Heat Transfer in the Thermal Entrance Region

Sparrow, E.M., Hallman, T.M., and Siegel, R., Turbulent Heat Transfer in the Thermal Entrance Region of a Pipe with Uniform Heat Rux , Appl. Sci. Rest. Section A, Vol. 7, p. 37. 1957. 

A. Quarmby, and R. K. Anand, Turbulent Heat Transfer in the Thermal Entrance Region of Concentric Annuli with Uniform Wall Heat Flux, Int. J. Heat Mass Transfer, (13) 395-411,1970. 

A. Roberts and H. Barrow, Turbulent Heat Transfer in the Thermal Entrance Region of an Internally Heated Annulus, Proc. Inst. Mech. Engrs., (182/3H) 268-276,1967. 

Laminar Heat Transfer in the Thermal Entrance Region... 

Worsoe-Schmidt PM. Heat transfer in the thermal entrance region of circular tubes and annular passages with fully developed laminar flow. International Journal of Heat and Mass Transfer 1967 10 541-551. 

For equilateral triangular ducts having rounded corners with a ratio of the corner radius of curvature to the hydraulic diameter of 0.15, Campbell and Perkins [180] have measured the local friction factor and heat transfer coefficients with the boundary condition on all three walls over the range 6000 < Re < 4 x 104. The results are reported in terms of the hydrodynamically developed flow friction factor in the thermal entrance region with the local wall (Tw) to fluid bulk mean (Tm) temperature ratio in the range 1.1 < TJTm < 2.11, 6000 < Re < 4 x 10 and 7.45 [Pg.382]

The prediction of the local laminar heat transfer coefficient for a power-law fluid in the thermal entrance region of a circular tube was reported by Bird and colleagues [41]. Both the constant wall heat flux and the constant wall temperature boundary condition have been studied. The results can be expressed by the following relationships [42-48]. 

It is interesting to note that the nonnewtonian effect has been taken into account by simply multiplying the corresponding newtonian result by [(3n + l)/4n]1/3. Equations 10.48 and 10.49 may be used to predict the local heat transfer coefficient of purely viscous and viscoelastic fluids in the thermal entrance region of a circular tube. Figure 10.6 shows a typical comparison of the measured local heat transfer coefficient of a viscoelastic fluid with the prediction for a power-law fluid. The good agreement provides evidence to support the applicability of Eq. 10.48 in the case of the constant heat flux boundary condition. 

Values of the asymptotic heat transfer factors jH in the thermal entrance region are reported for concentrated aqueous solutions of polyacrylamide and polyethylene oxide. The results are shown in Fig. 10.30, as a function of the Reynolds number Re . These values were measured in tubes of 0.98,1.30, and 2.25 cm (0.386,0.512, and 0.886 in) inside diameter in a recirculating-flow loop. The asymptotic turbulent heat transfer data in the thermal entrance region are seen to be a function of the Reynolds number Re and of the axial position xld. The following empirical correlation is derived from the data [35,37] ... 

FIGURE 10 JO Experimental results of turbulent heat transfer for concentrated solutions of polyethylene oxide and polyacrylamide in the thermal entrance region. 

Proportional to the ratio of thermal energy convected to the fluid to thermal energy conducted axially within the fluid the inverse of Pe indicates relative importance of fluid axial heat conduction Useful in describing the thermal entrance region heat transfer results... 

For turbulent flow, the thermal entrance region is shorter than for laminar flow (with the exception of liquid metals which have a very low Prandtl number), and thus the fully developed values of the Nusselt number are frequently used directly in heat transfer design without reference to the thermal entrance effects. The turbulent fully developed Nusselt number in a smooth channel can be expressed as a function of the Reynolds number and of the Prandtl number. 

Within the thermal entrance region, the local value of the heat transfer and the local Nusselt number N% steadily decreases as the thermal boundary layer increases until in the thermally fully developed region Nu reaches a constant value (Example 3.2.4). However, the value of the local Nusselt number is of little value in... 

In the Hausen correlation the Nusselt number is calculated as a sum of two terms the first term (Nu) is the fully developed value of the Nusselt number its value can be found in convective heat transfer in microchannels for the most common microchannel cross-sections. The second term takes into account the effects of the thermal entrance region. The values of the coefficients K, K2 and b for circular microchannels are quoted in Table 3. 

Parallel Plate Cross Section For laminar flows under the T boundary condition (see Convective Heat Transfer in Microchannels ) with a fully developed velocity profile (hydrodynamically fully developed and thermally developing flow Fig. 3), the following correlation, proposed originally by Shah for conventional channels, can be useful to calculate the mean Nusselt number in the entrance region of parallel plate microchannels as a function of the dimensionless axial coordinate z ... 

The equations given in this chapter for Nu are only valid for a fully developed laminar flow, that is, without a hydrodynamic entrance region. Similar considerations can be made for the heat transfer in a tube with both a thermal and a hydrodynamic entrance region, whereby the differences in the values of Nu and Nu are mostly small (VDI, 2002). 

Similar to the momentum boundary layer entrance length in a closed channel, there is a thermal boundary layer development region. For laminar fully developed flow (Re < 3000), an exact solution can be found for different boundary conditions. For fully developed and laminar heat transfer in a rectangular channel with equal depth and width, the heat transfer coefficient is constant and can be determined as follows... 

Entrance andExit SpanXireas. The thermal design methods presented assume that the temperature of the sheUside fluid at the entrance end of aU tubes is uniform and the same as the inlet temperature, except for cross-flow heat exchangers. This phenomenon results from the one-dimensional analysis method used in the development of the design equations. In reaUty, the temperature of the sheUside fluid away from the bundle entrance is different from the inlet temperature because heat transfer takes place between the sheUside and tubeside fluids, as the sheUside fluid flows over the tubes to reach the region away from the bundle entrance in the entrance span of the tube bundle. A similar effect takes place in the exit span of the tube bundle (12). 

Length Effect. The heat transfer coefficient can vary significantly in the entrance region of the laminar flow. For hydrodynamically developed and thermally developing flow, the local and mean heat transfer coefficients h, and h, for a circular tube or parallel plates are related as [19]... 

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