigh number Ra and Prandtl number Pr. Numerical calculations of constant viscosity convection partially fill the gap in the ranges $\mathit{Ra}= 1{0}^{3} {{\unicode{x2013}}}1{0}^{6} $ and $\mathit{Pr}= 1, 10, 100, 1000$ and $\infty $. Calculations begin with cold fluid everywhere and localized hot temperature at the centre of the bottom of a square two-dimensional chamber. For $\mathit{Ra}\gt 20\hspace{0.167em} 000$, temperature increases above the hot bottom and forms a rising plume head. The head has small internal recirculation and minor outward conduction of heat during ascent. The head approaches the top, flattens, splits and the two remnants are swept to the sidewalls and diffused away. The maximum velocity and the top centre heat flux climb to maxima during head ascent and then adjust toward constant values. Two steady cells are separated by a vertical thermal conduit. This sequence is followed for every value of $Pr$ number, although lower Pr convection lags in time. For $\mathit{Ra}\lt 20\hspace{0.167em} 000$ there is no plume head, and no streamfunction and heat flux maxima with time. For sufficiently large Ra and all values of Pr, an oscillation develops at roughly $t= 0. 2$, with the two cells alternately strengthening and weakening. This changes to a steady flow with two unequal cells that at roughly $t= 0. 5$ develops a second oscillation.

Roll-diameter dependence in Rayleigh convection and its effect upon the heat flux

1972 ◽  
Vol 54 (2) ◽  
pp. 351-367 ◽  
Author(s):  
G. E. Willis ◽  
J. W. Deardorff ◽  
R. C. J. Somerville
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Silicone Oil ◽  
Numerical Calculations ◽  
Two Dimensional ◽  
Numerical Integrations ◽  
Rayleigh Convection

The average roll diameter in Rayleigh convection for 2000 < R < 31000, where R is the Rayleigh number, has been measured from photographs of three convecting fluids: air, water and a silicone oil with a Prandtl number σ of 450. For air the average dimensionless roll diameter was found to depend uniquely upon R and to increase especially rapidly in the range 2000 < R < 8000. The fluids of larger σ exhibited strong hysteresis but also had average roll diameters tending to increase with R. The increase in average roll diameter with R tended to decrease with σ. Through use of two-dimensional numerical integrations for the case of air it was found that the increase in average roll diameter with R provides an explanation for the usual discrepancy in heat flux observed between experiment and two-dimensional numerical calculations which prescribe a fixed wavelength.

Numerical analysis of two dimensional pin fins with non-constant base heat flux

2005 ◽  
Vol 46 (6) ◽  
pp. 881-892 ◽  
Author(s):  
Yu-Ching Yang ◽  
Haw-Long Lee ◽  
Eing-Jer Wei ◽  
Jenn-Fa Lee ◽  
Tser-Son Wu
Keyword(s):  
Heat Flux ◽  
Numerical Analysis ◽  
Two Dimensional ◽  
Pin Fins

Finite Element Formulation for Two-Dimensional Inverse Heat Conduction Analysis

1992 ◽  
Vol 114 (3) ◽  
pp. 553-557 ◽  
Author(s):  
T. R. Hsu ◽  
N. S. Sun ◽  
G. G. Chen ◽  
Z. L. Gong
Keyword(s):  
Heat Flux ◽  
Finite Element ◽  
Heat Conduction ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Element Formulation ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
Discrete Point ◽  
Element Algorithm

This paper presents a finite element algorithm for two-dimensional nonlinear inverse heat conduction analysis. The proposed method is capable of handling both unknown surface heat flux and unknown surface temperature of solids using temperature histories measured at a few discrete point. The proposed algorithms were used in the study of the thermofracture behavior of leaking pipelines with experimental verifications.

scholarly journals Dryline Bulge Evolution in a Two-Dimensional Mixed-Layer Model

