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Convective Transport on a Flat Plate (Laminar Boundary Layers)
Published in Joel L. Plawsky, Transport Phenomena Fundamentals, 2020
The Reynolds analogy is a theoretical one that holds over a rather narrow range of conditions and is most useful for gases and certain liquids (water or ethanol) where the Prandtl and Schmidt numbers are close to 1. However, the power of the analogy concept is so great that investigators have long sought for ways to extend its applicability. One of the most successful extensions is the Chilton-Colburn analogy developed in 1933 [5,6]. This is an empirical extension inspired by a solution to the boundary layer equations. It increases the applicability of the Reynolds analogy to Prandtl and Schmidt numbers between 0.6 and 60 but one must take care when using it. It is not all that accurate. Nf=NuPr−1/3=ShSc−1/3Chilton-Colburn analogy
Limits of Air Cooling—A Methodical Approach
Published in Sung Jin Kim, Sang Woo Lee, for Electronic Equipment, 2020
Based on Equation 4, pressure drop as a result of physical constraints is a function of the flow resistance (D) and the volumetric flow rate. Reynolds analogy simply states that the drag force created as the result of fluid passing a heated rigid body is proportional to its heat transfer. This is expressed by the friction coefficient as a function of other nondimensional numbers: () Cf=2Nu/(RePr1/3)
Heat Transfer Fundamentals
Published in Ralph L. Webb, Nae-Hyun Kim, Principles of Enhanced Heat Transfer, 2004
The Reynolds analogy is an important tool that shows how flow friction may be related to the heat transfer coefficient. Although enhanced surfaces provide an increased heat transfer coefficient, they may also be expected to demonstrate increased flow friction, especially for single-phase flow. Applied to enhanced surfaces, the Reynolds analogy indicates the minimal friction increase that may be expected from an enhanced surface. The efficiency index provides a measure of how well one has used increased friction to obtain a given heat transfer enhancement ratio.
Heat and Mass Transfer Equations for Turbulent Flow with Wide Ranges of Prandtl and Schmidt Numbers
Published in Heat Transfer Engineering, 2022
Houjian Zhao, Xiaowei Li, Xinxin Wu
The right hand side of Eq. (21) can be calculated by the turbulent viscosity models with By setting in the whole cross section by Reynolds analogy [14], we can obtain Setting constant turbulent Prandtl number in the fully turbulent region is reasonable. Because turbulent diffusion dominates the diffusion process both for momentum and thermal in the fully turbulent region. However, the DNS results have shown that the turbulent Prandtl number increases with decreasing of wall distances in the viscous sublayer [22, 34]. In this region, the diffusion process for momentum and energy will be different. At least, pressure has effects on momentum field but not on energy field [36]. In the current investigation, Kays model [36] is used to calculate the variable turbulent Prandtl number. A modified Van Driest model is used to calculate the turbulent viscosity with Prandtl’s mixing length theory.
Study of unsteady nonequilibrium stratified suspended sediment distribution in open-channel turbulent flows using shifted Chebyshev polynomials
Published in ISH Journal of Hydraulic Engineering, 2022
The efficiency of the new analytical solutions using Chebyshev polynomials of fourth kind for suspended sediment distribution in open channels, is justified by comparing it with previous analytical solutions. For the evaluation of the unknown by the Chebyshev collocation method, higher order polynomials are used. In this study, in all cases, 20 Chebyshev nodes are considered which gives appropriate result. It can be observed from Equation 13 that and depends on the distribution of the sediment diffusivity. Among different models of sediment diffusivity, constant, linear and parabolic models are used by several authors (Kundu and Ghoshal 2012; van Rijn 1987; Ikeda 1981; Yang et al. 2006). In this study, these three different types of sediment diffusivity models along are considered for broad applicability of this study. According to the Reynolds analogy , where is inverse of the turbulent Schmidt number and is the dimensionless eddy viscosity (Graf 1971; Kundu and Ghoshal 2014). Several studies showed that the value of depends in particle size, density of the flow and others (Kundu and Ghoshal 2014). For simplicity in this study, is considered. Therefore different types of eddy viscosity models are expressed as
Experimental Study of Heat Transfer and Pressure Loss in Channels with Miniature V Rib-Dimple Hybrid Structure
Published in Heat Transfer Engineering, 2020
Figure 10 shows the comparisons of the Reynolds analogy factors of the V rib-dimpled channels at different Reynolds numbers. The Reynolds analogy factor is defined as below [19,20]: which indicates the heat transfer enhancement per unit pressure loss of the test channels, representing the thermal-hydraulic efficiency of a convective heat transfer enhancement structure. It can be seen that with the increase of the Reynolds numbers the Reynolds analogy factors of the V rib-dimpled channels with 0.6 mm, 1.0 mm and 1.5 mm rib heights all decrease appreciably. It is also seen that all the V rib-dimpled channels show lower Reynolds analogy factor values than the pure dimpled channel, and as the rib height increases the V rib-dimpled channel shows lower Reynolds analogy factor values. The pure dimpled channel shows the highest Reynolds analogy factor values within the studied Reynolds number range mostly due to its low pressure loss performance, while the V rib-dimpled channel with 1.5 mm rib height shows the lowest Reynolds analogy factor values, which are 25.0–36.0% lower than those of the dimpled channel within the studied Reynolds number range.