V Forced convection heat transfer to a fluid flowing in turbulent motion in a pipe is perhaps the most common heat transfer system in industry. VAlthough forced convection can be associated with laminar flow and natural convection with turbulent flow, these are cases of secondary importance. V Heat transfer coefficients are higher in turbulent flow than in laminar flow, and heat transfer equipment is usually designed to take advantage of this fact.
V The use of the Navier-Stokes equation in the analysis of isothermal turbulent flow is complicated by fluctuations in velocity motion. For the same reason, it is difficult to use the balance of the differential energy equation in the analysis of non-isothermal turbulent flow. V Once this inlet region is crossed, the heat transfer coefficients in the developed turbulent flow remain essentially constant.
We assume that the fluid enters at a uniform temperature and that the pipe wall is at some uniform temperature higher than that of the entering fluid. V Certain flow conditions at the entrance will be considered, and their effects on the local heat transfer coefficients are qualitatively deduced from the knowledge we have gained so far of hydrodynamic and heat transfer theory.
Entrance effects in a pipe
The fluid enters the tube in laminar flow with a uniform velocity profile at such a rate that Re>2100. This turbulent boundary layer increases with increasing downstream distance until it fills the tube with a turbulent core and a laminar sublayer at the wall. Downstream of this point, the system is identical in all respects to the system that would develop if the flow were turbulent from the inlet.
This flow behavior is reflected in the values of the local heat transfer coefficient, which decreases from infinity at the inlet to a minimum value at the critical point where the laminar boundary layer changes to a turbulent boundary layer. Near this point, the heat transfer coefficient increases in magnitude for a short distance, but then continues to decrease downstream until the turbulent boundary layers meet at the center of the tube.
Local coefficients of heat transfer
From the start of the heated length, a thermal boundary layer will build up, filling the tube at a downstream point. However, this entrance length for non-uniform turbulent flow usually does not have any significant effect on the local heat transfer coefficients above 10 pipe diameters, while entrance effects in laminar flow often persist for 50 or more pipe diameters. The local heat transfer coefficient at the beginning of the heated length is infinite in turbulent flow due to the temperature discontinuity, just as in laminar flow.
왼쪽 그림과 같이 유체가 평판과 만나면 경계층이 발달하기 시작하고 일정 거리를 지나면 층류 경계층이 난류 경계층으로 천이됩니다. 결과적으로 대류 열전달 계수(hc)와 벽 마찰(τs)은 왼쪽 이미지에 표시된 것과 유사한 경향을 갖습니다. 판의 시작점에서 매우 크게 나타나는 열전달 계수와 벽 마찰은 층류 경계층이 발달함에 따라 점차 감소하고 가벼운 층의 불안정으로 인해 흐름 전이가 발생합니다.
전이점에서 대류 열전달과 벽 마찰은 갑자기 증가한 다음 난류 경계층으로 들어가면서 흐름 방향으로 다시 점차 감소합니다. 이때 난류성분의 강화와 난류경계층에서의 혼합으로 인해 대류열전달과 벽마찰은 층류경계층에 비해 점차 감소하게 된다.
Analogy between Momentum Transfer and Heat Transfer
The similarity of heat and momentum transport
History of the Analogy theory
Reynolds analogy
Several considerations, which Reynolds did not specifically mention, led to the assumption that A and B were proportional to A' and B'. The proportionality of heat and momentum transfer can be stated in terms of four quantities, which we will define with reference to a fluid at a mass temperature tb flowing through a pipe and losing heat to the wall of the pipe, which is at .
Eddy thermal diffusivity and mixing length
Therefore, in this particular case, υ+υe= α+ αe, and (23-4) can be obtained without neglecting the molecular transport terms.
Reynolds Analogy: Pr=1Reynolds Analogy: Pr=1
Prandtl
Colburn Analogy for smooth pipe
Dittus-Boelter equation for smooth pipe Pr=1
Turbulent flow parallel to a flat plate
Heat transfer coefficients in the region of the laminar boundary layer on a flat plate were analyzed in the previous chapter, starting with basic differential balances. The problem could also be solved in a semi-empirical way with the so-called von von KKáármrmáánn integral integral method. In this chapter we are dealing with turbulent flow and cannot use the Navier-Stokes equations, so we will use the integral method to approximate the problem.
The use of the integral method for isothermal flow was already shown in Chapter 12. An empirical equation for the velocity distribution in the boundary layer was written, and a force and moment balance was made on the segment of the layer.
Overall energy balance
Local heat transfer coefficient
Local heat transfer coefficient (Pr=1)
Mean Nusselt number (Pr=1)
Local Nusselt number (Pr=1)
Local heat transfer coefficient (Pr≠1)
Local Nusselt number (Pr≠1)
Other study on local heat transfer coefficient (Pr≠1)
Summary
Homework
