Generalized Lévêque Solution for Ducts of Arbitrary Cross-Section

2021 ◽  
Author(s):  
Ted Bennett
Keyword(s):  
Heat Flux ◽  
Shear Stress ◽  
Cross Section ◽  
Constant Heat Flux ◽  
Arbitrary Cross Section ◽  
Regular Polygons ◽  
Constant Heat ◽  
Original Analysis ◽  
Wall Condition ◽  
Generalized Correlation

Abstract The asymptotic limit for perimeter averaged convection is generalized for short ducts of arbitrary cross-section. A correction factor to Lévêque's original analysis is derived in terms of the state of wall shear stress under conditions of fully developed flows for walls of constant temperature (T) and constant heat flux (H1 and H2). This analysis is performed for four duct geometries: elliptic, rhombic, rectangular, and regular polygons. The importance of this correction is greatest for the H2 wall condition and for ducts having walls with acute corners. The results of this analysis can be incorporated into a generalized correlation for the full Graetz problem in ducts of arbitrary cross-section.

Correlations for Convection in Hydrodynamically Developing Laminar Duct Flow

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
T. D. Bennett
Keyword(s):  
Heat Flux ◽  
Constant Heat Flux ◽  
Arbitrary Cross Section ◽  
First Principle ◽  
Duct Flow ◽  
Constant Heat ◽  
Aspect Ratios ◽  
New Correlation ◽  
Generalized Correlation ◽  
Better Than

Abstract A generalized correlation for combined entry convection in ducts of arbitrary cross section has been developed. The correlation is constructed for the average Nusselt number using knowledge of fully developed transport constants. The general correlation reproduces the first principle solutions for the well-established round and parallel plate duct geometries to within ±5% for both constant temperature and constant heat flux wall conditions when Pr ≥ 0.7. A survey of the literature demonstrates that the new generalized correlation performs as well or better than existing correlations, which are expressed for specific geometries and wall conditions. The new correlation is generally in good agreement with the first principle solutions of less common duct geometries so long as the duct has a convective surface equal to the wetted perimeter. The new correlation is not recommended for ducts having small aspect ratios that pinch the flow when convection is prescribed by the H2 constant heat flux wall condition.

Refinement of the Generalized Graetz Problem Correlation With New Benchmark Calculations

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
T. D. Bennett
Keyword(s):  
Constant Heat Flux ◽  
Fundamental Constants ◽  
Constant Heat ◽  
Fully Developed Flow ◽  
Flow Friction ◽  
Graetz Problem ◽  
Wall Condition ◽  
Benchmark Solutions ◽  
Annular Tube ◽  
Generalized Correlation

Abstract A recently proposed generalized correlation for the Graetz problem in heat transfer has two fitted constants that can be related back to two fundamental constants of fully developed transport. A new set of benchmark solutions for convection in annular tubes is used to assess the best linear relationship between fitted and fundamental constants used in this correlation for conditions spanning from circular tubes to parallel plate ducts. This work also improves the Lévêque limit of the general correlation by considering peripheral variation in flow friction. The refined Graetz problem correlation for fully developed flow is able to predict exact thermal entry region solutions to within ±1.2% for all annular tube geometries having either constant temperature (T) or constant heat flux (H1) wall condition.

scholarly journals Entropy Generation during Turbulent Flow of Zirconia-water and Other Nanofluids in a Square Cross Section Tube with a Constant Heat Flux

Entropy ◽  
2014 ◽  
Vol 16 (11) ◽  
pp. 6116-6132 ◽  
Author(s):  
Hooman Yarmand ◽  
Goodarz Ahmadi ◽  
Samira Gharehkhani ◽  
Salim Kazi ◽  
Mohammad Safaei ◽  
...  
Keyword(s):  
Heat Flux ◽  
Turbulent Flow ◽  
Cross Section ◽  
Entropy Generation ◽  
Constant Heat Flux ◽  
Constant Heat

Numerical investigation of CuO-water nanofluid turbulent convective heat transfer in square cross-section duct under constant heat flux

2016 ◽  
Vol 33 (6) ◽  
pp. 1714-1728 ◽  
Author(s):  
Hsien-Hung Ting ◽  
Shuhn-Shyurng Hou
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Convective Heat Transfer ◽  
Cross Section ◽  
Convective Heat ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Content Type