2004 ◽  
Vol 61 (21) ◽  
pp. 2528-2543 ◽  
Author(s):  
Glenn M. Auslander ◽  
Peter R. Bannon
Keyword(s):  
Heat Flux ◽  
Mixed Layer ◽  
Surface Heat Flux ◽  
Mixed Layer Depth ◽  
Surface Heat ◽  
Two Dimensional ◽  
Layer Model ◽  
Layer Depth ◽  
Inversion Strength ◽  
Mixed Layer Model

Abstract This study examines the diurnal response of a mixed-layer model of the dryline system to localized anomalies of surface heat flux, topography, mixed-layer depth, and inversion strength. The two-dimensional, mixed-layer model is used to simulate the dynamics of a cool, moist layer east of the dryline capped by an inversion under synoptically quiescent conditions. The modeled domain simulates the sloping topography of the U.S. Great Plains. The importance of this study can be related to dryline bulges that are areas with enhanced convergence that may trigger convection in suitable environmental conditions. All anomalies are represented by a Gaussian function in the horizontal whose amplitude, size, and orientation can be altered. A positive, surface-heat-flux anomaly produces increased mixing that creates a bulge toward the east, while a negative anomaly produces a westward bulge. Anomalies in topography show a similar trend in bulge direction with a peak giving an eastward bulge, and a valley giving a westward bulge. Anomalies in the initial mixed-layer depth yield an eastward bulge in the presence of a minimum and a westward bulge for a maximum. An anomaly in the initial inversion strength results in a westward bulge when the inversion is stronger, and an eastward bulge when the inversion is weak. The bulges observed in this study at 1800 LT ranged from 400 to 600 km along the dryline and from 25 to 80 km across the dryline. When the heating ceases at night, the entrainment and eastward movement of the line stops, and the line surges westward. This westward surge at night has little dependence on the type of anomaly applied. Whether a westward or eastward bulge was present at 1800 LT, the surge travels an equal distance toward the west. However, the inclusion of weak nocturnal friction reduces the westward surge by 100 to 200 km due to mechanical mixing of the very shallow leading edge of the surge. All model runs exhibit peaks in the mixed-layer depth along the dryline at 1800 LT caused by enhanced boundary layer convergence and entrainment of elevated mixed-layer air into the mixed layer. These peaks appear along the section of the dryline that is least parallel to the southerly flow. They vary in amplitude from 4 to 9 km depending on the amplitude of the anomaly. However, the surface-heat-flux anomalies generally result in peaks at the higher end of this interval. It is hypothesized that the formation of these peaks may be the trigger for deep convection along the dryline in the late afternoon.

Modeling of Mixed Convection Between Vertical Parallel Plates in Electric Equipment Immersed in High-Pr Liquids

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Thomas B. Gradinger ◽  
T. Laneryd
Keyword(s):  
Heat Flux ◽  
Reynolds Number ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Parallel Plates ◽  
One Dimensional ◽  
Electric Equipment

Natural-convection cooling with oil or other fluids of high Prandtl number plays an important role in many technical applications such as transformers or other electric equipment. For design and optimization, one-dimensional (1D) flow models are of great value. A standard configuration in such models is flow between vertical parallel plates. Accurate modeling of heat transfer, buoyancy, and pressure drop for this configuration is therefore of high importance but gets challenging as the influence of buoyancy rises. For increasing ratio of Grashof to Reynolds number, the accuracy of one-dimensional models based on the locally forced-flow assumption drops. In the present work, buoyancy corrections for use in one-dimensional models are developed and verified. Based on two-dimensional (2D) simulations of buoyant flow using finite-element solver COMSOL Multiphysics, corrections are derived for the local Nusselt number, the local friction coefficient, and a parameter relating velocity-weighted and volumetric mean temperature. The corrections are expressed in terms of the ratio of local Grashof to Reynolds number and a normalized distance from the channel inlet, both readily available in a one-dimensional model. The corrections universally apply to constant wall temperature, constant wall heat flux, and mixed boundary conditions. The developed correlations are tested against two-dimensional simulations for a case of mixed boundary conditions and are found to yield high accuracy in temperature, wall heat flux, and wall shear stress. An application example of a natural-convection loop with two finned heat exchangers shows the influence on mass-flow rate and top-to-bottom temperature difference.

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