Laminar flow heat transfer

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

Tso and Mahulikar [46, 47] proposed the use of the Brinkman number to explain the unusual behaviors in heat transfer and flow in microchannels. A dimensional analysis was made by the Buckingham vr theorem. The parameters that influence heat transfer were determined by a survey of the available experimental data in the literature as thermal conductivity, density, specihc heat and viscosity of the fluid, channel dimension, flow velocity and temperature difference between the fluid and the wall. The analysis led to the Brinkman number. They also reported that viscous dissipation determines the physical limit to the channel size reduction, since it will cause an increase in fluid temperature with decreasing channel size. They explained the reduction in the Nusselt number with the increase in the Reynolds number for the laminar flow regime by investigating the effect... 

S. Piva, An Analytical Approach to Fully Developed Heating of Laminar Flows in Circular Pipes, Int. Comm. Heat Mass Transfer, (22/6) 815-824,1995. 

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. 

Special solutions exist for a porous channel with one porous wall for laminar channel flow with heat transfer and flow of viscoelastic fluid with arbitrary uniform suction or injection (Kurtcebe and Erim, 2005) and for a channel with one porous wall with heat transfer and expanding walls with arbitrary uniform suction or injection (Tsai et al., 2009). 

Shah R.K., and T.C. London (1978) Flow forced convection in ducts. Advances in heat transfer-Laminar., Academic Press, New-York. 

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. 

Table 5. Correlations for Heat-Transfer and Darcy Friction Coefficients for Noncircular Laminar Duct Flow ...

A significant heat-transfer enhancement can be obtained when a nonckcular tube is used together with a non-Newtonian fluid. This heat-transfer enhancement is attributed to both the secondary flow at the corner of the nonckcular tube (23,24) and to the temperature-dependent non-Newtonian viscosity (25). Using an aqueous solution of polyacrjiamide the laminar heat transfer can be increased by about 300% in a rectangular duct over the value of water (23). 

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. 

I0-38Z ) is solved to give the temperature distribution from which the heat-transfer coefficient may be determined. The major difficulties in solving Eq. (5-38Z ) are in accurately defining the thickness of the various flow layers (laminar sublayer and buffer layer) and in obtaining a suitable relationship for prediction of the eddy diffusivities. For assistance in predicting eddy diffusivities, see Reichardt (NACA Tech. Memo 1408, 1957) and Strunk and Chao [Am. ln.st. Chem. Eng. J., 10, 269(1964)]. 

Laminar Flow Normally, laminar flow occurs in closed ducts when Nrc < 2100 (based on equivalent diameter = 4 X free area -i-perimeter). Laminar-flow heat transfer has been subjected to extensive theoretical study. The energy equation has been solved for a variety of boundaiy conditions and geometrical configurations. However, true laminar-flow heat transfer veiy rarely occurs. Natural-convecdion effects are almost always present, so that the assumption that molecular conduction alone occurs is not vahd. Therefore, empirically derived equations are most rehable. 

Annuli Approximate heat-transfer coefficients for laminar flow in annuh may be predicted by the equation of Chen, Hawkins, and Sol-berg [Tron.s. Am. Soc. Mech. Eng., 68, 99 (1946)] ... 

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 <... 

TABLE 5-5 Laminar-Flow Heat Transfer over Immersed Bodies [Eq (5-44)]... 

For laminar flow of power law fluids in channels of noncircular cross section, see Schecter AIChE J., 7, 445 48 [1961]), Wheeler and Wissler (AJChE J., 11, 207-212 [1965]), Bird, Armstrong, and Hassager Dynamics of Polymeric Liquids, vol. 1 Fluid Mechanics, Wiley, New York, 1977), and Skelland Non-Newtonian Flow and Heat Transfer, Wiley, New York, 1967). 

Economic Pipe Diameter, Laminar Flow Pipehnes for the transport of high-viscosity liquids are seldom designed purely on the basis of economics. More often, the size is dictated oy operability considerations such as available pressure drop, shear rate, or residence time distribution. Peters and Timmerhaus (ibid.. Chap. 10) provide an economic pipe diameter chart for laminar flow. For non-Newtouiau fluids, see SkeUand Non-Newtonian Flow and Heat Transfer, Chap. 7, Wiley, New York, 1967). 

Some of the devices covered here handle the solids burden in a static or laminar-flowing bed. Other devices can be considered as continuously agitated kettles in their heat-transfer aspect. For the latter, unit-area performance rates are higher. 

Topics that acquire special importance on the industrial scale are the quality of mixing in tanks and the residence time distribution in vessels where plug flow may be the goal. The information about agitation in tanks described for gas/liquid and slurry reactions is largely apphcable here. The relation between heat transfer and agitation also is discussed elsewhere in this Handbook. Residence time distribution is covered at length under Reactor Efficiency. A special case is that of laminar and related flow distributions characteristic of non-Newtonian fluids, which often occiu s in polymerization reactors. 

Outside heat transfer eoeffieients for unhaffled jaekets under laminar flow eonditions ean he ealeulated from. 

In a laminar boundary layer, no mixing takes place and the flow is parallel. In this case the heat transfer occurs mainly by conduction through the boundary layer. 

The preceding discussion has attempted to formulate the situation for laminar boundary layer flow as accurately as possible and to obtain precise correlation between the heat transfer and mass transfer factors. 

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