Thermal models, developing

Elastic Contact Conductance Models of Mikic and Greenwood and Williamson. Sridhar and Yovanovich [106] reviewed the elastic contact models proposed by Greenwood and Williamson [26] and Mikic [66] and compared the correlation equation with data obtained for five different metals. The models were developed for conforming rough surfaces they differ in the description of the surface metrology and the contact mechanics. The thermal model developed by Cooper et al. [14] was used. The details of the development of the models and the correlation equations are reviewed by Sridhar and Yovanovich [106]. The correlation equation derived from the Mikic [66] surface and asperity contact models is... 

Thermal Properties at Low Temperatures For sohds, the Debye model developed with the aid of statistical mechanics and quantum theoiy gives a satisfactoiy representation of the specific heat with temperature. Procedures for calculating values of d, ihe Debye characteristic temperature, using either elastic constants, the compressibility, the melting point, or the temperature dependence of the expansion coefficient are outlined by Barron (Cryogenic Systems, 2d ed., Oxford University Press, 1985, pp 24-29). 

Figure A-1 Development of the thermal model for power packages.

Hymes (1983) presents a fireball-specific formulation of the point-source model developed from the generalized formulation (presented in Section 3.5.1) and Roberts s (1982) correlation of the duration of the combustion phase of a fireball. According to this approach the peak thermal input at distance L is given by... 

To calculate the flow fields outside the evaporating meniscus we use the onedimensional model, developed by Peles et al. (1998, 2000, 2001). Assuming that the compressibility and the energy dissipation are negligible (a flow with moderate velocities), the thermal conductivity and viscosity are independent of the pressure and temperature, we arrive at the following system of equations ... 

A unified gas hydrate kinetic model (developed at ARC) coupled with a thermal reservoir simulator (CMG STARS) was applied to simulate the dynamics of CH4 production and C02 sequestration processes in the Mallik geological zones. The kinetic model contains two mass transfer equations one equation transfers gas and water into hydrate, and a decomposition equation transfers hydrate into gas and water (Uddin etal. 2008a). 

According to the above model developed for the interpretation of the Mossbauer spectra, iron is "mono-dispersed" on the Ti02 surface following low temperature thermal decomposition of Fe(C0)5, either as an oxidized species (Fe +) or as a subcarbonyl species. 

The mathematical model developed in the preceding section consists of six coupled, three-dimensional, nonlinear partial differential equations along with nonlinear algebraic boundary conditions, which must be solved to obtain the temperature profiles in the gas, catalyst, and thermal well the concentration profiles and the velocity profile. Numerical solution of these equations is required. 

Simple modifications to the model development presented in this work allow for simulating systems that do not include a central thermal well. For these cases, the heat transfer coefficients hlt and hls and the inner radius R0 are set equal to zero and the energy balance for the thermal well is neglected. In such cases, the dimensionality of the mathematical system is reduced by N, since one partial differential equation is eliminated. 

The theoretical model developed to explain these experiments is based on inelastic tunneling of electrons from the tip into the 2ir adsorbate resonance that induces vibrational excitation in a manner similar to that of the DIMET model (Figure 3.44(b)). Of course, in this case, the chemistry is induced by specific and variable energy hot electrons rather than a thermal distribution at Te. Another significant difference is that STM induced currents are low so that vibrational excitation rates are smaller than vibrational de-excitation rates via e-h pair damping. Therefore, coherent vibrational ladder climbing dominates over incoherent ladder climbing,... 

From the extensive experimental and model development work performed at CSM (during a period of over 15 years), it has been demonstrated that a heat transfer controlled model is able to most accurately predict dissociation times (comparing to laboratory experiments) without any adjustable parameters. The current model (CSMPlug see Appendix B for details and examples) is based on Fourier s Law of heat transfer in cylindrical coordinates for the water, ice, and hydrate layers, and is able to predict data for single- and two-sided depressurization, as well as for thermal stimulation using electrical heating (Davies et al 2006). A heat transfer limited process is controlled by the rate of heat supplied to the system. Therefore, a measurable intermediate (cf. activated state) is not expected for heat transfer controlled dissociation (Gupta et al., 2006). 

