Bulk Surface-Temperature Calculations

Relationship of surface/bulk transition temperatures calculated for LhilOO)... 

The impact process of a 3.8 mm water droplet under the conditions experimentally studied by Chen and Hsu (1995) is simulated and the simulation results are shown in Figs. 16 and 17. Their experiments involve water-droplet impact on a heated Inconel plate with Ni coating. The surface temperature in this simulation is set as 400 °C with the initial temperature of the droplet given as 20 °C. The impact velocity is lOOcm/s, which gives a Weber number of 54. Fig. 16 shows the calculated temperature distributions within the droplet and within the solid surface. The isotherm corresponding to 21 °C is plotted inside the droplet to represent the extent of the thermal boundary layer of the droplet that is affected by the heating of the solid surface. It can be seen that, in the droplet spreading process (0-7.0 ms), the bulk of the liquid droplet remains at its initial temperature and the thermal boundary layer is very thin. As the liquid film spreads on the solid surface, the heat-transfer rate on the liquid side of the droplet-vapor interface can be evaluated by... 

Calculate the heat-transfer coefficient for a fluid with the properties listed below flowing through a tube 20 ft (6.1 m) long and of 0.62-in (0.016-m) inside diameter. The bulk fluid temperature is 212°F (373 K), and the tube surface temperature is 122°F (323 K). Calculate the heat-transfer coefficient if the fluid is flowing at a rate of 2000 lb/h (907.2 kg/h). Also calculate the heat-transfer coefficient if... 

Consider the criteria requiredfor nucleate boiling. Nucleate boiling occurs when the difference between the temperature of the hot surface and the bulk fluid temperature is above a certain value. At temperature differences less than this value, heat transfer occurs as a result of natural convection. Nucleate-boiling heat-transfer coefficients for a steel tube may be calculated using the equation... 

The variation of temperature near the bounding wall continues to be a major determinant of heat transfer though the surface. However, when the continuum approach breaks down, tlie conventional Newton s taw of cooling using wall and bulk fluid temperature needs to be modified. Specifically, unlike in macroscale objects where the wall and adjacent fluid temperatures arc equal (T = Tg), in a micro device there is a temperature slip and the two values are different. One well-known relation for calculating the temperature jump at the wall of a microgeometry was derived by vonSmoluchowski in 1898,... 

Fig.6. The B2(110) surface average (solid lines) and sub-lattice (dotted lines) concentrations of the segregant in AB model alloy as a function of reduced temperature calculated in the FCEM approximation for different segregation/order factors r (indicated near the plots). The difference in sub-lattice concentrations corresponds to the surface LRO parameter that vanishes at the surface transition temperature Tg that coincides with the bulk transition temperature T independently of r.

Fig.7. The B2(110) alloy surface average concentration as a function of temperature calculated in the FCEM approximation for model AcB c alloys with stoichiometric (c=0.50) and near-stoichimetric (c=0.49,0.51) bulk concentrations (segregation/order factor r =8.9).

In these equations 6 is the adsorbate surface coverage calculated from surface pressure data by means of the Gibbs adsorption equation, x, Xg are the mole fractions of the adsorbate and solvent respectively in the bulk solution, a is the activity of the adsorbate in the bulk solution, II(= 7 — 7) is the experimental surface pressure of the adsorbed film, 7 is the surface tension of the test solution, 7° is the value of 7 of the pure solvent, R is the gas constant and T is the temperature. 

The boundary conditions at the external surface of the catalyst are T = Tsurface and Ca = Ca surface, and A effeciive is the effective thermal conductivity of the composite catalyst structure (i.e., 1.6 x 10 J/cm s K for alumina). Initially, the surface temperature and concentration of reactant A in Uie vicinity of a single isolated catalytic peUet are chosen to match the inlet values to the packed reactor. If external mass and heat transfer resistances are minimal, then bulk gas-phase temperature and reactant concentration at each axial position in the reactor represent the characteristic quantities that should be used to calculate the intrapellet Damkohler number for nth-order chemical kinetics ... 

The calculated time dependence of the surface temperature and temperature in the depth of QD incorporation (0.15 and 0.3 pm) for different energies shows that the nanocrystal temperature reaches the value of bulk Ge melting temperature at the irradiation energy density of 0.9 J/cm2. The difference in the temperatures of nanocrystals embedded at various depths (0.15 and 0.3 pm) is enlarged with the energy increase. The difference reaches about 100 K under irradiation with... 

Figure 10.10a shows propane conversion contours obtained from 2D CFD calculations for catalytic propane combustion in a non-adiabatic microchannel for the conditions mentioned in the caption [23]. Unlike the homogeneous combustion case, the preheating and combustion zones in catalytic microburners overlap since catalytic reactions can occur on the hot catalyst surface close to the reactor entrance. Figure 10.10b shows a discontinuity in the Nu profile, similar to the homogeneous combustion problem. In this case, it happens at the boundary between the preheat-ing/combustion zone and the post-combustion zone. At this point, the bulk gas temperature (cup-mixing average) and wall temperatures cross over and the direction... 

The effect of intraparticle gradients was assumed to have been included in the estimated parameters, i.e. the reaction rates at the whole catalyst particle was calculated with the surface conditions. The intr article gradients were not calculated, because a commercial FCC catalyst was used in the experiments. The bulk gas temperature was assumed to remain constant along the reactor length due to the surrounding heating oven. 

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