Turbulent flow heat transfer

For maximum heat transfer, the flow should be turbulent rather than laminar. This means that Reynolds number Re = GD/p > 2300. 

R. G. Deissler, Analysis of Turbulent Heat Transfer and Flow in the Entrance Regions of Smooth Passages, NACA TN 3016,1953. 

Viscosity. The critical Reynolds number for turbulent flow on the shell side is about 200 hence, when the fluid flow in the tubes is laminar, it may be turbulent if that same fluid is placed in the shell. However, if the flow is still laminar when in the shell, then it is best to place the fluid back inside the tubes, as it will be somewhat easier to predict both heat transfer and flow distribution. 

The heat-transfer phenomena for forced convection over exterior surfaces are closely related to the nature of the flow. The heat transfer in flow over tube bundles depends largely on the flow pattern and the degree of turbulence, which in turn are functions of the velocity of the fluid and the size and arrangement of the tubes. The equations available for the calculation of heat transfer coefficients in flow over tube banks are based entirely on experimental data because the flow Is too complex to be treated analytically. Experiments have shown that, in flow over staggered tube banks, the transition from laminar to turbulent flow Is more gradual than in flow through a pipe, whereas for in-line tube bundles the transition phenomena resemble those observed in pipe flow. In either case the transition from laminar to turbulent flow begins at a Reynolds number based on the velocity in the minimum flow area of about 100, and the flow becomes fully turbulent at a Reynolds number of about 3,000. The equation below can be used to predict heat transfer for flow across ideal tube banks. 

The general relation recommended for turbulent heat transfer to flowing non-Newtonians is that developed by Metzner and Friend [65]. This was done by analogy with momentum transport, assuming several points. These included constant heat flux, equality of eddy thermal and momentum diffusivities at all... 

Turbulence Combustion Radiation heat transfer Multiphase flows... 

In the forced convection heat transfer, the heat-transfer coefficient, mainly depends on the fluid velocity because the contribution from natural convection is negligibly small. The dependence of the heat-transfer coefficient, on fluid velocity, which has been observed empirically (1—3), for laminar flow inside tubes, is h for turbulent flow inside tubes, h and for flow outside tubes, h. Flow may be classified as laminar or... 

The convective heat-transfer coefficient and friction factor for laminar flow in noncircular ducts can be calculated from empirically or analytically determined Nusselt numbers, as given in Table 5. For turbulent flow, the circular duct data with the use of the hydrauhc diameter, defined in equation 10, may be used. 

The minimum velocity requited to maintain fully developed turbulent flow, assumed to occur at Reynolds number (R ) of 8000, is inside a 16-mm inner diameter tube. The physical property contribution to the heat-transfer coefficient inside and outside the tubes are based on the following correlations (39) ... 

Heat transfer in static mixers is intensified by turbulence causing inserts. For the Kenics mixer, the heat-transfer coefficient b is two to three times greater, whereas for Sulzer mixers it is five times greater, and for polymer appHcations it is 15 times greater than the coefficient for low viscosity flow in an open pipe. The heat-transfer coefficient is expressed in the form of Nusselt number Nu = hD /k as a function of system properties and flow conditions. 

This term is a measure of the unit s length. Sometimes it is referred to as the number of transfer units. This simply says that the optimum pressure drop increases as the heat exchanger gets longer, ie, has more transfer units. The forms of F, and F both foUow from the fact that in turbulent flow the... 

Flow in tubular reactors can be laminar, as with viscous fluids in small-diameter tubes, and greatly deviate from ideal plug-flow behavior, or turbulent, as with gases, and consequently closer to the ideal (Fig. 2). Turbulent flow generally is preferred to laminar flow, because mixing and heat transfer... 

For turbulent flow of a fluid past a solid, it has long been known that, in the immediate neighborhood of the surface, there exists a relatively quiet zone of fluid, commonly called the Him. As one approaches the wall from the body of the flowing fluid, the flow tends to become less turbulent and develops into laminar flow immediately adjacent to the wall. The film consists of that portion of the flow which is essentially in laminar motion (the laminar sublayer) and through which heat is transferred by molecular conduction. The resistance of the laminar layer to heat flow will vaiy according to its thickness and can range from 95 percent of the total resistance for some fluids to about I percent for other fluids (liquid metals). The turbulent core and the buffer layer between the laminar sublayer and turbulent core each offer a resistance to beat transfer which is a function of the turbulence and the thermal properties of the flowing fluid. The relative temperature difference across each of the layers is dependent upon their resistance to heat flow. 

Individual Coefficient of Heat Transfer Because of the comphcated structure of a turbulent flowing stream and the impracti-cabifity of measuring thicknesses of the several layers and their temperatures, the local rate of beat transfer between fluid and solid is defined by the equations... 

When heat transfer occurs during immersed flow, the rate is dependent upon the configuration of the body, the position of the body, the proximity of other bodies, and the flow rate and turbulence of the... 

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 <... 

Transition Region Turbulent-flow equations for predicting heat transfer coefficients are usually vahd only at Reynolds numbers greater than 10,000. The transition region lies in the range 2000 < < 10,000. 

Circular Tubes Numerous relationships have been proposed for predicting turbulent flow in tubes. For high-Prandtl-number fluids, relationships derived from the equations of motion and energy through the momentum-heat-transfer analogy are more complicated and no more accurate than many of the empirical relationships that have been developed. 

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