Heat Transfer in Circular Tubes

2 Experimental Investigations 4.2.1 Heat Transfer in Circular Tubes 

The schemes of the test sections used by some investigators are shown in Fig. 4.2. The geometrical parameters are presented in Tables 4.2 and 4.3. 

Author Number of Inner dia- Outer dia- Heating Dimension- Reynolds 

The micro-channels utilized in engineering systems are frequently connected with inlet and outlet manifolds. In this case the thermal boundary condition at the inlet and outlet of the tube is not adiabatic. Heat transfer in a micro-tube under these conditions was studied by Hetsroni et al. (2004). They measured heat transfer to water flowing in a pipe of inner diameter 1.07 mm, outer diameter 1.5 mm, and 0.600 m in length, as shown in Fig. 4.2b. The pipe was divided into two sections. The development section of Lj = 0.245 m was used to obtain fully developed flow and thermal fields. The test section proper, of heating length Lh = 0.335 m, was used for collecting the experimental data. 

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Kays, W.M., Numerical Solution for Laminar Row Heat Transfer in Circular Tubes , Trans. ASME, Vol. 77, pp. 1265-1274, 1955. 

No. 67016 (1967) Forced convection heat transfer in circular tubes. Part I, turbulent flow. 

Larrode, F.E., Housiadas, C. and Drossinos, Y., Slip Flow Heat Transfer in Circular Tubes, Int. J. Heat Mass Transfer, 2000, 43, 2669-2680. 

Larrode, F. E., C. Housiadas, and Y. Drossinos, 2000, Slip Flow Heat Transfer in Circular Tubes, International Journal of Heat and Mass Transfer, 43 (2000) 2669-2680. 

Turbulent Heat Transfer in Circular Tube and Plane Channel... 

Larrode EE, Housiadas C, Drossinos Y (2000) Slip flow heat transfer in circular tubes. Int J Heat Mass Transf 43 2669-2680... 

There are numerous correlations for convective heat transfer in circular tubes at supercritical pressures [for details, see in Pioro and Duffey (2007)]. However, an analysis of these conelalions has shown that they are more or less accurate only within the particular dataset, which was used to derive the correlation, but show a significant deviation in predicting other experimental data. Therefore, only selected correlations are listed below. 

Chapter 4 is devoted to single-phase heat transfer. Data on heat transfer in circular micro-tubes and in rectangular, trapezoidal and triangular ducts are presented. Attention is drawn to the effect of energy dissipation, axial conduction and wall roughness on the thermal characteristics of flow. Specific problems connected with electro-osmotic heat transfer in micro-channels, three-dimensional heat transfer in micro-channel heat sinks and optimization of micro-heat exchangers are also discussed. 

Now consider a fluid at a uniform temperature entering a circular tube whose surface is maintained at a different temperature. This time, the fluid particles in the layer in contact with the surface of the tube assume the surface temperature. Tins initiates convection heat transfer in the tube and Ihe development of a thermal hoimdaiy layer along the tube. The thickness of this boundary layer also increases in tfle flow direction until Ihe boundary layer reaches the tube center and thus fills the entire tube, as sliown in Fig. 8-7. 

The sample with porous coating has advantage to compare with plain tube. The best results were obtained with heat transfer in circular mini-channel. To understand these phenomena the visual observing and photographing of various stage of process were curried out. The photos are presented in Figure 11. 

Yoo, S, S.i Ph.D. Thesis, University of Illinois, Chicago (1974). Heat transfer and friction factors for non-Newtonian fluids in circular tubes. 

The analysis of the behavior of the fluid temperature and the Nusselt number performed for a circular tube at the thermal wall boundary condition 7(v = const, also reflects general features of heat transfer in micro-channels of other geometries. 

In Ulrichson and Schmit s work on laminar flow heat transfer in the entrance region of circular tubes the following results were obtained. 

Siegel, R., Sparrow, E.M., and Hallman, T.M., Steady Laminar Heat Transfer in a Circular Tube with Prescribed Wall Heat Flux , Appl. Sci. Res., Sect. A, Vol. 7, p. 386,1958. 

Reynolds, W.C., Turbulent Heat Transfer in a Circular Tube with Variable Circumferential Heat Flux , Int. J. Heat Mass Transfer, Vol. 6, pp. 445-454,1963. 

Flow in circular tubes is of interest to many corrosion engineers. A large number of correlations exist for mass transport due to turbulent flow in a smooth straight pipe (4,9). The flow is transitionally turbulent at Re 2 X 103 and is fully turbulent at Re 105 (4). The most frequently used expression for turbulent conditions at a straight tube wall is that given by Chilton and Colburn using the analogy from heat transfer (13) ... 

SOLUTION Circular aluminum alloy fins are to be attached to the tubes of a heating system. The increase in heat transfer from the tubes per unit length as a result of adding fins is to be determined. 

J. H. Kim, Heat transfer in longitudinal laminar flow along circular cylinders in a square array. Fluid Flow and Heat Transfer over Rod or Tube Bundles (S.C. Yao and P.A. Pfund, eds.), Winter annual meeting of the American Society of Mechanical Engineers, December 2-7, New York, 1979, p. 155. 

Knudsen and Katz [54] have shown that it is valid for Re Pr- djl >10. Equation 19.21 cannot be used for long tubes, since it would yield zero heat transfer coefficient. Sarti et al. have employed a different Equation 19.16 to estimate the heat transfer coefficient for laminar flow in circular tubes (shown in Table 19.1). 

In this section, we instead consider two well-known examples of heat transfer in the fully developed, laminar, and unidirectional flow of a Newtonian fluid in a straight circular tube. We begin with a problem in which there is a prescribed heat flux into the fluid at the walls of the tube, so that there is a steady-state temperature distribution in the tube. At the end of the section, we consider the transient evolution of the temperature distribution beginning with an initially sharp temperature jump within the fluid at a fixed position (say z = 0), which illustrates an important phenomenon that is known as Taylor dispersion. 

Figure 3-13. A sketch of the configuration for heat transfer in flow through a heated or cooled section of a circular tube.

I. Steady-State Heat Transfer in Fully Developed Flow through a Heated (or Cooled) Section of a Circular Tube... 

In this section we consider a second problem involving heat transfer in Poiseuille flow through a circular tube. In this case, we assume that the fluid in the region — 8 < z < 8 is initially heated to a temperature 0, while the temperature elsewhere, i.e., z > 8, is held at a constant temperature 60. The wall of the tube is insulated for all z so that there is no heat loss or gain to the surroundings. Precisely the same problem could be formulated as a mass transfer problem for the redistribution of a solute in a solvent with an initial solute concentration C for —5 < z < 5 and concentration Co for z > 8, with tube walls that are impermeable to the solute. The only difference is that the thermal diffusivity k is replaced with the species diffusion coefficient/). However, to make the discussion as straightforward as possible, the analysis in this section is presented as a heat transfer problem. 

The problem was solved by R. Siegel, E. M. Sparrow, and T. M. Hallman, Steady laminar heat transfer in a circular tube with a prescribed wall heat flux, Appl. Sci. Res. 7, 386-92 (1958). The description here follows the textbook by J. C. Slattery, Advanced Transport Phenomena (Cambridge University Press, Cambridge, 1958). 

More detailed information about heat transfer in turbulent nonisothermal flows through a circular tube or plane channel, as well as various relations for Nusselt numbers, can be found in the books [185,254,267,406], which contain extensive literature surveys. 

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