Energy source terms

The last term Sh is the volumetric heat source, which may include user-defined energy source terms. The sensible enthalpy, h, is defined as... 

One-Dimensional Conduction In the absence of energy source terms, Q is constant with distance, as shown in Fig. 5-la. For steady conduction, the integrated form of (5-1) for a planar system with constant k and A is Eq. (5-2) or (5-3). F or the general case of variables k (k is a function of temperature) and A (cylindrical and spherical systems with radial coordinate r, as sketched in Fig. 5-2), the average heat-transfer area and thermal conductivity are defined such that... 

For the particular systems where gravity is the only external force considered, the corresponding energy source terms vanish. 

The two phases are coupled explicitly with mass flux and energy flux preserved. Thermal radiation from gas phase reaction is neglected in this model only laser radiation and conductive heat feedback from adjacent gas phase grids are taken into account as energy source terms for the condensed phase, which is critical to realize the pressure dependence of the mass burning rate. 

For an LES approach, the k-e model has to be replaced with an appropriate SGS model discussed in the section LES Turbulence Modeling. The important difference between RANS and LES for sprays is that the LES models do not require a spray source term. This is because the large eddies, which contain most of the turbulent energy, are resolved and, therefore, the work done by the turbulence on the droplets is taken into account by the droplet energy source term. ... 

Po - dimensionless energy source term, defined in Table 2.2.2 Xm - weight fraction monomer To - initial particle temperature, K T - surface particle temperature, K... 

Based on the kinetic results from the previous subsections, Dar (1999) estimated interior particle temperatures for FRRPP of styrene in ether. He used the same approach as the quasi-steady-state approximation in Section 2.2, which resulted in the use of the same differential equation and boundary conditions (Eqs. 2.2.1 and 2.2.2). The difference is that he employed a temperature-independent energy source term wherein the rate of reaction was based on the calculated derivative of monomer concentration with respect to time within a certain population of polymer-rich particles thus. 

From the table, it is evident that the dimensionless energy source term... 

T, absolute temperature Q, conductive plus radiative heat flux functions S, energy source term (units of energy/time/volume) from chemical reactions, transmutation reactions, mass conversions to energy, etc. 

According to the theory of relativity, E = ntc, nuclear fission decreases mass and converts it to energy. However, because the mass reduction is insignificant for engineering purposes (one atomic mass imit for 931.4 MeV), energy and mass conservation equations are normally decoupled in thermodynamics. Instead, mass is considered to be conserved and fission energy is treated as an energy source term. 

The laws of convection and conduction are contained directly in Eq. (25.8), whereas radiation requires an additional radiation model and is taken into account using the energy source density ai or an additional source term. The terms keff and describe the effective conductivity and effective stress tensor, respectively, and comprise a laminar and a turbulent part. The other production and applied densities are summarized in a simpHfied form in the energy source term St, in Eq. (25.8). 

And collision part of energy source term can be written as... 

Cp is heat capacity, pp pellet density, and Ap effective thermal conductivity of the porous solid as obtained from an Effective Medium Approach by Marcussen (ref. 10). Qod is the isosteric heat of adsorption which gives rise to the energy source term in above equation. 

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