Heat sink coefficient

In some appHcations, large quantities of waste or low cost heat are generated. The absorption cycle can be directly powered from such heat. It employs two intermediate heat sinks. Its theoretical coefficient of performance is described by... 

Sindlady, heating surface area needs are not direcdy proportional to the number of effects used. For some types of evaporator, heat-transfer coefficients decline with temperature difference as effects are added the surface needed in each effect increases. On the other hand, heat-transfer coefficients increase with temperature level. In a single effect, all evaporation takes place at a temperature near that of the heat sink, whereas in a double effect half the evaporation takes place at this temperature and the other half at a higher temperature, thereby improving the mean evaporating temperature. Other factors to be considered are the BPR, which is additive in a multiple-effect evaporator and therefore reduces the net AT available for heat transfer as the number of effects is increased, and the reduced demand for steam and cooling water and hence the capital costs of these auxiUaries as the number of effects is increased. 

A typical example of calculation of the thermal coefficient of performance for forced convection of air is shown in Fig. 2.69. COP surfaces are presented for the maximum and least material aluminum heat sink configurations in the design flow space between 0.01-0.04 m /s and 20-80 Pa. 

Because most applications for micro-channel heat sinks deal with liquids, most of the former studies were focused on micro-channel laminar flows. Several investigators obtained friction factors that were greater than those predicted by the standard theory for conventional size channels, and, as the diameter of the channels decreased, the deviation of the friction factor measurements from theory increased. The early transition to turbulence was also reported. These observations may have been due to the fact that the entrance effects were not appropriately accounted for. Losses from change in tube diameter, bends and tees must be determined and must be considered for any piping between the channel plenums and the pressure transducers. It is necessary to account for the loss coefficients associated with singlephase flow in micro-channels, which are comparable to those for large channels with the same area ratio. 

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... 

The detail experimental study of flow boiling heat transfer in two-phase heat sinks was performed by Qu and Mudawar (2003b). It was shown that the saturated flow boiling heat transfer coefficient in a micro-channel heat sink is a strong function of mass velocity and depends only weakly on the heat flux. This result, as well as the results by Lee and Lee (2001b), indicates that the dominant mechanism for water micro-channel heat sinks is forced convective boiling but not nucleate boiling. 

The large heated wall temperature fluctuations are associated with the critical heat flux (CHE). The CHE phenomenon is different from that observed in a single channel of conventional size. A key difference between micro-channel heat sink and a single conventional channel is the amplification of the parallel channel instability prior to CHE. As the heat flux approached CHE, the parallel channel instability, which was moderate over a wide range of heat fluxes, became quite intense and should be associated with a maximum temperature fluctuation of the heated surface. The dimensionless experimental values of the heat transfer coefficient may be correlated using the Eotvos number and boiling number. 

Effectively, Eqs. (86) and (87) describe two interpenetrating continua which are thermally coupled. The value of the heat transfer coefficient a depends on the specific shape of the channels considered suitable correlations have been determined for circular or for rectangular channels [100]. In general, the temperature fields obtained from Eqs. (86) and (87) for the solid and the fluid phases are different, in contrast to the assumptions made in most other models for heat transfer in porous media [117]. Kim et al. [118] have used a model similar to that described here to compute the temperature distribution in a micro channel heat sink. They considered various values of the channel width (expressed in dimensionless form as the Darcy number) and various ratios of the solid and fluid thermal conductivity and determined the regimes where major deviations of the fluid temperature from the solid temperature are found. 

A heat transfer coefficient is defined as the ratio of the area-normalized heat flow to the temperature difference between the heat source (the shelf) and the heat sink (the frozen product). For the case of vials resting directly on the freeze dryer shelf, the vial heat transfer coefficient, Kv, is defined by... 

The rate at which heat is transferred to a system can be expressed in terms of an overall heat transfer coefficient U, the area through which the heat exchange occurs and on which U is based, and the difference between the temperature of the heat source (or sink) Tm9 and that of the reactor contents T. 

Consider the reaction used as the basis for Illustrations 10.1 to 10.3. Determine the volume required to produce 2 million lb of B annually in a plug flow reactor operating under the conditions described below. The reactor is to be operated 7000 hr annually with 97% conversion of the A fed to the reactor. The feed enters at 163 C. The internal pipe diameter is 4 in. and the piping is arranged so that the effective reactor volume can be immersed in a heat sink maintained at a constant temperature of 160 °C. The overall heat transfer coefficient based on the... 

Note that as the coolant flow rate is increased at lower rates, the capability of the heat sink to remove thermal energy is enhanced. This effect has diminishing retnrns at high rates due to the increased dependency on condnctive rather than convective heat transfer. At low flow rates and at reduced effective heat-transfer coefficients, the resnlts are somewhat impractical. In these cases, adjacent IGBTs are not maintained at equal temperatures. This condition would generate imbalances in the electrical current sharing, resulting in nndesirable switch performance. 

Taking into account typical numbers for a and D, this underlines that the channel width should be considerably smaller than 1 mm (1000 pm) in order to achieve short residence times. Actually, heat exchangers of such small dimensions are not completely new, because liquid cooled microchannel heat sinks for electronic applications allowing heat fluxes of 790 watts/cm2 were already known in 1981 [46]. About 9 years later a 1 cm3 cross flow heat exchanger with a high aspect ratio and channel widths between 80 and 100 pm was fabricated by KFK [10, 47]. The overall heat transport for this system was reported to be 20 kW. This concept of multiple, parallel channels of short length to obtain small pressure drops has also been realized by other workers, e.g. by PNNL and IMM. IMM has reported a counter-current flow heat exchanger with heat transfer coefficients of up to 2.4 kW/m2 K [45] (see Fig. 3). 

Example 2.4. Two metal objects Bi and B2 (with constant masses m and m2 and constant heat capacities Cp and Cp2, respectively), initially at different temperatures (Tji0 and T2io), are brought into contact. Heat transfer occurs over a contact area A, with a heat-transfer coefficient U. The objects are assumed to be isolated from the environment however, the insulation on B2 is not perfect and heat is lost to the environment over a similar area A the heat transfer coefficient U, between l>2 and the environment is, however, much lower than U. The environment is assumed to act as a heat sink at a constant temperature Te. 

A slab separates two fluids of different temperatures as shown in Fig. 4. There are no heat sources or sinks in the slab. Heat will be transferred from the fluid of higher temperature to the slab, then conducted through the slab, and then transferred from the wall to the fluid of lower temperature. Under steady state conditions, the heat transfer will be the same on both surfaces and through the slab. If the heat transfer coefficients h and h2 at each side of the slab are constant, the following equations apply ... 

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