Heat flux parameterization

A = TIBL factor containing physics needed for TIBL parameterization (including heat flux) (m)... 

The preliminary investigation showed that lower pressures result in significantly higher heat fluxes. It s possible to approaeh 50 W/em while maintaining the wall temperature below 85 °C with little optimization. A more eomprehensive parameterization study will be addressed such as pore size, geometry, and other effeets as the limits of graphite foam evaporator performance [34-35]. 

Drag Coefficients for Wind Stress and for the Sensible and Latent Heat Flux For the numerical simulations of the Baltic Sea circulation discussed here, the parameterization of Smith and Banke (1975)... 

Further, a model has been introduced that predicts via molecular diffusion phenomena an isothermal bow at small scales and that the minimum wave velocity can be subsonic. A parameterization of the shear stresses and heat flux at the wall has led to new jump conditions [9]. 

The surface heat flux depends on cloud temperature, and therefore it is a function of cloud dilution and time history of the heat flux upslream of the observation point. The effect of surface heat flux has to be considered in the context of dispersion and to this end we shall apply a simplistic box model containing the essential cloud dynamics. The heat flux

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Equation (3) forms the basis for the parameterization of surface fluxes in all models of atmospheric circulations. This approach can be generalized to account for heat fluxes that are accompanied by buoyant acceleration of fluid elements. In this case, a must be replaced by a function where is a nondimensional parameter that measures the relative contributions of buoyancy and mechanically induced effects on fluid accelerations. Further extensions to account for a variety of other effects (most notably surface heterogeneity) not included in the formulation above are invariably also based on elaborations of (3) and remain an active area of research (Fairall et al., 2003). 

De Rosnay et al. (2000) assessed the reliability of schemes that parameterize land surface processes to find the correspondence between calculated mean annual fluxes of energy and moisture depending on detailed consideration of the vertical structure of soil. These schemes are used in general circulation models of the atmosphere (GCMAs). The calculations testify to the strong dependence of fluxes on vertical resolution. The 11-layer scheme parameterizing heat and moisture transfer in the top 1 mm thick layer of soil was found to be adequate. 

The conventional parameterizations used describing molecular transport of mass, energy and momentum are the Fick s law (mass diffusion), Fourier s law (heat diffusion or conduction) and Newton s law (viscous stresses). The mass diffusivity, Dc, the kinematic viscosity, i/, and the thermal diffusivity, a, all have the same units (m /s). The way in which these three quantities are analogous can be seen from the following equations for the fluxes of mass, momentum, and energy in one-dimensional systems [13, 135] ... 

The definitions of the heat and mass transfer fluxes are thus merely based on empirical arguments, so in the literature there are given more than one way to interpret the transfer coefficients [15, 139]. Basically, the transfer coefficients are either treated as an alternative model to the fundamental diffusion models (i.e., the Fourier s and Pick s laws) or the transfer coefficients are taking both diffusive and convective mechanisms into account through empirical parameterizations. However, in reaction engineering practice the distingtion between these approaches is rather blurred so it is not always clear which of the fundamental transport processes that are actually implemented. 

In this section the heat and mass transport coefficients for turbulent boundary layers are examined. In this case the model derivation is based on the governing Reynolds averaged equations. In these equations statistical covariances appear which involve fluctuating velocities, temperatures and concentrations. The nature of these terms is not known a priori and their effects must by estimated by semi-empirical turbulence modeling. The resulting parameterizations allow us to express the unknown turbulent fluctuations in terms of the mean flow field variables. It is emphasized that the Reynolds equations are not actually solved, merely semi-empirical relations are derived for the wall fluxes through the inner boundary layer. 

The modeling procedure can be sketched as follows. First an approximate description of the velocity distribution in the turbulent boundary layer is required. The universal velocity profile called the Law of the wall is normally used. The local shear stress in the boundary layer is expressed in terms of the shear stress at the wall. From this relation a dimensionless velocity profile is derived. Secondly, a similar strategy can be used for heat and species mass relating the local boundary layer fluxes to the corresponding wall fluxes. From these relations dimensionless profiles for temperature and species concentration are derived. At this point the concentration and temperature distributions are not known. Therefore, based on the similarity hypothesis we assume that the functional form of the dimensionless fluxes are similar, so the heat and species concentration fluxes can be expressed in terms of the momentum transport coefficients and velocity scales. Finally, a comparison of the resulting boundary layer fluxes with the definitions of the heat and mass transfer coefficients, indiates that parameterizations for the engineering transfer coefficients can be put up in terms of the appropriate dimensionless groups. 

It is noted that Sideman and Pinczewski [135], among others, have examined this hypothesis in further details and concluded that there are numerous requirements that need to be fulfilled to achieve similarity between the momentum, heat and mass transfer fluxes. On the other hand, there are apparently fewer restrictions necessary to obtain similarity between heat and low-flux mass transfer. This observation has lead to the suggestion that empirical parameterizations developed for mass transfer could be applied to heat transfer studies simply by replacing the Schmidt number Sct = ) by the Prandtl number Prt = and visa versa. 

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