Purpose – The purpose of this paper is to numerically investigate the convective heat transfer of water-based CuO nanofluids flowing through a square cross-section duct under constant heat flux in the turbulent flow regime. Design/methodology/approach – The numerical simulation is carried out at various Peclet numbers and particle concentrations (0.1, 0.2, 0.5, and 0.8 vol%). The finite volume formulation is used with the semi-implicit method for pressure-linked equations algorithm to solve the discretized equations derived from the partial nonlinear differential equations of the mathematical model. Findings – The heat transfer coefficients and Nusselt numbers of CuO-water nanofluids increase with increases in the Peclet number as well as particle volume concentration. Also, enhancement of the heat transfer coefficient is much greater than that of the effective thermal conductivity at the same nanoparticle concentration. Research limitations/implications – Simulation of nanofluids turbulent forced convection at very high Reynolds number is worth for further study. Practical implications – The heat transfer rates through non-circular ducts are smaller than the circular tubes. Nevertheless, the pressure drop of the non-circular duct is less than that of the circular tube. This study clearly presents that the nanoparticles suspended in water enhance the convective heat transfer coefficient, despite low volume fraction between 0.1 and 0.8 percent. Adding nanoparticles to conventional fluids may enhance heat transfer performance through the non-circular ducts, leading to extensive practical applications in industries for the non-circular ducts. Originality/value – Few papers have numerically studied convective heat transfer properties of nanofluids through non-circular ducts. The present numerical results show a good agreement with the published experimental data.

scholarly journals Heat transfer coefficient in elliptical tube at the constant heat flux

2019 ◽  
Vol 23 (Suppl. 4) ◽  
pp. 1323-1332
Author(s):  
Stanislaw Lopata ◽  
Pawel Oclon ◽  
Tomasz Stelmach ◽  
Pawel Markowski
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Cross Section ◽  
Measurement Data ◽  
Constant Heat Flux ◽  
Working Fluid ◽  
Constant Heat ◽  
The Heat Transfer Coefficient

Cross-flow heat exchangers with elliptical tubes are often used in industrial application. In comparison with round tubes, the elliptical tubes have a better aero-dynamic shape, which results in a lower pressure drop of working fluid flowing through the inter-tubular space of heat exchanger. Also, a higher heat flux is transferred from gas to the wall of such a tube due to the more intense heat exchange process. To prove this thesis, the values of the heat transfer coefficient from the wall of the elliptical pipe to the water flowing inside were determined, using the data from the conducted measurements. This study presents also research stand with a vertically positioned tube. In order to obtain a constant heat flux through the wall of elliptical tube, a resistance wire is used, evenly wound on the external surface of tube measuring section. The use of thermal insulation minimized heat loss to the environment to a negligible value. Installed K-type thermocouples allowed one to obtain, for various measurement conditions, the temperature distribution within the elliptical tube wall (for a given cross-section) and the water flowing inside it (in a given cross-section, at different depths, for both axes of the ellipse). The design of the stand allows such measurements in several locations along the length of the measurement section. The measurement results were used to verify numerical calculations. The relative error of the heat transfer coefficient value determined on the basis of CFD calculations using the SST-TR turbulence model in relation to the one determined on the basis of the measurement data is about 11%.

Rate of Sublimation of Ice by Radiative Heating in Freeze-Etching

1980 ◽  
Vol 38 ◽  
pp. 618-619
Author(s):  
Yeshayahu Talmon
Keyword(s):  
Heat Flux ◽  
Freeze Fracture ◽  
Constant Heat Flux ◽  
Radiative Heating ◽  
Constant Heat ◽  
Entire Sample ◽  
Simplified Method ◽  
Freeze Etching ◽  
Sublimation Rates ◽  
Fractured Surface

To bring out details in the fractured surface of a frozen sample in the freeze fracture/freeze-etch technique,the sample or part of it is warmed to enhance water sublimation.One way to do this is to raise the temperature of the entire sample to about -100°C to -90°C. In this case sublimation rates can be calculated by using plots such as Fig.1 (Talmon and Thomas),or by simplified formulae such as that given by Menold and Liittge. To achieve higher rates of sublimation without heating the entire sample a radiative heater can be used (Echlin et al.). In the present paper a simplified method for the calculation of the rates of sublimation under a constant heat flux F [W/m2] at the surface of the sample from a heater placed directly above the sample is described.

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