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Internal Forced Convection
Published in Je-Chin Han, Lesley M. Wright, Analytical Heat Transfer, 2022
Figure 8.2 also shows that the heat transfer coefficient decreases from the entrance along the tube length and becomes a constant value when the thermal boundary layer reaches the fully developed condition, and the heat transfer coefficient increases with Reynolds number (because of a thinner boundary layer from the entrance and the longer entrance length). It is noted that the thermal entrance length is identical to the hydrodynamic entrance length if Pr = 1. For turbulent flow, the thermal entrance length can only be estimated; similar to the hydrodynamic entrance length, the thermal entrance length is approximately 10–20 tube diameters. It is difficult to distinguish whether the turbulent flow is thermally and fully developed in the region from 10 to 20 tube diameters within the tube due to the mixing associated with the turbulent flow.
Internal Forced Convection
Published in Je-Chin Han, Analytical Heat Transfer, 2016
Figure 8.2 also shows that the heat transfer coefficient decreases from the entrance along the tube and becomes a constant value when thermal boundary layer reaches the fully developed condition, and the heat transfer coefficient increases with Reynolds number (because of a thinner boundary layer from the entrance and the longer entrance length). It is noted that the thermal entrance length is identical to the hydrodynamic entrance length if Pr = 1. For the turbulent flow, the thermal entrance length is harder to determine; just like the hydrodynamic entrance length, the thermal entrance length is around 10–20 tube diameter. It is hard to distinguish whether the turbulent flow is thermally fully developed or not from 10 to 20 tube diameter downstream.
Forced Convection in Turbulent Flow
Published in Sadik Kakaç, Yaman Yener, Anchasa Pramuanjaroenkij, Convective Heat Transfer, 2013
Sadik Kakaç, Yaman Yener, Anchasa Pramuanjaroenkij
Turbulent heat transfer in the thermal entrance region of a circular duct with uniform heat flux has been studied using a method similar to the Graetz formulation for laminar thermal entry region problem [55]. It is assumed that the fluid enters the pipe with a uniform temperature and a fully developed turbulent velocity profile. In the course of flow through the heated pipe, the temperature profile will change until, at some distance from the entrance, a fully developed shape is substantially achieved. The thermal entrance length is that length required for the local heat-transfer coefficient to approach its asymptotic value within a few percent (e.g., 5%). Energy equation (7.128) has been solved under the following inlet and boundary conditions for the function T(x,r): ()T(0,r)=Ti,∂T(x,r0)∂r=qw″k,∂T(x,0)∂r=0.
A simplified model of low Re, immiscible, gas–liquid flow, and heat transfer in porous media numerical solution with experimental validation
Published in Experimental Heat Transfer, 2022
Gamal B. Abdelaziz, M. Abdelgaleel, Z.M. Omara, A. S. Abdullah, Emad M.S. El-Said, Swellam W. Sharshir, Ashraf M. Elsaid, Mohamed A. Dahab
This fact means that at constant Reynolds number, the thermal entrance length depends only on the properties of flowing fluids, i.e., Prandtl number. At constant Reynolds number, the mean velocity of the flow is the same, which gives the same thermal boundary layer and in turn the same thermal entrance length. By increasing Reynolds number, the flow becomes faster and the boundary layer becomes thinner, which leads to higher values of the thermal entrance length. Figure 6 shows also that the relation between the thermal entrance length and Re is linear for different values of Pr and Rm.
Heat transfer and pressure drop correlations for laminar flow in an in-line and staggered array of circular cylinders
Published in Numerical Heat Transfer, Part A: Applications, 2019
Hannes Fugmann, Lena Schnabel, Bettina Frohnapfel
For several applications, it is helpful to know the thermal entrance length of a flow through a structure beyond which the flow is thermally developed. This knowledge allows an estimation whether the entrance region has to be considered in performance evaluation or could be neglected. Following the definition in Eq. (12), the thermal entrance length is nondimensionalized as