scholarly journals Modelling turbulent heat transfer in rough channels using phenomenological theory

2021 ◽  
Vol 2116 (1) ◽  
pp. 012025
Author(s):  
J W R Peeters
Keyword(s):  
Heat Transfer ◽  
Phenomenological Theory ◽  
Velocity Fields ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Wall Roughness ◽  
Thermal Fields ◽  
Nusselt Numbers ◽  
Rough Walls ◽  
Friction Factors

Abstract Rough walls are often encountered in industrial heat transfer equipment. Even though it is well known that a rough wall affects velocity fields and thermal fields differently (and therefore also skin friction factors and Stanton or Nusselt numbers), predicting the effect of rough walls on turbulent heat transfer remains difficult. A relation between the scalar spectrum and the Stanton number is derived for channels with both smooth and rough walls. It is shown that the new relation agrees reasonably well with recent DNS experiments for wall roughness sizes of k + < 150 and when Pr = 0.7 − 1.0. Under these conditions, a thermal analogue of Moody’s diagram can be created using the newly developed relation.

Turbulent Heat Transfer and Fluid Flow in an Unsymmetrically Heated Triangular Duct

1980 ◽  
Vol 102 (4) ◽  
pp. 590-597 ◽  
Author(s):  
C. A. C. Altemani ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Hydraulic Diameter ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
General Applicability ◽  
Thermal Boundary Conditions ◽  
Nusselt Numbers ◽  
Friction Factors ◽  
Turbulent Airflow ◽  
Thermal Entrance

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.

Periodically Converging-Diverging Tubes and Their Turbulent Heat Transfer, Pressure Drop, Fluid Flow, and Enhancement Characteristics

1984 ◽  
Vol 106 (1) ◽  
pp. 55-63 ◽  
Author(s):  
P. Souza Mendes ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Surface Area ◽  
Equal Mass ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Transfer Coefficients ◽  
Pressure Drops ◽  
Heat Transfer Coefficients ◽  
Friction Factors

A comprehensive experimental study was performed to determine entrance region and fully developed heat transfer coefficients, pressure distributions and friction factors, and patterns of fluid flow in periodically converging and diverging tubes. The investigated tubes consisted of a succession of alternately converging and diverging conical sections (i.e., modules) placed end to end. Systematic variations were made in the Reynolds number, the taper angle of the converging and diverging modules, and the module aspect ratio. Flow visualizations were performed using the oil-lampblack technique. A performance analysis comparing periodic tubes and conventional straight tubes was made using the experimentally determined heat transfer coefficients and friction factors as input. For equal mass flow rate and equal transfer surface area, there are large enhancements of the heat transfer coefficient for periodic tubes, with accompanying large pressure drops. For equal pumping power and equal transfer surface area, enhancements in the 30–60 percent range were encountered. These findings indicate that periodic converging-diverging tubes possess favorable enhancement characteristics.

Turbulent Heat Transfer in an Enclosure With a Horizontal Permeable Plate in the Middle

2006 ◽  
Vol 128 (11) ◽  
pp. 1122-1129 ◽  
Author(s):  
Edimilson J. Braga ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Heat Transfer ◽  
Porous Plate ◽  
Porous Matrix ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Turbulent Natural Convection ◽  
Nusselt Numbers ◽  
Model Solutions ◽  
Volume Method ◽  
Rayleigh Numbers

Turbulent natural convection in a vertical two-dimensional square cavity, isothermally heated from below and cooled at the upper surface, is numerically analyzed using the finite volume method. The enclosure has a thin horizontal porous obstruction, made of a highly porous material and extremely permeable, located at the cavity midheight. Governing equations are written in terms of primitive variables and are recast into a general form. For empty cavities, no discrepancies result for the Nusselt number when laminar and turbulent model solutions are compared for Rayleigh numbers up to 107. Also, in general the porous obstruction decreases the heat transfer across the heated walls showing overall lower Nusselt numbers when compared with those without the porous obstruction. However, the presence of a porous plate in the cavity seems to force an earlier separation from laminar to turbulence model solutions due to higher generation rates of turbulent kinetic energy into the porous matrix.

