Heat transfer laminar-flow 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 first relation gives the average heat transfer coefficient for die entire plate when the flow is laminar over the etUire plate. The second relation gives the average heal transfer coefficient for the entire plate only when the flow is iiir-bulent over the entire plate, or when the laminar flow region of the plate is too small relative to the turbulent flow region. 

Heat Transfer in Transition Region between Laminar and Turbulent Flow... 

Question by J. A. Clark, University of Michigan What would be the influence of the transient term in the differential equation on the results In a paper by P. J. Schneider [Trans, ASME, Vol. 79, p. 765 (1957)] the effect of axial heat conduction on heat transfer in entrance regions in laminar flow was investigated. 

Sometimes flow in tubes is in laminar flow region and turbulatois are used to insert in tubes to increase the fluid turbulent to improve heat transfer,... 

In the flow region between laminar and fully developed turbulent flow heat-transfer coefficients cannot be predicted with certainty, as the flow in this region is unstable, and the transition region should be avoided in exchanger design. If this is not practicable the coefficient should be evaluated using both equations 12.11 and 12.13 and the least value taken. 

Transfer coefficients in catalytic monolith for automotive applications typically exhibit a maximum at the channel inlet and then decrease relatively fast (within the length of several millimeters) to the limit values for fully developed concentration and temperature profiles in laminar flow. Proper heat and mass transfer coefficients are important for correct prediction of cold-start behavior and catalyst light-off. The basic issue is to obtain accurate asymptotic Nu and Sh numbers for particular shape of the channel and washcoat layer (Hayes et al., 2004 Ramanathan et al., 2003). Even if different correlations provide different kc and profiles at the inlet region of the monolith, these differences usually have minor influence on the computed outlet values of concentrations and temperature under typical operating conditions. 

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

The presence of the solid wall has a considerable influence on the turbulence structure near the wall. Because there can be no flow normal to the wall near the wall, v decreases as the wall is approached and as a result the turbulent stress and turbulent heat transfer rate are negligible in the region very near the wall. This region in which the effects of the turbulent stress and turbulent heat transfer rate can be neglected is termed the sublayer or, sometimes, the laminar sublayer [1],[2], [26],[27],[28],[29]. In this sublayer ... 

While the engineer may frequently be interested in the heat-transfer characteristics of flow systems inside tubes or over flat plates, equal importance must be placed on the heat transfer which may be achieved by a cylinder in cross flow, as shown in Fig. 6-7. As would be expected, the boundary-layer development on the cylinder determines the heat-transfer characteristics. As long as the boundary layer remains laminar and well behaved, it is possible to compute the heat transfer by a method similar to the boundary-layer analysis of Chap. 5. It is necessary, however, to include the pressure gradient in the analysis because this influences the boundary-layer velocity profile to an appreciable extent. In fact, it is this pressure gradient which causes a separated-flow region to develop on the back side of the cylinder when the free-stream velocity is sufficiently large. 

Transition Region Turbulent-flow equations for predicting heat transfer coefficients are usually valid only at Reynolds numbers greater than 10,000. The transition region lies in the range 2000 < Npe < 10,000. No simple equation exists for accomplishing a smooth mathematical transition from laminar flow to turbulent flow. Of the relationships proposed, Hausen s equation [Z Ver. EHsch. Ing. Beth. Verfahrenstech., No. 

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