Heat Transfer Modeling and the Assumption of Zero Wall Temperature Fluctuations

1994 ◽  
Vol 116 (4) ◽  
pp. 855-863 ◽  
Author(s):  
T. P. Sommer ◽  
R. M. C. So ◽  
H. S. Zhang
Keyword(s):  
Heat Transfer ◽  
Wall Temperature ◽  
Transfer Problem ◽  
Solid Wall ◽  
Temperature Fluctuations ◽  
Wall Turbulence ◽  
Turbulent Heat ◽  
Fluctuating Temperature ◽  
Temperature Variance ◽  
Near Wall

At present, it is not clear how the fluctuating temperature at the wall can be properly specified for near-wall turbulent heat-flux models. The conventional approach is to assume zero fluctuating temperature or zero gradient for the temperature variance at the wall. These are idealized specifications and the latter condition could lead to an ill-posed problem for fully developed pipe and channel flows. In this paper, the validity and extent of the zero fluctuating wall temperature condition for heat transfer calculations are examined. The approach taken is to assume Taylor series expansions in the wall normal coordinate for the fluctuating quantities that are general enough to account for both zero and nonzero temperature fluctuations at the wall and to develop a near-wall turbulence model allowing finite values of the wall temperature variance. As for the wall temperature variance boundary condition, it is estimated by solving the coupled heat transfer problem between the fluid and the solid wall. The eddy thermal conductivity is calculated from the temperature variance and its dissipation rate. Heat transfer calculations assuming both zero and nonzero fluctuating wall temperature reveal that the zero fluctuating wall temperature assumption is quite valid for the mean field and the associated integral heat transfer properties. The effects of nonzero fluctuating wall temperature on the fluctuating field are limited only to a small region near the wall for most fluid/solid combinations considered.

Numerical Investigation of Near-Wall Turbulent Heat Transfer Taking Into Account the Unsteady Heat Conduction in the Solid Wall

1989 ◽  
Vol 111 (2) ◽  
pp. 385-392 ◽  
Author(s):  
N. Kasagi ◽  
A. Kuroda ◽  
M. Hirata
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Solid Wall ◽  
Wall Turbulence ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Turbulence Structure ◽  
Temperature Variance ◽  
Unsteady Heat Conduction ◽  
Near Wall

The deterministic near-wall turbulence model developed by Kasagi et al. (1984b) is used in a numerical analysis of turbulent heat transfer, in which the unsteady heat conduction inside the wall associated with the turbulent flow unsteadiness is taken into account. Unlike the typical methodology based on Reynolds decomposition, the algebraic expressions for the three fluctuating velocities given by the model are directly introduced into the governing energy equation. From the numerical results of the unsteady conjugate heat transfer, the statistical quantities, such as temperature variance, turbulent heat flux, and turbulent Prandtl number, are obtained for fluids of various Prandtl numbers. It is demonstrated that the near-wall behavior of these quantities is strongly influenced by the thermal properties and thickness of the wall. In addition, the budget of the temperature variance associated with coherent turbulence structure is calculated and, except for dissipation, each budget term is in qualitative agreement with the experiment.

A Stochastic Lagrangian Model for Near-Wall Turbulent Heat Transfer

1997 ◽  
Vol 119 (1) ◽  
pp. 46-52 ◽  
Author(s):  
S. Mazumder ◽  
M. F. Modest
Keyword(s):  
Heat Transfer ◽  
Joint Probability ◽  
Molecular Transport ◽  
Temperature Fluctuations ◽  
Reynolds Stress Model ◽  
Constant Heat Flux ◽  
Lagrangian Model ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Near Wall

The modeling of near-wall turbulent heat transfer necessitates appropriate description of near-wall effects, namely, molecular transport, production of turbulence by inhomogeneities, and dissipation of the temperature fluctuations by viscosity. A stochastic Lagrangian model, based on the velocity-composition joint probability density function (PDF) method, has been proposed. The proposed model, when compared with experimental and direct numerical simulation (DNS) data, overdamps the dissipation of the temperature fluctuations in the inertial sublayer, but reaches the correct limit at the wall. The performance of the model has also been compared to the standard k-ε and the algebraic Reynolds stress model (ARSM) for both constant heat flux and constant temperature boundary conditions at large Reynolds numbers. The Lagrangian nature of the model helps eliminate numerical diffusion completely.

DNS of Turbulent Heat Transfer in Channel Flow With Heat Conduction in the Solid Wall

2001 ◽  
Vol 123 (5) ◽  
pp. 849-857 ◽  
Author(s):  
Iztok Tiselj ◽  
Robert Bergant ◽  
Borut Mavko ◽  
Ivan Bajsic´ ◽  
Gad Hetsroni
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Channel Flow ◽  
Temperature Fluctuations ◽  
Heat Fluxes ◽  
Wall Turbulence ◽  
Temperature Fields ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Fluid Temperature

The Direct Numerical Simulation (DNS) of the fully developed velocity and temperature fields in the two-dimensional turbulent channel flow coupled with the unsteady conduction in the heated walls was carried out. Simulations were performed at constant friction Reynolds number 150 and Prandtl numbers between 0.71 and 7 considering the fluid temperature as a passive scalar. The obtained statistical quantities like root-mean-square temperature fluctuations and turbulent heat fluxes were verified with existing DNS studies obtained with ideal thermal boundary conditions. Results of the present study were compared to the findings of Polyakov (1974), who made a similar study with linearization of the fluid equations in the viscous sublayer that allowed analytical approach and results of Kasagi et al. (1989), who performed similar calculation with deterministic near-wall turbulence model and numerical approach. The present DNS results pointed to the main weakness of the previous studies, which underestimated the values of the wall temperature fluctuations for the limiting cases of the ideal-isoflux boundary conditions. With the results of the present DNS it can be decided, which behavior has to be expected in a real fluid-solid system and which one of the limiting boundary conditions is valid for calculation, or whether more expensive conjugate heat transfer calculation is required.

