Heat transport coefficient

Dimensionless numbers (Reynolds number = udip/jj., Nusselt number = hd/K, Schmidt number = c, oA, etc.) are the measures of similarity. Many correlations between them (known also as scale-up correlations) have been established. The correlations are used for calculations of effective (mass- and heat-) transport coefficients, interfacial areas, power consumption, etc. 

Other parameters of the simulation are specified in subroutine SPECS. The quantity solcon is the solar constant, available here for tuning within observational limits of uncertainty. The quantity diffc is the heat transport coefficient, a freely tunable parameter. The quantity odhc is the depth in the ocean to which the seasonal temperature variation penetrates. In this annual average simulation, it simply controls how rapidly the temperature relaxes into a steady-state value. In the seasonal calculations carried out later in this chapter it controls the amplitude of the seasonal oscillation of temperature. The quantity hcrat is the amount by which ocean heat capacity is divided to get the much smaller effective heat capacity of the land. The quantity hcconst converts the heat exchange depth of the ocean into the appropriate units for calculations in terms of watts per square meter. The quantity secpy is the number of seconds in a year. 

Borkink, J.G.H., vande Watering, C.G. and Westerterp, K.R. (1992), The statisticalcharacter of bed-scale effective heat transport coefficients for packed beds, Trans. IChemE, 70(A), 610-619. 

Winterberg, M. and Tsotsas, E., 2000a. Correlations for Effective Heat Transport Coefficients in Beds Packed with Cylindrical Particles. Chemical Engineering Science, 55(23) 5937-5943. 

Heat transport coefficient between gas and solid phase... 

Heat transport coefficient in the hrst layer near the tube wall... 

Overall heat transport coefficient between the external and reaction bed Overall heat transfer coefficient between reaction and permeation zone Gas superficial velocity... 

Practically, mathematical models are based on the conservation laws of mass, energy and momentum, which lead to mass, energy and momentum balances. The balances, together with transport and kinetics equations, form a set of equations (ODE or PDE) whose solution gives the component concentrations, temperature and pressure profiles inside the reactor. Mass and heat transport coefficients, reactants and products physical properties, catalyst efficiency factor and all parameters appearing in model equations have to be expressed. 

Heterogeneous models, by which the fluid and solid phases are modeled separately, imposing balance equations for eaeh phase. Mass and heat fluxes between the solid and fluid phases are expressed in terms of partiele-to-fluid mass and heat transport coefficients. 

The global heat transport coefficient U is calculated from the sum of different heat resistances in a series. For a packed bed reactor, the heat transport resistances concern ... 

Different expressions are reported in the literature to evaluate the effective radial thermal conductivity [5] and the heat transport coefficient in the first layer near the tube wall fiw [6-9] for the pseudo-homogeneous fluid/solid phase. For ideal models, momentum balance is expressed as ... 

In Eq. 4.35 Omem is the membrane thermal conductivity, and 4nem,o are the internal and external membrane diameter, and hp xm is the convective heat transport coefficient in the permeation zone. 

Fj is the component molar flowrate i = H2O, CO, COj, H2, Inert) rj is the catalyst effectiveness factor e is the catalyst bed porosity (assumed to be equal to 0.5) is the shell tube radius r,i is the membrane tube radius (fco) is the rate of WGS reaction is the reaction temperature (K) n is the number of chemical species cpt is specific heat [J/mol Kj AHreaz is AH of reaction at temperature T [J/molj and U2 is a global heat transport coefficient from catalytic zone to permeation one [J/m -s-K]. 

This helps us to understand the meaning of the first two terms in Eqs (3.62) and (3.63). These terms arise due to asymmetry in the heat transport coefficients, conductivities and thicknesses of the anode and the cathode catalyst layers. In other words, these terms take into account the crossover of Joule heat (the terms with aj ) and of reaction heat (the terms with aj) through the membrane. As it should be, in the expression for total heat flux (3.64) the crossover terms cancel out. 

Table I summarizes the data for which a range of multiplicity was found by calculation. The table also includes numbers for the various heat transport coefficients of equations (1) and (2). These coefficients are determined experimentally ...

Express these dimensionless groups in terms of fundamental heat transport coefficients. 

Effective thermal conductivity of catalyst bed Overall heat transfer coefficient of the reactor shell Overall heat transfer coefficient of the membrane tube Gas/wall convective heat transport coefficient on the catalyst side Gas/membrane convective heat transfer coefficient on the catalyst side... 

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