Turbulent Heat Transfer in Corrugated-Wall Channels With and Without Fins

1987 ◽  
Vol 109 (1) ◽  
pp. 62-67 ◽  
Author(s):  
R. S. Amano ◽  
A. Bagherlee ◽  
R. J. Smith ◽  
T. G. Niess
Keyword(s):  
Heat Transfer ◽  
Numerical Study ◽  
Reynolds Stress Model ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Reynolds Stresses ◽  
Flow Recirculation ◽  
Nusselt Numbers ◽  
Visible Effect ◽  
Corrugated Wall

A numerical study is performed examining flow and heat transfer characteristics in a channel with periodically corrugated walls. The complexity of the flow in this type of channel is demonstrated by such phenomena as flow impingement on the walls, separation at the bend corners, flow reattachment, and flow recirculation. Because of the strong nonisotropic nature of the turbulent flow in the channel, the full Reynolds-stress model was employed for the evaluation of turbulence quantities. Computations are made for several different corrugation periods and for different Reynolds numbers. The results computed by using the present model show excellent agreement with experimental data for mean velocities, the Reynolds stresses, and average Nusselt numbers. The study was further extended to a channel flow where fins are inserted at bends in the channel. It was observed that the insertion of fins in the flow passage has a visible effect on flow patterns and skin friction along the channel wall.

Turbulent Heat Transfer Downstream of an Unsymmetric Blockage in a Tube

1978 ◽  
Vol 100 (4) ◽  
pp. 588-594 ◽  
Author(s):  
K. K. Koram ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Turbulent Heat Transfer ◽  
Working Fluid ◽  
Initial Increase ◽  
Turbulent Heat ◽  
Transfer Coefficients ◽  
Tube Cross Section ◽  
Nusselt Numbers ◽  
Prandtl Numbers

Pipe flow experiments were performed to study the heat transfer in the separation, reattachment, and redevelopment regions downstream of a wall-attached blockage in the form of a segmental orifice plate. Water was the working fluid, and the Reynolds number encompassed the range from about 10,000–60,000. The extent of the flow blockage was varied from one-fourth to three-fourths of the tube cross section. Heat transfer coefficients were determined both around the circumference of the uniformly heated tube and along its length. The axial distributions of the circumferential average Nusselt numbers show an initial increase, then attain a maximum, and subsequently decrease toward the fully developed regime. These Nusselt numbers are much higher than those for a conventional thermal entrance region. The unsymmetric blockage induces variations of the Nusselt number around the circumference of the tube. Axial distributions of the Nusselt number at various fixed angular positions reveal the presence of two types of maxima. One of these is associated with the reattachment of the flow and the other occurs due to the impingement of flow deflected by the blockage onto the tube wall. The circumferential variations decay with increasing downstream distance, but the rate of decay for the case of the smallest blockage is remarkably slow. Although most of the tests were performed for Pr = 4, supplementary experiments for Pr = 8 showed that the results are valid for a range of Prandtl numbers.

An Experimental and Numerical Investigation on the Thermal-Hydraulic Performance of Double Notched Plate

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Lei Zhang ◽  
Defu Che
Keyword(s):  
Heat Transfer ◽  
Swirling Flow ◽  
Reynolds Numbers ◽  
Velocity Fields ◽  
Local Information ◽  
Transfer Coefficients ◽  
Enhanced Heat Transfer ◽  
Heat Transfer Coefficients ◽  
Nusselt Numbers ◽  
Friction Factors

The double notched (DN) plate is commonly used in rotary air preheaters, but relevant investigations are rare. Thus, thermal-hydraulic performances of the DN plate are investigated in this paper. A single-blow, transient technique is refined and then used to measure the overall mean heat transfer coefficients and friction factors. A validated numerical method is also utilized to provide local information. The measured results show that the performance of the DN plate approaches that of the double undulated (DU) plate and lies between that of the cross corrugated (CC) plate and the parallel plate. No swirling flow pattern is identified in the predicted velocity fields. Basically, two types of flow are observed: wavy channel flow and pipe flow. High or low Nusselt numbers, Nu, are obtained at the luff or lee side of undulations and notches, respectively. Nu values increase and Nu distributions become more homogenous with increasing Reynolds numbers, Re. A recommendation is made that the DN plate be operated under moderate Re to achieve homogenous and enhanced heat transfer, given the allowable pressure drop.

