Convected-mean average

Two consequences follow from these assumptions firstly, the convected (ensemble-) average field is close to homogeneity on a scale L 1q and secondly, the scalar fluctuations Xx X - X are much smaller then the mean value X. Moreover, the assumptions for u imply restriction to the domain close to the homogeneous limit (ideal mixing) ... 

In buildings away from outside perimeter walls, air and surface temperatures are usually approximately equal. The heat losses from a person by radiation (q ) and convection (q ) are then flowing to the same temperature level. In such uniform spaces, the radiant and convective losses are about equal and together account for about 80-90% of the total heat loss of a sedentary comfortable individual. In the presence of hot or cold surfaces, as may occur in perimeter or other locations in a building, the average surface temperature of the surroundings (called mean radiant temperature) as seen by the person s body may be substantially different from air temperature. If the mean radiant temperature (MRT) is greater or less than air temperature (T,) the person will feel warmer or colder than in a thermally uniform space where MRT =. ... 

Similar convection-diffusion equations to the Navier-Stokes equation can be formulated for enthalpy or species concentration. In all of these formulations there is always a superposition of diffusive and convective transport of a field quantity, supplemented by source terms describing creation or destruction of the transported quantity. There are two fundamental assumptions on which the Navier-Stokes and other convection-diffusion equations are based. The first and most fundamental is the continuum hypothesis it is assumed that the fluid can be described by a scalar or vector field, such as density or velocity. In fact, the field quantities have to be regarded as local averages over a large number of particles contained in a volume element embracing the point of interest. The second hypothesis relates to the local statistical distribution of the particles in phase space the standard convection-diffusion equations rely on the assumption of local thermal equilibrium. For gas flow, this means that a Maxwell-Boltzmann distribution is assumed for the velocity of the particles in the frame-of-reference co-moving with the fluid. Especially the second assumption may break dovm when gas flow at high temperature or low pressure in micro channels is considered, as will be discussed below. 

In the convection zone of the heater, some heat also is transferred by direct radiation and reflection. The several contributions to overall heat transfer specifically in the convection zone of fired heaters were correlated by Monrad [Ind. Eng. Chem. 24,505 (1932)]. The combined effects are approximated by item 10 of Table 8.16, which is adequate for estimating purposes. The relation depends on the temperature of the gas film which is taken to be the sum of the average process temperature and one-half of the log mean temperature difference between process and flue gas over the entire tube bank. The temperature of the gas entering the convection zone... 

After evaluation of the net solar heat input rates to the salt water, as monthly averages (or more frequently if desired), they and the atmospheric temperature averages are substituted in Equations 5 and 6. The two equations can then be solved by trial for the mean basin and cover temperatures each month. Distillation rate is then Qbtained by substitution of these values in Equation 4. The first and second terms on the right-hand side of Equation 5 may be separately evaluated for convection and radiation losses from basin to cover. 

The Eulerian (bottom-up) approach is to start with the convective-diffusion equation and through Reynolds averaging, obtain time-smoothed transport equations that describe micromixing effectively. Several schemes have been proposed to close the two terms in the time-smoothed equations, namely, scalar turbulent flux in reactive mixing, and the mean reaction rate (Bourne and Toor, 1977 Brodkey and Lewalle, 1985 Dutta and Tarbell, 1989 Fox, 1992 Li and Toor, 1986). However, numerical solution of the three-dimensional transport equations for reacting flows using CFD codes are prohibitive in terms of the numerical effort required, especially for the case of multiple reactions with... 

B. Single sphere, creeping flow with forced convection Nsh = = [4 ° + 1-21 [T] Use with log mean concentration difference. Average over sphere. Numerical calculations. (.NReNSc) < 10,000 Nrs < 1.0. Constant sphere diameter. Low mass-transfer rates. [46] [88] p. 114 [105] [138] p. 214... 

Tlie convection heal transfer coefficient, in general, varies along the flow (or X-) direction. The average or mean convection heat transfer coefficient for a surface in such cases is determined by properly averaging the local convection heat tran.sfcr coefficients over the entire surface. 

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