Power temperature distributions

A variety of studies can be found in the literature for the solution of the convection heat transfer problem in micro-channels. Some of the analytical methods are very powerful, computationally very fast, and provide highly accurate results. Usually, their application is shown only for those channels and thermal boundary conditions for which solutions already exist, such as circular tube and parallel plates for constant heat flux or constant temperature thermal boundary conditions. The majority of experimental investigations are carried out under other thermal boundary conditions (e.g., experiments in rectangular and trapezoidal channels were conducted with heating only the bottom and/or the top of the channel). These experiments should be compared to solutions obtained for a given channel geometry at the same thermal boundary conditions. Results obtained in devices that are built up from a number of parallel micro-channels should account for heat flux and temperature distribution not only due to heat conduction in the streamwise direction but also conduction across the experimental set-up, and new computational models should be elaborated to compare the measurements with theory. 

The authors developed a multi-layered microreactor system with a methanol reforma- to supply hydrogen for a small proton exchange membrane fiiel cell (PEMFC) to be used as a power source for portable electronic devices [6]. The microreactor consists of four units (a methanol reformer with catalytic combustor, a carbon monoxide remover, and two vaporizers), and was designed using thermal simulations to establish the rppropriate temperature distribution for each reaction, as shown in Fig. 3. 

The spatially periodic temperature distribution produces the corresponding relxactive index distribution, which acts as an optical phase grating for the low-power probing laser beam of the nonabsorbed wavelength in the sample. The thermal diffusivity is determined by detecting the temporal decay of the first-order diffracted probing beam [°o exp(-2t/x)] expressed by... 

Dodelet and Freeman, 1975 Jay-Gerin et ah, 1993). The main outcome from such analysis is that the free-ion yield, and therefore by implication the (r(h) value, increases with electron mobility, which in turn increases with the sphericity of the molecule. The heuristic conclusion is that the probability of inter-molecular energy losses decreases with the sphericity of the molecule, since there is no discernible difference between the various hydrocarbons for electronic or intramolecular vibrational energy losses. The (rth) values depend somewhat on the assumed form of distribution and, of course, on the liquid itself. At room temperature, these values range from -25 A for a truncated power-law distribution in n-hexane to -250 A for an exponential distribution in neopentane. 

Figure 12.20 shows the ceiling jet temperature distribution normalized by the maximum rise in the jet as a function of distance from the ceiling normalized with the jet thickness. The results apply to salt concentrations or temperature, and show that the distribution is independent of the distance from the plume. This saltwater analog technique is a powerful method for examining fire-induced flows, in particular with the technology demonstrated by Yao and Marshall [27]. 

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. 

In case of a homogeneous temperature distribution in the heated area, h corresponds to the temperature coefficient of the heater material, otherwise h includes the effects of temperature gradients on the hotplate. As a consequence of the aheady mentioned self-heating, the applied power is not constant over time, and the hotplate cannot be simply modelled using a thermal resistance and capacitance. Replacing the right-hand term in Eq. (3.28) by Eq. (3.35) leads to a new dynamic equation ... 

With the development of modern computation techniques, more and more numerical simulations occur in the literature to predict the velocity profiles, pressure distribution, and the temperature distribution inside the extruder. Rotem and Shinnar [31] obtained numerical solutions for one-dimensional isothermal power law fluid flows. Griffith [25], Zamodits and Pearson [32], and Fenner [26] derived numerical solutions for two-dimensional fully developed, nonisothermal, and non-Newtonian flow in an infinitely wide rectangular screw channel. Karwe and Jaluria [33] completed a numerical solution for non-Newtonian fluids in a curved channel. The characteristic curves of the screw and residence time distributions were obtained. 

Iwata M., Hikosaka T., Morita M., Iwanari T., Ito K., Onda K., Esaki Y., Sakaki Y., Nagata S., 2000. Performance analysis of planar-type unit SOFC considering current and temperature distribution. Journal of Power Sources 132, 297-308. 

Finally, a steady 1-D lumped stack model is introduced which uses a 0-D lumped approach for each cell in the stack. The model takes the current and power produced by each cell in the stack as input and predicts the 1 -D temperature distribution across the cells of the stack. Such models have the advantage of faster calculation time and are thus better suited for initial design calculations and control system modeling. In this model, each fuel cell is divided into three components, air channel, fuel channel and solid region (electrodes, electrolyte and the interconnect). The control volumes used for air and fuel channel components are shown by the dashed lines in Figure 5.6. The specie concentrations at the exit of air and fuel channels could be calculated using the mass and specie balances for these control volumes which are in the form... 

Maggio, G., Recupero, V. and Mantegazza, C. (1996) Modelling of temperature distribution in a solid polymer electrolyte fuel cell stack, Journal of Power Sources 62, 167-174. 

The occurrence of demixing morphologies characteristic for the metastable regime between the binodal and the spinodal can be understood from Fig. 17. The red dot marks the initial position of the sample with c = 0.3. Upon laser heating the temperature within the laser focus rises by AT and the distance to the binodal first increases. A stationary temperature distribution is rapidly reached and the Laplacian of the temperature field T(r,t) is obtained from the stationary solution of the heat equation (5) with the power absorbed from the laser as source term ... 

To proceed further, the relation between (T. - Tm) and (7, - T/) must be obtained. This could be done by integrating the temperature distributions obtained for each of the three layers. However, sufficient accuracy for most purposes is obtained by using the approximate l/7th power law, i.e., by assuming that the velocity and temperature distributions are effectively given by ... 

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