Heat Transfer and Pressure Drop in an Annular Gap With Surface Spoilers

1961 ◽  
Vol 83 (2) ◽  
pp. 189-197 ◽  
Author(s):  
G. A. Kemeny ◽  
J. A. Cyphers
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Annular Space ◽  
Circular Tubes ◽  
Annular Gap ◽  
Friction Factors ◽  
Inner Surface ◽  
Turbulent Water

Heat-transfer and pressure drop data are presented for turbulent water flow in the annular space between concentric tubes. Heat was transferred to the liquid from the inner surface which was equipped with various surface spoiler configurations. A common outer tube was used which was maintained smooth and adiabatic for all tests. An empirical formula is given which correlates friction factors for circular tubes and annular gaps, or narrow flat passages, with semicircular spoilers on either one or both sides. The use of such friction factors in the Martinelli equation for turbulent heat transfer gives satisfactory estimates of the heat transfer for spoiler configurations.

Turbulent Heat Transfer Augmentation and Friction in Periodic Fully Developed Channel Flows

1992 ◽  
Vol 114 (1) ◽  
pp. 56-64 ◽  
Author(s):  
T.-M. Liou ◽  
J.-J. Hwang
Keyword(s):  
Heat Transfer ◽  
Hot Spots ◽  
Channel Flows ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Heat Transfer Augmentation ◽  
Relative Contribution ◽  
Friction Factors

Measurements are presented of the distribution of average friction factors (f) as well as local and average (Nu) heat transfer coefficients for fully developed channel flows with two rib-roughened opposite walls. The temperature measurements were made by using both a laser holographic interferometer and thermocouples. In addition, the reattachment length was determined by flow visualization. The Reynolds number (Re) was varied from 5.0 × 103 to 5.4 × 104; the rib pitch-to-height ratios (Pi/H) were 10, 15, and 20; and the rib height-to-hydraulic diameter ratios (H/De) were 0.063, 0.081, and 0.106. The detailed results allowed the peaks of heat transfer augmentation and the regions susceptible to hot spots to be located and allowed the relative contribution of the rib surface and the channel wall to the heat transfer augmentation to be determined. Moreover, relative to a smooth duct, the enhancement of both Nu and f at various Re, Pi/H, and H/De was documented in detail. Furthermore, compact correlations in terms of Re, Pi/H, and H/De were developed for both Nu and f.

Turbulent Heat Transfer in a Horizontal Enclosure With a Thin Porous Obstruction in the Middle

2003 ◽  
Author(s):  
Edimilson J. Braga ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Heat Transfer ◽  
Porous Matrix ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Turbulent Regime ◽  
Square Cavity ◽  
Turbulent Natural Convection ◽  
Nusselt Numbers ◽  
Volume Method ◽  
Generalized Coordinate

Turbulent natural convection in a horizontal two-dimensional square cavity, isothermally heated from below and cooled at the upper surface, is numerically analyzed using the finite volume method and a generalized coordinate system. The enclosure has a thin horizontal porous obstruction located at the cavity mid height. Governing equations are written in terms of primitive variables and are recast into a general from. In general, the porous obstruction decreases the heat transfer across the heated walls showing an overall lower Nusselt numbers when compared with those without the same porous obstruction. However, the presence of a porous obstruction. However, the presence of a porous obstruction in a square cavity seems to force an earlier transition from laminar to turbulent regime due to higher generation rates of turbulent kinetic energy into the porous matrix.

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