Heat transfer coefficient index

In model equations, Uf denotes the linear velocity in the positive direction of z, z is the distance in flow direction with total length zr, C is concentration of fuel, s represents the void volume per unit volume of canister, and t is time. In addition to that, A, is the overall mass transfer coefficient, a, denotes the interfacial area for mass transfer ifom the fluid to the solid phase, ah denotes the interfacial area for heat transfer, p is density of each phase, Cp is heat capacity for a unit mass, hs is heat transfer coefficient, T is temperature, P is pressure, and AHi represents heat of adsorption. The subscript d refers bulk phase, s is solid phase of adsorbent, i is the component index. The superscript represents the equilibrium concentration. 

Here the index i distinguishes the different regions, Q is the overall heat flux from outside into the system through the i-th region, which is maintained at the temperature Ij. If we have only two surfaces with temperatures Tj and Tn, then Qj = —Qn by the conservation of energy. Referring the heat transfer to some surface S0, we determine the heat transfer coefficient... 

For the numerical calculation of the pressure drop, as well as the velocity held, one must iterate the pressure at every radial position until the how rate in the cavity is the same as that across the tube entrance. In both Eqs. 13.1-4 and 13.1-5, the consistency index m varies with z, since the temperature varies in the thickness direction. Two boundary conditions used in the energy equation are of interest. At the advancing front r = rlk, the heat transferred to the air in the mold dictates that the term 2r, h(Tn -Ta)/(rjk — rfk, ) be included in the right-hand side of Eq. 13.1-2, where h is the heat-transfer coefficient to the air. At the mold wall... 

Considering these Biot numbers, we can observe that they are similar to the Nusselt and Sherwood numbers. The only difference between these dimensionless numbers is the transfer coefficient property characterizing the Biot numbers transfer kinetics for the external phase (a x heat transfer coefficient for the external phase, k ex- mass transfer coefficient for the external phase). We can conclude that the Biot number is an index of the transfer resistances of the contacting phases. 

Included among the factors is the effectiveness index. It is a measure of the cost-effectiveness of an exchanger, and is defined as /= overall heat-transfer coefficient/heat-ex-changer cost. With coefficients expressed in Biu/(h) ft )CF), and purchase costs in /ft, Elis given as Btu/(h) °F)( ). Such indices are shown in the table, and these are averages for a variety of heat-exchanger sizes (250, 500, 750 and 1,000 ft )... 

Note that the operative temperature will be the arithmetic average of the ambient and surrounding surface temperatures when the convection and radiation heat transfer coefficients are equal to each other. Another environmental index used in thermal comfort analysis is the effective temperature, which combines the effects of temperature and humidity. Two environments with the same effective temperature evokes the same thermal response in people even though they are at different temperatures and humidities. 

The results for the TEA--water mixtures at atmospheric pressure are shown in Figure 6. These are for TEA mole fractions of x 0.05 and 0.59. The LOST is 18.2 at x - 0.09. We also obtained a very similar data set at the latter mole fraction, but we omitted it for clarity. For contrast and comparison, a data set for pure water is shown. These mixture results again show a sharp rise in heat transfer coefficient as condensate first appeared. In fact, the appearance was remarkably similar to the n-decane--C02 results for x - 0.973 discussed above, but the visibility of the phase separation was enhanced by the presence of a fine emulsion at the phase interface and the absence of strong refractive index gradients characteristic of the supercritical systems. This permitted the structure of the interface to be seen more clearly. In Figure 7 we show photographs that typify the appearance of the two phases. In all cases observed here, both in supercritical vapor--liquid and in liquid--liquid systems, the dense phase appears to wet the cylinder surface regardless of composition. 

TABLE 12-30 Values of the Index n in Correlations for the Volumetric Heat-Transfer Coefficient (after Baker 1983)... 

Following on from the definition equation (1.23) for the heat transfer coefficient, the molar flow transferred to the surface (index 0) is described by... 