Turbulent Statistics of Rarefield Flows in Microchannel Flow and Heat Transfer

2004 ◽  
Author(s):  
G. X. Li ◽  
W. Q. Tao ◽  
Z. Y. Li ◽  
B. Yu
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Shear Stress ◽  
Reynolds Shear Stress ◽  
Wall Region ◽  
Turbulent Heat ◽  
Time Step ◽  
Temperature Variance ◽  
Flow And Heat Transfer ◽  
Turbulent Statistics

Direct numerical simulation has been carried out to investigate the effect of weak rarefaction on turbulent gas flow and heat transfer characteristics in mirochannel. The Reynolds number based on the friction velocity and the channel half width is 150. Grid number is 64×128×64. Fractional time step method is employed for the unsteady Navier-Stokes equations, and the governing equations are discretized with Finite Difference Method. Statistical quantities such as turbulent intensity, Reynolds shear stress, turbulent heat flux and temperature variance are obtained under various Knudsen number from 0 to 0.05. The results show that rarefaction can influence the turbulent flow and heat transfer statistics. The streamwise mean velocity and temperature increase with increase of Kn number. In the near wall region rarefaction can increase the turbulent intensities and temperature variance. The effect of rarefaction on Reynolds shear stress and wall-normal heat flux are presented. The instantaneous velocity fluctuations in the vicinity of the wall are visualized and the influence of Kn number on the flow structure is discussed.

Effect of Constant Heat Flux Boundary Condition on Wall Temperature Fluctuations

2000 ◽  
Vol 123 (2) ◽  
pp. 213-218 ◽  
Author(s):  
A. Mosyak ◽  
E. Pogrebnyak ◽  
G. Hetsroni
Keyword(s):  
Boundary Conditions ◽  
Wall Temperature ◽  
Solid Wall ◽  
Rectangular Channel ◽  
Temperature Fluctuations ◽  
Temperature Fields ◽  
Flux Boundary Condition ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Thermal Entrance

An experimental study of the wall temperature fluctuations under different thermal-wall boundary conditions was carried out. Statistics obtained from the experiments are compared with existing experimental and numerical data. The wall temperature fields are also examined in terms of the coherent thermal structures. In addition the effect of the thermal entrance region on the wall temperature distribution is also studied. For water flow in a flume and in a rectangular channel, the mean spacing of the thermal streaks does not depend on the thermal entrance length and on the type of thermal-wall boundary conditions. The wall temperature fluctuations depend strongly on the type of wall thermal boundary conditions. Overall, the picture that emerges from this investigation confirms the hypothesis that moderate-Prandtl-number heat transfer at a solid wall is governed by the large-scale coherent flow structures.

Molecular Dynamics Simulations of Coupling between Flow and Heat Transfer in a Nanochannel

2012 ◽  
Vol 455-456 ◽  
pp. 155-160
Author(s):  
Zhi Hai Kou ◽  
Min Li Bai
Keyword(s):  
Heat Transfer ◽  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Wall Temperature ◽  
Solid Wall ◽  
Slip Length ◽  
Three Dimensional ◽  
Flow And Heat Transfer ◽  
Kapitza Length ◽  
Dynamics Simulations

Simulation of microscale thermo-fluidic transport has attracted considerable attention in recent years owing to rapid advances in nanoscience and nanotechnology. The three-dimensional molecular dynamics simulations are performed for coupling between flow and heat transfer in a nanochannel. Effects of interface wettability, shear rate and wall temperature are discussed. It is found that there exist the relatively immobile solid-like layers adjacent to each solid wall with higher number density. Both slip length and Kapitza length at the solid-liquid interface increase linearly with the increasing wall temperature. The Kapitza length decreases monotonously with the increasing shear rates. The slip length is found to be overestimated by 5.10% to 10.27%, while Kapitza length is overestimated by 8.92% to 19.09% for the solid-solid interaction modeled by the Lennard-Jones potential.

Coherent motions and heat transfer in a wall turbulent shear flow

1995 ◽  
Vol 305 ◽  
pp. 127-157 ◽  
Author(s):  
Y. Nagano ◽  
M. Tagawa
Keyword(s):  
Heat Transfer ◽  
Heat Transport ◽  
Phase Relationship ◽  
Transport Processes ◽  
Wall Turbulence ◽  
Ar Model ◽  
Turbulent Heat Transfer ◽  
Good Time ◽  
Turbulent Shear ◽  
Turbulent Heat

In wall turbulence, it is widely accepted that the coherent motions determine the essential features of turbulent transport phenomena. In the present study, we have refined a trajectory-based detection algorithm for coherent motions and have investigated the relationship between coherent motions and scalar (heat) transfer from a structural point of view, i. e. trajectory analysis of the VITA heat transfer events, extraction of key flow modules and the relevant heat transport, and the prediction of passive scalar transfer by means of an autoregressive (AR) model. As a result, it is shown that the phase relationship of fluctuating velocity components dominates the essential characteristics of the transport processes of heat and momentum in wall turbulence and there exist distinct differences in individual correspondence between the coherent motions and heat transport processes, neither of which can be revealed by the widely used VITA technique. Also, the AR model is shown to provide good time-series predictions for turbulent heat transfer associated with coherent structures near the wall.

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