Heat transfer model comparison

Comparisons of the complete heat-transfer model with pilot-scale rotary kiln data are shown iu Figure 5 (21) for moisture levels ranging from 0 to 20 wt %. The tremendous thermal impact of moisture is clearly visible iu the leveling of temperature profiles at 100°C. 

Weislogel MM, Lichter S (1998) Capillary flow in an interior corner. 1 Eluid Mech 373 349-378 Wu PY, Little WA (1984) Measurement of the heat transfer characteristics of gas flow a fine channels heat exchangers used for microminiature refrigerators. Cryogenics 24 415 20 Xu X, Carey VP (1990) Film evaporation from a micro-grooved surface an approximate heat transfer model and its comparison with experimental data. J Thermophys 4(4) 512-520 Yarin LP, Ekelchik LA, Hetsroni G (2002) Two-phase laminar flow in a heated micro-channels. Int J Multiphase Flow 28 1589-1616... 

V. Dupont, J. Thome, and A. Jacobi. Heat transfer model for evaporation in microchannels, part 11 comparison with the database . International Journal of Heat and Mass Transfer, 47, pp. 3387-3401 (2004). 

A more recent study of the heat fluxes inside the reactor as well as a comparison of the theoretical data predicted by a radiation heat transfer model showed that radiation is the main mode of heat transfer in the multiple hearth reactor configuration used (10). 

Figure 5.21 Comparison between the heat-transfer models in the PBMR (a) averaged temperature profiles, Cq, = 5 vol.%...

Di Maio PP, Di Renzo A, Trevisan D Comparison of heat transfer models in DEM-CFD simulations of fluidized beds with an immersed probe. Powder Technol 193 257—265, 2009. 

Another concept sometimes used as a basis for comparison and correlation of mass transfer data in columns is the Clulton-Colbum analogy (35). This semi-empirical relationship was developed for correlating mass- and heat-transfer data in pipes and is based on the turbulent boundary layer model... 

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. 

The results of calculations of the Nusselt number are presented in Fig. 10.19. Here also the data of the calculated heat transfer by the quasi-one-dimensional model by Khrustalev and Faghri (1996) is shown. The comparison of the results related to one and two-dimensional model shows that for relatively small values of wall superheat the agreement between the one and two-dimensional model is good enough (difference about 3%), whereas at large At the difference achieves 30%. 

Anderson, R. P., and D. R. Armstrong, 1973, Comparison between Vapor Explosion Models and Recent Experimental Results, AIChE Preprint 16, 14th Natl. Heat Transfer Conf., Atlanta, GA. (2)... 

The heat transfer from tubes in the freeboard was also measured for the 20 MW model. Figure 45 shows a comparison of the measured overall heat transfer coefficient in the 20 MW pilot plant versus that predicted from the scale model test. When the bed height is lowered, uncovering some tubes, the heat transfer is reduced because there are fewer particles contacting the tube surface. Although the scale model did not include proper scaling for convective heat transfer, the rate of change of the overall heat transfer should be a function of the hydrodynamics. 

Figure 26. Comparison of predictions from cluster-based model to heat transfer data. (From Lints and Glicksman, 1993.)...

The parameter C in Eq. (25) is a dimensionless parameter inversely proportional to the average residence time of single particles on the heat transfer surface. It is suggested that this parameter be treated as an empirical constant to be determined by comparison with actual data in fast fluidized beds. The lower two dash lines in Fig. 17 represent predictions by Martin s model, with C taken as 2.0 and 2.6. It is seen that an appropriate adjustment of this constant would achieve reasonable agreement between prediction and data. 

In the common case of cylindrical vessels with radial symmetry, the coordinates are the radius of the vessel and the axial position. Major pertinent physical properties are thermal conductivity and mass diffusivity or dispersivity. Certain approximations for simplifying the PDEs may be justifiable. When the steady state is of primary interest, time is ruled out. In the axial direction, transfer by conduction and diffusion may be negligible in comparison with that by bulk flow. In tubes of only a few centimeters in diameter, radial variations may be small. Such a reactor may consist of an assembly of tubes surrounded by a heat transfer fluid in a shell. Conditions then will change only axially (and with time if unsteady). The dispersion model of Section P5.8 is of this type. 

De Wasch and Froment (1971) and Hoiberg et. al. (1971) published the first two-dimensional packed bed reactor models that distinguished between conditions in the fluid and on the solid. The basic emphasis of the work by De Wasch and Froment (1971) was the comparison of simple homogeneous and heterogeneous models and the relationships between lumped heat transfer parameters (wall heat transfer coefficient and thermal conductivity) and the effective parameters in the gas and solid phases. Hoiberg et al. (1971)... 

In accordance with the usual process conditions, the initial temperature of the reactive mixture To and the upper cap temperature Tw are constant during filling, and the temperature of the insert Ti equals the ambient temperature (20°C). The model takes into account that during filling the temperature of the insert increases due to heat transfer from the reactive mix. It is assumed that the thermal properties and density of both the reactive mass and the insert are constant. It is reasonable to neglect molecular diffusion, because the coefficient of diffusion is very small 264 therefore, the diffusion term is negligible in comparison with the other terms in the mass balance equation. 

Figure 1. Sorption of i-octane on 13X at U03 K (a) comparison of the experimental uptake with the best fit obtained by the present model (b) uptake with no internal heat transfer resistance and (c) uptake for an isothermal case.

FIGURE 20.4 Comparison of measured and modeled HRR in room corner test on particle board. Model calculations are for total HRR calculated with heat transfer limited pyrolysis model. (Adapted from Yan, Z. and Holmstedt, G Fire Saf../., 27, 201, 1996.)... 

The heat transfer coefficient h was calculated according to Hand-ley and Heggs (24) with the Reynolds number based upon an equivalent diameter, namely that of a sphere with the same volume as the actual particle. The overall heat transfer coefficient U was calculated from the heat transfer parameters of the two dimensional pseudohomogeneous model (since the interfacial At was found to be negligible), to allow for a consistent comparison with two dimensional predictions and to try to predict as closely as possible radially averaged temperatures in the bed (25). Therefore ... 

Kuznetsov A.V., Vafai K. (1995) Analytical comparison and criteria for heat and mass transfer models in metal hydrides packed beds. Int J Hydrogen Energy, 38, 2873-2884. 

Fig. 25. Comparison of experimental heat transfer coefficients with model, Eq. (7) (Bai et al, 1991).

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