In this section we develop a dynamic model from the same basis and assumptions as the steady-state model developed earlier. The model will include the necessarily unsteady-state dynamic terms, giving a set of initial value differential equations that describe the dynamic behavior of the system. Both the heat and coke capacitances are taken into consideration, while the vapor phase capacitances in both the dense and bubble phase are assumed negligible and therefore the corresponding mass-balance equations are assumed to be at pseudosteady state. This last assumption will be relaxed in the next subsection where the chemisorption capacities of gas oil and gasoline on the surface of the catalyst will be accounted for, albeit in a simple manner. In addition, the heat and mass capacities of the bubble phases are assumed to be negligible and thus the bubble phases of both the reactor and regenerator are assumed to be in a pseudosteady state. Based on these assumptions, the dynamics of the system are controlled by the thermal and coke dynamics in the dense phases of the reactor and of the regenerator. 

Wang15 investigated heat and mass transport and electrochemical kinetics in the cathode catalyst layer during cold start, and identified the key parameters characterizing cold-start performance. He found that the spatial variation of temperature was small under low current density cold start, and thereby developed the lumped thermal model. A dimensionless parameter, defined as the ratio of the time constant of cell warm-up to that of ice... 

Thermal stress calculations in the five cell stack for the temperature distribution presented above were performed by Vallum (2005) using the solid modeling software ANSYS . The stack is modeled to be consisting of five cells with one air channel and gas channel in each cell. Two dimensional stress modeling was performed at six different cross-sections of the cell. The temperature in each layer obtained from the above model of Burt et al. (2005) is used as the nodal value at a single point in the corresponding layer of the model developed in ANSYS and steady state thermal analysis is done in ANSYS to re-construct a two-dimensional temperature distribution in each of the cross-sections. The reconstructed two dimensional temperature is then used for thermal stress analysis. The boundary conditions applied for calculations presented here are the bottom of the cell is fixed in v-dircction (stack direction), the node on the bottom left is fixed in x-direction (cross flow direction) and y-direction and the top part is left free to... 

Matlab-Simulink was used to develop a solver for the Coupled Lumped SOFC Thermal Model problem presented in Section 9.4.2. This solver was then applied to the problem of predicting the cell thermal transient due to a load change. The Simulink subsystems developed for this model are shown in Appendix A9.1, along with the list of model input parameters. 

Sewell and co workers [145-148] have performed molecular dynamics simulations using the HMX model developed by Smith and Bharadwaj [142] to predict thermophysical and mechanical properties of HMX for use in mesoscale simulations of HMX-containing plastic-bonded explosives. Since much of the information needed for the mesoscale models cannot readily be obtained through experimental measurement, Menikoff and Sewell [145] demonstrate how information on HMX generated through molecular dynamics simulation supplement the available experimental information to provide the necessary data for the mesoscale models. The information generated from molecular dynamics simulations of HMX using the Smith and Bharadwaj model [142] includes shear viscosity, self-diffusion [146] and thermal conductivity [147] of liquid HMX. Sewell et al. have also assessed the validity of the HMX flexible model proposed by Smith and Bharadwaj in molecular dynamics studies of HMX crystalline polymorphs. 

Figure 11 Adapted from Holmblad et al. [52]. Arrhenius plot of S0 vs. 1 /Tvlb for CH4 on Ni(l 0 0). Shown in the plot is the calculated thermal sticking coefficient from the model developed by Holmblad et al. [52]. Also shown are the separate contributions from the methane v = 0, v = 1, and v = 2 vibrational excitations, along with data obtained by Chorkendorff et al. [54],...

Pyrolysis as defined is a process of thermal decomposition occurring in the absence of oxygen. Pyrolysis of biomass is a complicated multistage reaction for which many pathways and mechanisms have been proposed.551-558 The best known is the model developed by Broido and Shafizadeh559,560 for pyrolysis of cellulose that can be also applied, at least qualitatively, to whole biomass (Fig. 33.30). 

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