Modeling heat transfer enhancement

Various recent fin tube models include surface tension effects [89, 93, 94, 95, 96, 97]. The best model for design purposes, because of its relative simplicity, is due to Rose [95]. His expression for the heat transfer enhancement ratio a7- (defined as the average heat transfer coefficient for the finned tube divided by the average value for the smooth tube, both based on the smooth tube surface area at fin root diameter and for the same film temperature difference (Ts - Two)) for trapezoidal-shaped fins is [89] ... 

Ultrasound can thus be used to enhance kinetics, flow, and mass and heat transfer. The overall results are that organic synthetic reactions show increased rate (sometimes even from hours to minutes, up to 25 times faster), and/or increased yield (tens of percentages, sometimes even starting from 0% yield in nonsonicated conditions). In multiphase systems, gas-liquid and solid-liquid mass transfer has been observed to increase by 5- and 20-fold, respectively [35]. Membrane fluxes have been enhanced by up to a factor of 8 [56]. Despite these results, use of acoustics, and ultrasound in particular, in chemical industry is mainly limited to the fields of cleaning and decontamination [55]. One of the main barriers to industrial application of sonochemical processes is control and scale-up of ultrasound concepts into operable processes. Therefore, a better understanding is required of the relation between a cavitation coUapse and chemical reactivity, as weU as a better understanding and reproducibility of the influence of various design and operational parameters on the cavitation process. Also, rehable mathematical models and scale-up procedures need to be developed [35, 54, 55]. 

Performing this reaction primarily served as a model to show the feasibility of micro flow processing for soHd/Hqnid reactions [19]. In a similar way as for catalyzed gas-phase reactions, micro-reactor processing was expected to show benefits in terms of mass and heat transfer. Particularly this relates to transfer enhancement when using porous media. 

The second approach assigns thermal resistance to a gaseous boundary layer at the heat transfer surface. The enhancement of heat transfer found in fluidized beds is then attributed to the scouring action of solid particles on the gas film, decreasing the effective film thickness. The early works of Leva et al. (1949), Dow and Jacob (1951), and Levenspiel and Walton (1954) utilized this approach. Models following this approach generally attempt to correlate a heat transfer Nusselt number in terms of the fluid Prandtl number and a modified Reynolds number with either the particle diameter or the tube diameter as the characteristic length scale. Examples are ... 

The variation of efficiencies is due to interaction phenomena caused by the simultaneous diffusional transport of several components. From a fundamental point of view one should therefore take these interaction phenomena explicitly into account in the description of the elementary processes (i.e. mass and heat transfer with chemical reaction). In literature this approach has been used within the non-equilibrium stage model (Sivasubramanian and Boston, 1990). Sawistowski (1983) and Sawistowski and Pilavakis (1979) have developed a model describing reactive distillation in a packed column. Their model incorporates a simple representation of the prevailing mass and heat transfer processes supplemented with a rate equation for chemical reaction, allowing chemical enhancement of mass transfer. They assumed elementary reaction kinetics, equal binary diffusion coefficients and equal molar latent heat of evaporation for each component. 

It is noted that most of the models and correlations that are developed are based on bubbling fluidization. However, most of them can be extended to the turbulent regime with reasonable error margins. The overall heat transfer coefficient in the turbulent regime is a result of two counteracting effects, the vigorous gas-solid movement, which enhances the heat transfer and the low particle concentration, which reduces the heat transfer. 

Experiments have shown that Eq. (11.63) tends to underestimate the heat transfer rate from a column of tubes, and is thus conservative for design purposes. The actual heat transfer rates are enhanced by several factors not accounted for in the theoretical model discussed above. These factors include such effects as splashing of the film when it impinges on a lower tube, additional condensation on the subcooled film as it falls between tubes, and uneven run-off because of bowed or slightly inclined tubes. 

In this chapter, emphasis will be given to heat transfer in fast fluidized beds between suspension and immersed surfaces to demonstrate how heat transfer depends on gas velocity, solids circulation rate, gas/solid properties, and temperature, as well as on the geometry and size of the heat transfer surfaces. Both radial and axial profiles of heat transfer coefficients are presented to reveal the relations between hydrodynamic features and heat transfer behavior. For the design of commercial equipment, the influence of the length of heat transfer surface and the variation of heat transfer coefficient along the surface will be discussed. These will be followed by a description of current mechanistic models and methods for enhancing heat transfer on large heat transfer surfaces in fast fluidized beds. Heat and mass transfer between gas and solids in fast fluidized beds will then be briefly discussed. 

Numerical procedure to calculate the heat transfer during evaporation has heen developed for the rectangular minichannel. Some conductive calculations are shown to compare with the experimental data. They illustrate the non-uniform nature of local heat transfer around the perimeter of the channel. Rivulet and dry spot formation are descrihed. Numerical calculations show the enhancement of the heat transfer at large liquid Reynolds numbers caused at least in part by liquid suction to channel s corner where the area of microscale heat transfer arises. At small liquid Reynolds numbers the heat transfer reduction occurs due to dry spot formation. By comparing the model with the experimental data, it is shown that these conclusions are in consistent with the experimental results. 

It is possible, indeed desirable in some cases, to use combined heat transfer modes, e.g., convection and conduction, convection and radiation, convection and dielectric fields, etc., to reduce the need for increased gas flow that results in lower thermal efficiencies. Use of such combinations increases the capital costs, but these may be offset by reduced energy costs and enhanced product quality. No generalization can be made a priori without tests and economic evaluation. Finally, the heat input may be steady (continuous) or time-varying also, different heat transfer modes may be deployed simultaneously or consecutively depending on the individual application. In view of the significant increase in the number of design and operational parameters resulting from such complex operations, it is desirable to select the optimal conditions via a mathematical model. 

Flow through the porous bed enhances the radial effective or apparent thermal conductivity of packed beds [10, 26]. Winterberg andTsotsas [26] developed models and heat transfer coefficients for packed spherical particle reactors that are invariant with the bed-to-particle diameter ratio. The radial effective thermal conductivity is defined as the summation of the thermal transport of the packed bed and the thermal dispersion caused by fluid flow, or ... 

W. Nakayama, T. Daikoku, H. Kuwahara, and T. Nakajima, Dynamic Model of Enhanced Boiling Heat Transfer on Porous Surface—Parts I and II, J. Heat Transfer (102) 445-456,1980. 

Nucleate pool boiling has been very widely studied, and it would be impossible in the present context to give a detailed review of the vast amount of work done. Rather, some of the more salient points are addressed. The effect of various system parameters on pool boiling is first discussed, and then the mechanisms of nucleate pool boiling are reviewed with emphasis on recent findings. A number of the most widely used correlations for pool heat transfer are presented, and predictive models are discussed based on a more phenomenological approach. The effect of multicomponent mixtures on nucleate pool boiling and the various methods by which enhanced heat transfer can be obtained are also discussed. 

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