Discussion: “Experiments on Turbulent Heat Transfer in a Tube With Circumferentially Varying Thermal Boundary Conditions” (Black, A. W., and Sparrow, E. M., 1967, ASME J. Heat Transfer, 89, pp. 258–268)

Experiments were performed to determine entrance-region and fully developed heat transfer characteristics for turbulent airflow in an unsymmetrically heated equilateral triangular duct; friction factors were also measured. Two of the walls were heated while the third was not directly heated. The resulting thermal boundary conditions consisted of uniform heating per unit axial length and circumferentially uniform temperature on the heated walls. Special techniques were employed to minimize extraneous heat losses, and numerical finite-difference solutions played an important role in both the design of the apparatus and in the data reduction. The thermal entrance lengths required to attain thermally developed conditions were found to increase markedly with the Reynolds number and were generally greater than those for conventional pipe flows—a behavior which can be attributed to the unsymmetric heating. The fully developed Nusselt numbers were compared with circular tube correlations from the literature, from which it was shown that the hydraulic diameter is not fully sufficient to rationalize the circular and noncircular duct results. However, excellent Nusselt number predictions were obtained by employing the Petukhov-Popou correlation in conjunction with the measured friction factors for the triangular duct. This approach may have general applicability for predicting noncircular duct heat transfer. The friction factor results also affirmed the inadequacies of the hydraulic diameter but supported a general noncircular duct correlation available in the literature.

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Conjugated turbulent heat transfer with axial conduction in wall and convection boundary conditions in a parallel-plate channel

International Journal of Heat and Fluid Flow ◽

10.1016/0142-727x(92)90002-q ◽

1992 ◽

Vol 13 (4) ◽

pp. 322-328 ◽

Cited By ~ 6

Author(s):

R.O.C. Guedes ◽

M.N. Özişik

Keyword(s):

Heat Transfer ◽

Boundary Conditions ◽

Parallel Plate ◽

Turbulent Heat Transfer ◽

Turbulent Heat ◽

Axial Conduction ◽

Convection Boundary ◽

Plate Channel

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Experiments on Turbulent Heat Transfer in a Tube With Circumferentially Varying Thermal Boundary Conditions

Journal of Heat Transfer ◽

10.1115/1.3614375 ◽

1967 ◽

Vol 89 (3) ◽

pp. 258-268 ◽

Cited By ~ 22

Author(s):

A. W. Black ◽

E. M. Sparrow

Keyword(s):

Heat Transfer ◽

Heat Flux ◽

Boundary Conditions ◽

Wall Heat Flux ◽

Turbulent Heat Transfer ◽

Working Fluid ◽

Turbulent Heat ◽

Turbulent Diffusivity ◽

Transfer Coefficients ◽

Heat Transfer Coefficients

An experimental investigation, supported by analysis, was performed to determine the heat transfer characteristics for turbulent flow in a circular tube with circumferentially varying wall temperature and wall heat flux. Air was the working fluid. The desired boundary conditions were achieved by electric heating within the wall of a tube whose thickness varied circumferentially. In this way, ratios of maximum-to-minimum wall heat flux as large as two were attained. Local heat transfer coefficients, deduced from the experimental data, display a circumferential variation that is substantially smaller than the heat flux variation. In general, lower heat transfer coefficients correspond to circumferential locations of greater heating, while higher coefficients correspond to locations of lesser heating. The predictions of prior analyses appear to overestimate the circumferential variation of the heat transfer coefficient. A specially designed probe was employed to measure the radial and circumferential temperature distributions within the flowing airstream. On the basis of these measurements, as well as from the heat transfer results, it is concluded that, in the neighborhood of the wall, the tangential turbulent diffusivity is greater than the radial turbulent diffusivity. The axial thermal development was found to be more rapid on the lesser-heated side of the tube than on the greater-heated side. Experimentally determined circumferential-average heat transfer coefficients agreed well with the predictions of analysis.

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Rough-wall turbulent heat transfer with step-wall temperature boundary conditions

Journal of Thermophysics and Heat Transfer ◽

10.2514/3.322 ◽

1992 ◽

Vol 6 (1) ◽

pp. 84-90 ◽

Cited By ~ 1

Author(s):

Robert P. Taylor ◽

M. H. Hosni ◽

James W. Garner ◽

Hugh W. Coleman

Keyword(s):

Heat Transfer ◽

Boundary Conditions ◽

Wall Temperature ◽

Rough Wall ◽

Turbulent Heat Transfer ◽

Turbulent Heat ◽

Temperature Boundary

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

Journal of Heat Transfer ◽

10.1115/1.1389060 ◽

2001 ◽

Vol 123 (5) ◽

pp. 849-857 ◽

Cited By ~ 66

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.

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