In the same way as shown in the previous section, the heat transfer coefficient and from that the mean Nusselt number Nume = amed/A (the index e stands for entry flow) can be obtained from the temperature profile. The Nusselt number can be calculated from an empirical equation of the form... 

The index s signifies the material properties of the condensate film at the saturation temperature, whilst index 0, indicates those properties that are formed at the wall temperature. The heat transfer coefficient QtNu according to Nusselt s film condensation theory, (4.12), is calculated with the mean material properties... 

Surface roughening is used for the Advanced Gas-Cooled Reactors in the United Kingdom and is being considered for the gas-cooled fast-breeder reactors being studied in the United States. A doubling of the heat-transfer coefficient is obtained, for example, by tripling the friction factor (27), thus improving the merit index h f 18). 

A sheet of polymethyl methacrylate 0.20 in. thick is heated radiantly to a surface temperature of 2000°F for 519 s. The convective heat-transfer coefficient is 8.85 Btu/h F. What heat transfer would be needed to yield the same evenness index for the same time of exposure Explain the difference in the two situations. 

In order to investigate the regulatory operability of the process, additionally the anticipated ranges of disturbances needs to be specified, that will define the Expected Disturbance Space (EDS). For the steady-state case, the EDS may also reflect the uncertainties in some of the important model parameters employed in the design, such as kinetic constants, heats of reaction, heat-transfer coefficients, etc. The regulatory operability index is defined from the inputs required to compensate for the effect of disturbances while maintaining the plant at its nominal set point, as ... 

The flow pattern, mixing characteristics and heat transfer performance of this combined impeller were studied on the basis of laboratory cold simulation tests. The results were expected to form the foundation for the development of the combined impeller. The equation of the power munber and the heat transfer coefficient were obtained by experiment. Factors affecting the mixing time and segregation index were analysed. 8 refs. 

Tables 2,3, and 4 outline many of the physical and thermodynamic properties ofpara- and normal hydrogen in the sohd, hquid, and gaseous states, respectively. Extensive tabulations of all the thermodynamic and transport properties hsted in these tables from the triple point to 3000 K and at 0.01—100 MPa (1—14,500 psi) are available (5,39). Additional properties, including accommodation coefficients, thermal diffusivity, virial coefficients, index of refraction, Joule-Thorns on coefficients, Prandti numbers, vapor pressures, infrared absorption, and heat transfer and thermal transpiration parameters are also available (5,40). Thermodynamic properties for hydrogen at 300—20,000 K and 10 Pa to 10.4 MPa (lO " -103 atm) (41) and transport properties at 1,000—30,000 K and 0.1—3.0 MPa (1—30 atm) (42) have been compiled. Enthalpy—entropy tabulations for hydrogen over the range 3—100,000 K and 0.001—101.3 MPa (0.01—1000 atm) have been made (43). Many physical properties for the other isotopes of hydrogen (deuterium and tritium) have also been compiled (44).

After writing mass balances, energy balances, and equilibrium relations, we need system property data to complete the formulation of the problem. Here, we divide the system property data into thermodynamic, transport, transfer, reaction properties, and economic data. Examples of thermodynamic properties are heat capacity, vapor pressure, and latent heat of vaporization. Transport properties include viscosity, thermal conductivity, and difiusivity. Corresponding to transport properties are the transfer coefficients, which are friction factor and heat and mass transfer coefficients. Chemical reaction properties are the reaction rate constant and activation energy. Finally, economic data are equipment costs, utility costs, inflation index, and other data, which were discussed in Chapter 2. 

The theoretical treatments considered so far have been based on the assumption that the thermo-physical properties are constant (i.e. independent of temperature and therefore the velocity profiles do not change over the heat transfer section of the tube. Christiansen and Craig [1962] investigated the effect of temperature-dependent power-law viscosity on the mean values of Nusselt number for streamline flow in tubes with constant wall temperature. They postulated that the flow behaviour index, n was constant and that the variation of the consistency coefficient, m, with temperature could be represented by equation (6.45) giving ... 

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