Heat entrance region

Limiting Nusselt numbers for laminar flow in annuli have been calculated by Dwyer [Nucl. Set. Eng., 17, 336 (1963)]. In addition, theoretical analyses of laminar-flow heat transfer in concentric and eccentric annuh have been published by Reynolds, Lundberg, and McCuen [Jnt. J. Heat Ma.s.s Tran.sfer, 6, 483, 495 (1963)]. Lee fnt. J. Heat Ma.s.s Tran.sfer, 11,509 (1968)] presented an analysis of turbulent heat transfer in entrance regions of concentric annuh. Fully developed local Nusselt numbers were generally attained within a region of 30 equivalent diameters for 0.1 < Np < 30, lO < < 2 X 10, 1.01 <... 

The thermal entrance region in a hydrodynamically fully developed flow in a rectangular duct may be studied by the use of the integral method. In this section, the uniform wall temperature and the uniform wall heat flux cases are discussed. The physical model is based on the following assumptions ... 

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

Discuss the modifications required to the computer program given for flow in the thermal entrance region of a plane duct to deal with the case where there is a uniform heat flux at one wall of the duct and where there is a uniform specified temperature at the other wall of the duct. 

Sparrow, E.M., Analysis of Laminar - orced Convection Heat Transfer in the Entrance Region of Rat Rectangular Ducts , NACA TN 3331, 1955. 

Water flows at a rate of 1 kg/s through a 3-cm diameter smooth pipe. The water enters the pipe a( a temperature of 15°C and must leave the the pipe at a mean temperature of 50°C. The pipe wall is heated in such a way that the wall temperature is 14°C higher than the local mean water temperature at all points along the pipe. What length of pipe is required Ignore entrance region effects. 

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. 

Deissler, R.G., Turbulent Heat Transfer and Friction in the Entrance Regions of Smooth Passages , Trans. ASME, Vol. 77, pp. 1211-1234, 1955. 

Lin, Jenn Nan, Yen, Chen Shy ong. and Chou, Fu Chu, Laminar Mixed Convection in the Entrance Region of Shrouded Arrays of Heated Rectangular Blocks". Canadian J. of Chem. Eng., Vol. 66. June 88. pp. 361-366, 1988. 

Wang, M., Tsuji, T., and Nagano, Y., Mixed Convection with Row Reversal in the Thermal Entrance Region of Horizontal and Vertical Pipes , Int. J. Heat Mass Transfer, Vol. 37, pp. 2305-2319,1994. 

Narusawa. U., Numerical Analysis of Mixed Convection at the Entrance Region of a Rectangular Duct Heated from Below", Int. J. Heat and Mass Transfer, Vol. 36, pp. 2375-2380, 1993. 

Temperature Profile and the Nusselt Number 467 Constant Surface Heat Flux 467 Constant Surface femperaturc 468 I aminar Ftow in Noncircular Tubes 469 Developing laminar Flow in the Entrance Region 470... 

Developing Turbulent Flov/ in the Entrance Region 4/6 Turbulent Flo. v in N oncircular Tubes 476 Flow through Tube Annulus 477 Heat Transler Enhancement 477... 

The Nusselt numbers and thus the convection heat transfer coefficients are much higher in the entrance region. 

The Nusselt numbers for the uniform. surface temperature and uniform surface heat flux conditions are identical in the fully developed regions, and nearly identical in the entrance regions. Therefore, Nusselt number... 

Precise correlations for the friction and heat transfer coefficients for the entrance regions are available in Ihe literature. However, the tubes used in practice in forced convection are usually -several times the length of either entrance region, and thus the flow through the tubes is often assumed to be fully developed for the entire length of the tube. This simplistic approach gives reasonable results for the rate of heat transfer for long tubes and conservative results for short ones. 

R. G. Deissler. Analysis ofThrbulent Heat Transfer and Flow in the Entrance Regions of Smooth Passages. 1953. Referred lo in Handbook of Single-Phase Convective Heal Transfer, ed. S. Kaka9, R. K. Shah, and W. Aung. New York Wiley Intcrscience, 1987. 

Gui, F. and Scaringe, R.P., Enhanced Heat Transfer in the Entrance Region of Microchannels, lECEC Paper No. ES-40, ASME, 1995, 289-294. 

Joule heat generated by the ionic current is removed through cooling jackets mounted on the transverse walls. This creates a transverse temperature gradient which drives a stable and usually deleterious convective flow (3). Furthermore, the axial temperature gradient in the thermal entrance region (10,11) near the tips of the electrodes may drive a buoyancy instability when the thermal gradient exceeds a critical value (4,12). Apart from the physical properties of the carrier fluid, the critical temperature... 

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]

Prakash and Liu [266] have numerically analyzed laminar flow and heat transfer in the entrance region of an internally finned circular duct. In this study, the fully developed / Re is compared with those reported by Hu and Chang [265] and Masliyah and Nandakumar [267]. The incremental pressure drop K(°°) and hydrodynamic entrance length L+hy together with /Re are given in Table 5.48, in which the term n refers to the number of fins, while / denotes the relative length of the fins. 

A trapezoidal duct is displayed in the inset of Fig. 5.50. Fully developed laminar flow and the heat transfer characteristics of trapezoidal ducts have been analyzed by Shah [172]. The fully developed /Re, NuHn and NuH2 are given in Figs. 5.50 and 5.51. Farhanieh and Sunden [276] numerically investigated the laminar flow and heat transfer in the entrance region of trapezoidal ducts. The fully developed values off Re, K(°°), and Nu were in accordance with the results from Shah [172]. 

J. W. Ou, and K. C. Cheng, Viscous Dissipation Effects on Thermal Entrance Region Heat Transfer in Pipes with Uniform Wall Heat Flux, Appl. Sci. Res., (28) 289-301,1973. 

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