Heat transfer small Reynolds number

One particular characteristic of conduction heat transfer in micro-channel heat sinks is the strong three-dimensional character of the phenomenon. The smaller the hydraulic diameter, the more important the coupling between wall and bulk fluid temperatures, because the heat transfer coefficient becomes high. Even though the thermal wall boundary conditions at the inlet and outlet of the solid wall are adiabatic, for small Reynolds numbers the heat flux can become strongly non-uniform most of the flux is transferred to the fluid at the entrance of the micro-channel. Maranzana et al. (2004) analyzed this type of problem and proposed the model of channel flow heat transfer between parallel plates. The geometry shown in Fig. 4.15 corresponds to a flow between parallel plates, the uniform heat flux is imposed on the upper face of block 1 the lower face of block 0 and the side faces of both blocks... 

John C. Berg, Andreas Acrivos, and Michel Boudart, Evaporation Convection H. M. Tsuchiya, A. G, Fredrickson, and R. Aiis, Dynamics of Microbial Cell Populations Samuel Sideman, Direct Contact Heat Transfer between Immiscible Liquids Howard Brenner, Hydrodynamic Resistance of Particles at Small Reynolds Numbers... 

Rushton et al. (R15) gave the first data on the use of vertical coils to act as baffles as well as heat transfer surfaces. Using Mixing Equipment Company flat-blade turbines, they noted that the heat transfer was best when the turbine was midway between tank bottom and water surface, based on tests with the liquid depth equal to tank diameter. The entries in Table VI are for this condition. Values of heat transfer coefficients on the order of 300-1200 B.T.U./(hr.) (ft.2) (°F.) were observed. Only one liquid was used and only a small Reynolds-number range was covered. 

Small Reynolds Number Flow, Re < 1. The slow viscous motion without interfacial mass transfer is described by the Hadamard (66)-Rybcynski (67) solution. For infinite liquid viscosity the result specializes to that of the Stokes flow over a rigid sphere. An approximate transient analysis to establish the internal motion has been performed (68), Some simplified heat and mass transfer analyses (69, 70) using the Hadamard-Rybcynski solution to describe the flow field also exist. These results are usually obtained through numerical integration since analytical solutions are usually difficult to obtain. 

Rimmer, P.L. (1968), Heat transfer from a sphere in a stream of small Reynolds number, J. Fluid Mech., 32, 1-7. 

It is important to recognize that the analysis presented in this section is generally applicable to any high-Peclet-number heat transfer process that takes place across a region of closed-streamline flow. In particular, the limitation to small Reynolds number is not an intrinsic requirement for any of the development from Eq. (9-309) to Eq. (9-334). It is only in the specification of a particular form for the function V( ) that we require an analytic solution for f and thus restrict our attention to the creeping-flow limit. Indeed all of (9-309)-(9-334) apply for any closed-streamline flow at any Reynolds number, provided only... 

This relation may be regarded as the counterpart of Stokes equations, Eqs. (7)-(8). Roughly speaking, Eq. (301) bears the same relationship to Eq. (299) at very small Peclet (and Reynolds) numbers as do Stokes equations to the complete Navier-Stokes equations at very small Reynolds numbers. Hence, many of the results of Section II pertaining to the solutions of Stokes equations have analogs in the theory of heat- (and mass-) transfer at asymptotically small Peclet numbers. It will suffice, therefore, to illustrate these analogs by a few salient examples. 

Since for liquids Sc 1, it follows from (5.116) that Peu 1 for values Re > 1, that is the convective flux dominates over the diffusion in liquids at finite (and sometimes at small) Reynolds numbers. In high-viscous liquids, Pr 1 and from (5.115) it follows that Pej 1 at not very small numbers Re. Hence, in this case the heat transfer is basically due to convection. 

The product of the cold area and fourth power of absolute temperature of the cold wall is insignificantly small. Thus, the warm area of the external shell governs the heat loss of a dewar. To keep the surface of the warm emitter as small as possible, an efficient design of a dewar vessel must strive for minimum spacing between the cold inner vessel and the warm outer shell. As the work of M. M. Fulk and M. M. Reynolds [2] has shown, the emissivity as a surface property has a minimum which cannot be improved by further polishing or surface treatment. The only way to achieve further reduction of the heat loss is to employ a multiplicity of radiation shields between the warm and cold surfaces. Various techniques have been developed for the installation of such shields between the cool and warm surfaces. Each of these shields, to be effective as a heat transfer barrier, must be allowed to assume proper equilibrium temperature. The heat transfer between each pair of successive shields obeys again the Stefan-Boltzmann law and the over-all heat transfer across any number of shields can be calculated by matrix algebra. 

Turboexpanders eurrently in operation range in size from about 1 hp to above 10,000 hp. In the small sizes, the problems are miniaturization, Reynolds Number effeets, heat transfer, seal, and meehanieal problems, and often inelude bearing and eritieal speed eoneerns. In intermediate sizes, these problems beeome less signifieant, but bearing rubbing speeds and vibration beeome inereasingly important. 

Judy J, Maynes D, Webb BW (2002) Characterization of frictional pressure drop for liquid flows through micro-channels. Int J Heat Mass Transfer 45 3477-3489 Kandlikar SG, Joshi S, Tian S (2003) Effect of surface roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Heat Transfer Eng 24 4-16 Koo J, Kleinstreuer C (2004) Viscous dissipation effects in microtubes and microchannels. Int J Heat Mass Transfer 47 3159-3169... 

Heat transfer in micro-channels occurs under superposition of hydrodynamic and thermal effects, determining the main characteristics of this process. Experimental study of the heat transfer in micro-channels is problematic because of their small size, which makes a direct diagnostics of temperature field in the fluid and the wall difficult. Certain information on mechanisms of this phenomenon can be obtained by analysis of the experimental data, in particular, by comparison of measurements with predictions that are based on several models of heat transfer in circular, rectangular and trapezoidal micro-channels. This approach makes it possible to estimate the applicability of the conventional theory, and the correctness of several hypotheses related to the mechanism of heat transfer. It is possible to reveal the effects of the Reynolds number, axial conduction, energy dissipation, heat losses to the environment, etc., on the heat transfer. 

There are two causes for oscillations of the heat flux, with 7 = const. (1) fluctuations of the heat transfer coefficient due to velocity fluctuations, and (2) fluctuations of the fluid temperature. At small enough Reynolds numbers the heat transfer coefficient is constant (Bejan 1993), whereas at moderate Re (Re 10 ) it is a weak function of velocity (Peng and Peterson 1995 Incropera 1999 Sobhan and Garimella 2001). Bearing this in mind, it is possible to neglect the influence of velocity fluctuations on the heat transfer coefficient and assume that heat flux flucmations are expressed as follows ... 

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