Thermally simulated conductivity

POWDERS,HANDLING - DISPERSION OF POWDERS IN LIQUIDS] (Vol 19) Thermally simulated conductivity... 

The thermal resistance will be temperature-dependent as canbe seen in Eq. (3.24), which is not only a consequence of the temperature dependence of the thermal heat conduction coefficients. The measured membrane temperature, Tm, is related to the location of the temperature sensor, so that the temperature distribution across the heated area will also influence the thermal resistance value. The nonlinearity in Eq. (3.24) is, nevertheless, small. The expression thermal resistance consequently often refers to the coefficient t]o only, which is used as a figure of merit and corresponds, according to Eqs. (3.24) and (3.25), to the thermal resistance or thermal efficiency of the microhotplate at ambient temperature, Tq. The temperature Tm can be determined from simulations with distinct heating powers. The thermal resistance then can be extracted from these data. 

Values of the thermal conductivity of different chars are shown in Fig. 3. together with the conductivities of the cellulose pellets, and for reference, gaseous nitrogen. The chars tested for thermal diffusivity (conductivity) had fairly uniform properties because they were prepared in a pyrolysis furnace, and not in the simulated fire apparatus. This tended to minimize temperature gradients, but there was no assurance of absolutely uniform density, for the reasons noted above. Preparation of the chars followed a temperature history designed to simulate that in the simulated fire apparatus. 

Figure 2. Simulated temperature field in a X-section of the European ice sheet at its maximum last glaciation extent. The basal thermal gradient conducts away heat from the bed. The horizontal extent is 1200 km and the vertical 2,100m.

Ong, et al. Molecular dynamics simulation of thermal boundary conductance between carbon nanotubes and sio. Phys. Rev. B. 2010, 81. 

To explain the difference in the behavior of L-1 curves for the two LEDs, thermal simulation was carried out using FEMLAB. The steady-state heat diffusion equation in 2D was solved and Joule heating in the LED was assumed to be the sole heat source. It was also assumed that the heat extraction was from the back of the wafer. In the simulation, it was assumed that the thermal conductivity of free-standing m-plane GaN was assumed as 1.3 W cm ... 

The thermal conductivity of polymeric fluids is very low and hence the main heat transport mechanism in polymer processing flows is convection (i.e. corresponds to very high Peclet numbers the Peclet number is defined as pcUUk which represents the ratio of convective to conductive energy transport). As emphasized before, numerical simulation of convection-dominated transport phenomena by the standard Galerkin method in a fixed (i.e. Eulerian) framework gives unstable and oscillatory results and cannot be used. 

When experiments are carried out to select a suitable dryer and to obtain design data, the effect of changes in various extern variables is studied. These experiments should be conducted in an experimental unit that simulates the large-scale diyer from both the thermal and the material-handling aspects, and only material which is truly representative of full-scale production should be used. 

Moisture-transport simulation includes transport as well as storage phenomena, quite similar to the thermal dynamic analysis, where heat transfer and heat storage in the building elements are modeled. The moisture content in the building construction can influence the thermal behavior, because material properties like conductance or specific heat depend on moisture content. In thermal building-dynamics simulation codes, however, these... 

In many industrial halls, conduction inro the ground is a major factor for heat loss. Therefore, an adequate modeling of the floor slab and the underlying, thermally active, soil is very crucial for reliable simulation resuirs. In this case, the soil model in the TRNSYS model was established using results from an additionally performed finite-element program analysis. 

The objectives of this presentation are to discuss the general behavior of non isothermal chain-addition polymerizations and copolymerizations and to propose dimensionless criteria for estimating non isothermal reactor performance, in particular thermal runaway and instability, and its effect upon polymer properties. Most of the results presented are based upon work (i"8), both theoretical and experimental, conducted in the author s laboratories at Stevens Institute of Technology. Analytical methods include a Semenov-type theoretical approach (1,2,9) as well as computer simulations similar to those used by Barkelew LS) ... 

Transient Heat Conduction. Our next simulation might be used to model the transient temperature history in a slab of material placed suddenly in a heated press, as is frequently done in lamination processing. This is a classical problem with a well known closed solution it is governed by the much-studied differential equation (3T/3x) - q(3 T/3x ), where here a - (k/pc) is the thermal diffuslvity. This analysis is also identical to transient species diffusion or flow near a suddenly accelerated flat plate, if q is suitably interpreted (6). 

Forced-Convection Flow. Heat transfer in pol3rmer processing is often dominated by the uVT flow advectlon terms the "Peclet Number" Pe - pcUL/k can be on the order of 10 -10 due to the polymer s low thermal conductivity. However, the inclusion of the first-order advective term tends to cause instabilities in numerical simulations, and the reader is directed to Reference (7) for a valuable treatment of this subject. Our flow code uses a method known as "streamline upwindlng" to avoid these Instabilities, and this example is intended to illustrate the performance of this feature. 

Figure 3. Finite element simulation of plane Couette flow with thermal dissipation and conductive heat transfer. (f) — fixed temperature condition (c) — convective boundary condition.

Sindzinger and Gillan have calculated the thermal conductivity for NaCl and KCl melts as well as for sohds on the basis of MD simulations in Ml thermal equilibrium using the Green-Kubo relations (Table 17). In a single molten salt system, the local fluxes jz and of charge and energy... 

Simulation Results for the Thermal Conductivity of Molten NaCl and KCP"... 

The spatial temperature distribution established under steady-state conditions is the result both of thermal conduction in the fluid and in the matrix material and of convective flow. Figure 2. 9.10, top row, shows temperature maps representing this combined effect in a random-site percolation cluster. The convection rolls distorted by the flow obstacles in the model object are represented by the velocity maps in Figure 2.9.10. All experimental data (left column) were recorded with the NMR methods described above, and compare well with the simulated data obtained with the aid of the FLUENT 5.5.1 [40] software package (right-hand column). Details both of the experimental set-up and the numerical simulations can be found in Ref. [8], The spatial resolution is limited by the same restrictions associated with spin... 

Figure 8. The dimensionless thermal conductivity, b1tljcjljX,(t), at p = 0.8 and T0 = 2. The symbols are the simulation data, with the triangles using the instantaneous velocity at the end of the interval, X/(t), Eq. (277), and the circles using the coarse velocity over the interval, Eq. (278). The solid line is the second entropy asymptote, essentially Eq. (229), and the dotted curve is the Onsager-Machlup expression om(t)> Eq. (280). (Data from Ref. 6.)...

Figure 7 also shows results for the thermal conductivity obtained for the slit pore, where the simulation cell was terminated by uniform Lennard-Jones walls. The results are consistent with those obtained for a bulk system using periodic boundary conditions. This indicates that the density inhomogeneity induced by the walls has little effect on the thermal conductivity. 

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