Heat generation velocity

In the Couette flow inside a cone-and-plate viscometer the circumferential velocity at any given radial position is approximately a linear function of the vertical coordinate. Therefore the shear rate corresponding to this component is almost constant. The heat generation term in Equation (5.25) is hence nearly constant. Furthermore, in uniform Couette regime the convection term is also zero and all of the heat transfer is due to conduction. For very large conductivity coefficients the heat conduction will be very fast and the temperature profile will... 

Other gradient forces as in local heating generated by the exothermic hydrogen peroxide reaction were determined to be negligible because their contribution to velocity was less than a micron/second. Therefore, the interfacial force due to a concentration gradient appears to be the most reasonable dominant driving force for the Pt/Au nanorods. 

Fluidized-bed combustion (FBC) is a different technology from conventional pulverized-coal-fired boilers. A mixture of powdered rather than pulverized coal and a sorbent (usually limestone) are injected directly into the furnace and burned while suspended on a bed of high-velocity air. The turbulent mixing of coal and sorbent causes the solids to behave as a pseudo-fluid, enhancing heat generation and transfer at much lower temperatures (800-900 °C) compared to conventional pulverized-coal-fired furnaces (1500 °C) (US Department of Energy 1992). 

At low pressures (curve 1) the gas will initially heat up, because at T0, the heat generated is greater than the heat dissipated. Therefore, the reaction velocity will increase until temperature Tx is reached. At this point no further increase in the reaction velocity can occur, as the rate at which heat is generated is equal to its rate of removal. At high pressures (curve 3), the rate of heat generation is always greater than the rate of heat removal, so that the temperature of the gas, and consequently the reaction velocity, will rapidly increase until an explosion occurs. 

Typically, there are two types of boundaries in reacting flows. The first is a solid surface at which a reaction may be occurring, where the flow velocity is usually set to zero (the no-slip condition) and where either a temperature or a heat flux is specified or a balance between heat generated and lost is made. The second type of boundary is an inflow or outflow boundary. Generally, either the species concentration is specified or the Dankwerts boundary condition is used wherein a flux balance is made across the inflow boundary (64). The gas temperature and gas velocity profile are usually specified at an inflow boundary. At outflow boundaries, choices often become more difficult. If the outflow boundary is far away from the reaction zone, the species concentration gradient and temperature gradient in the direction of flow are often assumed to be zero. In addition, the outflow boundary condition on the momentum balance is usually that normal or shear stresses are also zero (64). 

The only dynamic phenomena of interest within the solid materials of an SOFC (cell, interconnects, end plates, etc.) is thermal energy transport. Here, the same formulation used for the gas-phase, Equation (9.10), can be used, except that here the velocity, V, is zero. While the solid body components do not show chemical reactions, Ri, there is internal heat generation through electrical ohmic losses. Hence, the model equation is ... 

Note that /ep in Eq. (5.238) is replaced with /Ep for Eq. (5.240), where /Ep is the heat generated by thermal radiation per unit volume and Qap is the heat transferred through the interface between gas and particles. Thus, once the gas velocity field is solved, the particle velocity, particle trajectory, particle concentration, and particle temperature can all be obtained directly by integrating Eqs. (5.235), (5.237), (5.231), and (5.240), respectively. Since the equations for the gas phase are coupled with those for the solid phase, final solutions of the governing equations may have to be obtained through iterations between those for the gas and solid phases. 

Another questionable assumption is that of constant temperature. Frictional forces lead to surface-heat generation. The total power introduced through the shaft is partly dissipated into heat at the barrel, flights, and root of the screw surfaces, and is partly used to generate pressure. However, most of the power is dissipated into heat at the barrel surface (Fig. 9.30). This quantity is given by the product of the force F and the relative velocity between barrel surface and solid plug (35)... 

Examination revealed that the sample contained both spherical and irregular particles, although the vast majority of particles were spherical. The spherical particles could originate from the considerable heat generated when a high velocity bullet strikes a hard surface, such as vehicle glass or bodywork.196... 

Isothermally Operated Reactors. In an isothermal reactor the temperature of the reactant stream is constant in axial direction. Hence this stream does not take up reaction heat (in the case of an exothermic reaction) and all heat generated within the bed must be transported radially to the reactor wall. If the bed radius is too large and the effective heat conductivity of the bed too low, a radial temperature profile will develop with appreciable differences between the centre of the bed and near the wall. The temperature profile will be more pronounced as the radial distances are longer and as fluid velocities are lower, hence, wide and short reactors are likely to suffer most from radial temperature inhomogeneity. 

With honeycombs (monoliths), pressure drop could be reduced by a factor of 100 or more, with corresponding reductions in equipment and operating costs. The total absence of radial flow in such structures, however, precludes their use in multitube reactors the bulk heat generated by the reaction would not be transported to the tube walls, the selectivity of the process would decrease dramatically, and prevention of reaction runaway would prove difficult. Furthermore, the lack of radial vectors means that inhomogeneities in radial velocity profiles would be maintained these inequalities in residence time would reduce selectivity and result in poor utilization of the catalyst in many of the channels. 

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