Radiative convective calculation

Fig. 1. Model Spectra re-binned to CRIRES Resolution To demonstrate the potential for precise isotopic abundance determination two representative sample absorption spectra, normalized to unity, are shown. They result from a radiative transfer calculation using a hydrostatic MARCS model atmosphere for 3400 K. MARCS stands for Model Atmosphere in a Radiative Convective Scheme the methodology is described in detail e.g. in [1] and references therein. The models are calculated with a spectral bin size corresponding to a Doppler velocity of 1 They are re-binned to the nominal CRIRES resolution (3 p), which even for the slowest rotators is sufficient to resolve absorption lines. The spectral range covers ss of the CRIRES detector-array and has been centered at the band-head of a 29 Si16 O overtone transition at 4029 nm. In both spectra the band-head is clearly visible between the forest of well-separated low- and high-j transitions of the common isotope. The lower spectrum is based on the telluric ratio of the isotopes 28Si/29Si/30Si (92.23 4.67 3.10) whereas the upper spectrum, offset by 0.4 in y-direction, has been calculated for a ratio of 96.00 2.00 2.00.

Charlock, T. P., and W. D. Sellers, 1980. Aerosol effects on climate calculations with time-dependent and steady-state radiative-convective models, J. Atmos. Sci., 37, 1327-1341. 

Based on calculations for 3M using a one-dimensional radiative convective model developed by... 

Pollack and Ackerman (1983) have reported the results of calculation with a one-dimensional radiative-convective model which predict the El Chichon cloud to have caused an increase of planetary albedo of 10%, a decrease in total radiation at the ground of 2-3%, and an increase in temperature of 3.5 degrees at the 30 mbar level. The GCM of the European Center for Medium Range Forecast was utilised to model the perturbation introduced by a fixed layer with an optical thickness of 0.15 added to the background a stratospheric warming of 3.5 C in the stratosphere and a cooling of about 0.1 C near the surface was obtained (Tanre and Geleyn, 1984). 

Other factors that need to be considered in any natural convection calculation include the geometry of the container (if any), flows generated from (or limited by) other surfaces in the vicinity, the interaction with forced flows, and possible radiative heat-transfer interactions. Because natural... 

The relationship between heat transfer and the boundary layer species distribution should be emphasized. As vaporization occurs, chemical species are transported to the boundary layer and act to cool by transpiration. These gaseous products may undergo additional thermochemical reactions with the boundary-layer gas, further impacting heat transfer. Thus species concentrations are needed for accurate calculation of transport properties, as well as for calculations of convective heating and radiative transport. 

The room models implemented in the codes can be distinguished further by how detailed the models of the energy exchange processes are. Simple models use a combined convective-radiative heat exchange. More complex models use separate paths for these effects. Mixed forms also exist. The different models can also be distinguished by how the problem is solved. The energy balance for the zone is calculated in each time step of the simulation. 

During the flight of droplets in the spray, the forced convective and radiative heat exchanges with the atomization gas lead to a rapid heat extraction from the droplets. A droplet undergoing cooling and phase change may experience three states (a) fully liquid, (b) semisolid, and (c) fully solid. If the Biot number of a droplet in all three states is smaller than 0.1, the lumped parameter model 1561 can be used for the calculation of droplet temperature. Otherwise, the distributed parameter model 1541 should be used. 

A conservative estimate of the resulting surface temperature is obtained by assuming no convective heat losses from the target structures. Equation 5-23 is used to calculate the surface temperature of the equipment due to an incident radiative heat flux from the fire and accounting for only radiation losses from the target. 

Another major and as yet unresolved issue centers upon precisely why SK-202-69 was a blue supergiant, and not a red one. This issue has been recently reviewed by Woosley (1987) and will be briefly summarized here. The essential problem is that there exist multiple solutions to the structure equations for the stellar atmosphere (see also Wheeler, this volume). Two stars having the same helium core mass and only slightly different luminosities, for example, can have radically different envelope structures, either a convective red supergiant or one that is radiative and blue (Woosley, Pinto, and Ensman 1987). There are several physical parameters that may break this symmetry and cause the star to chose one solution and not the other. Among them axe metallicity, (extreme) mass loss, and the theory of convection used in calculating the stellar model. 

Typically, a fire growth model is evaluated by comparing its calculations (predictions) of large-scale behavior to experimental HRR measurements, thermocouple temperatures, or pyrolysis front position. The overall predictive capabilities of fire growth models depend on the pyrolysis model, treatment of gas-phase fluid mechanics, turbulence, combustion chemistry, and convective/radiative heat transfer. Unless simulations are truly blind, some model calibration (adjusting various input parameters to improve agreement between model calculations and experimental data) is usually inherent in published results, so model calculations may not truly be predictions. 

Table 21.1. Bottom half of Table O.l s 3rd catalyst bed heatup path-equilibrium curve intercept worksheet. Input and output gas enthalpies are shown in rows 43 and 44. Note that they are the same. This is because our heatup path calculations assume no convective, conductive or radiative heat loss during catalytic SO2+V2O2 —> SO3 oxidation, Section 11.9. 1st and 2nd catalyst bed enthalpies are calculated similarly - using Tables J.2 and M.2. 

An adiabatic refractory surface of area Ar and emissivity er, for which Qr = 0, proves quite important in practice. A nearly radiatively adiabatic refractory surface occurs when differences between internal conduction and convection and external heat losses through the refractory wall are small compared with the magnitude of the incident and leaving radiation fluxes. For any surface zone, the radiant flux is given by Q = A(W - H) = tA(E - H) and Q = eA/p( - W) (if p 0). These equations then lead to the result that if Qr = 0,Er = Hr = Wrfor all 0 < er< 1. Sufficient conditions for modeling an adiabatic refractory zone are thus either to put , = 0 or to specify directly that Q, = 0 with , 0. If er = 0, SrSj = 0 for all 1 < j < M which leads directly by definition to Qr = 0. For er = 0, the refractory emissive power Er never enters the zoning calculations. For the special case of 0 and Mr = 1, a sin-... 

The heat transfer coefficients am and rad are approximately equal. This infers that free convection to the air and radiative exchange transport almost the same amount of heat. This is not true for forced convection, where m, depending on the flow velocity, is one to two powers of ten larger than the value calculated here. However, ra[Pg.29]

CALCULATE THE COMBINED CONVECTIVE AND RADIATIVE HEAT TRANSFER COEFFICIENT. 

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