Modified latent heat

X Modified latent heat of vaporisation per unit mass defined by (13.68) J/kg 1 T 2... 

The heat transfer across the vapor layer and the temperature distribution in the solid, liquid, and vapor phases are shown in Fig. 13. In the subcooled impact, especially for a droplet of water, which has a larger latent heat, it has been reported that the thickness of the vapor layer can be very small and in some cases, the transient direct contact of the liquid and the solid surface may occur (Chen and Hsu, 1995). When the length scale of the vapor gap is comparable with the free path of the gas molecules, the kinetic slip treatment of the boundary condition needs to be undertaken to modify the continuum system. Consider the Knudsen number defined as the ratio of the average mean free path of the vapor to the thickness of the vapor layer ... 

Therefore, to include subcooling effects, hfg is simply replaced by a modified latent heat, hy, which is>given by ... 

Rohsenow [32] has improved on the above analysis by performing an integral analysis that drops the assumption of a lirjear temperature protile. Based on this analysis, the following equation for the modified latent heat is recommended ... 

Eq. (11.35) therefore indicates that the effect of film subcooling will be small. The modified latent heat is given by ... 

Thomas presented an interesting paper (2021) relating H bonding and viscosity, and he was quick to point out the approximate nature of his treatment. He combined a modification of Andrade s viscosity equation with a relation between vapor pressure and latent heat of vaporization and still another function relating the heat of H bonding with the degree of association. From these he calculated an approximate heat of vaporization and compared it to a nonassociated value from a modified Trouton rule equation. The difference is called... 

Other propeities axe as listed before in connection with Eq. 10-2, We used a modified latent heat of vaporization in Eq. lO-.l to account for the heat tran.s-fet as.sociated with the superheating of the vapor. 

The Kirchhoff equation as derived above riiould be applicable to both chemical and physical processes, but one highly important limitation must be borne in mind. For a chemical reaction there is no difficulty concerning (dAH/dT)p, i.e., the variation of AH with temperature, at constant pressure, since the reaction can be carried out at two or more temperatures and AH determined at the same pressure, e.g., 1 atm., in each case. For a phase change, such as fusion or vaporization, however, the ordinary latent heat of furion or vaporization (AH) is the value under equilibrium conditions, when a change of temperature is accompanied by a change of pressure. If equation (12.7) is to be applied to a phase change the AH s must refer to the same pressure at different temperatures these are consequently not the ordinary latent heats. If the variation of the equilibrium heat of fusion, vaporization or transition with temperature is required, equation (12.7) must be modified, as will be seen in 271. 

HUMIDITY CHARTS FOR SYSTEMS OTHER THAN AIR-WATER. A humidity chart may be constructed for any system at any desired total pressure. The data required are the vapor pressure and latent heat of vaporization of the condensable component as a function of temperature, the specific heats of pure gas and vapor, and the molecular weights of both components. If a chart on a mole basis is desired, all equations can easily be modified to the use of molal units. If a chart at a pressure other than 1 atm is wanted, obvious modificatioi in the above equations may be made. Charts for several common systems besides air-water have been published. ... 

At a different point in the packed distillation column of Example 3.6, the methanol content of the bulk of the gas phase is 76.2 mol% that of the bulk of the liquid phase is 60 mol%. The temperature at that point in the tower is around 343 K. The packing characteristics and flow rates at that point are such that Fg = 1.542 x 10-3 kmol/m2-s and Fr = 8.650 x 10-3 kmol/m2-s. Calculate the interfacial compositions and the local methanol flux. To calculate the latent heat of vaporization at the new temperature, modify the values given in Example 3.6 using Watson s method (Smith et al., 1996) ... 

An estimation of the heat removed is complex since it not only involves latent heat of fusion, but sensible heat effects that may not be insignificant where large systems are involved. A further complication arises where natural convection in the water at the water ce interface occurs, i.e. modifying the simple conduction concept implied in Equation 9.5. 

In this study, the thermal properties of the rock mass were modified to take the effect of groundwater and latent heat of freezing into account. The result of the analysis with these modified thermal properties shows good agreement with the measured temperature distribution. 

Therefore, we conducted the analysis to predict the temperature distribution using modified thermal properties that is calculated by considering the effect of groundwater and latent heat of freezing. Initial thermal properties were estimated considering 20% of volume fraction of groundwater. 

During the numerical calculation, thermal properties were changed into modified values considering the latent heat of freezing when temperature of rock mass is reached 0°C. The modification was made by using the numerical formula (1) and (2). And latent heat term is considered to evaluate the energy need to freezing the water in unit volume of rock mass. 

Next, a constant, irreversible thermal process with a latent heat is added to the modulation cycles, as is found on cold crystallization of PET (see Figs. 4.74 and 4.136-139). A latent heat does not change the temperatures of Fig. A. 13.1, so that the heat-flow rates need to be modified, as is shown in the upper graph of Fig. A. 13.2. The constant latent heat is indicated by the vertically shaded blocks and is chosen to compensate the effect of the underlying heating rate, so that the level of Ps is moved to zero. The reversing specific heat capacity is given by ... 

For horizontal tube, L is replaced by the tube diameter, D, and constant 0.943 becomes 0.725. An improvement to the Nusselt model was made by Rohsenow (1956) who considered the effects of subcooling within the liquid film and also allowed for a nonlinear distribution of temperature through the film due to energy convection. The latent heat of vaporization, / fg, was replaced by a modified form /zfg = /Zfg + 0.68Cpf(Tsat - Ts ) in the above equation. 

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