Conduction enthalpy flow

At the outlet of the anode the gas (RG) consists of the non-utilised fuel and the reaction products CO2 and H2O. This mass flow is equal to the mass flow of the utilised fuel and of the transferred oxygen by the ion conduction through the electrolyte. The stoichiometric demand of oxygen related to the inlet fuel mass flow is given by the figure //.o2o- Finally, we get for the enthalpy flow at the anode outlet... 

The conduction entropy flow consists of the heat flow j" and the diffusion flow j,-. The j" is reduced heat flow that is the difference between the change in energy and the change in enthalpy due to matter flow. With the... 

As Pe oo, the contribution of axial conduction relative to axial enthalpy flow becomes negligible in Eqs. (2.150) and (2.152). For all practical problems... 

Axial conduction in the coolant is negligible compared to axial enthalpy flow. 

So far, we have demonstrated how to utilize numerical techniques to solve two-dimensional steady conduction problems. We now proceed to problems involving enthalpy flow. 

Qh being the longitudinal net enthalpy flow, >2 the enthalpy, flow across the two-phase interface, and Qk the conduction. In situations involving phase change, the Jacob number denoting the ratio of sensible heat to latent heat,... 

Using the relation between the chemical potential and enthalpy /x, = / , — Tsj = m, + Pv, — Ps, we can relate the second law heat flow J", the conduction energy flow J , and the pure heat flow as follows ... 

Space craft are exposed to extreme conditions on reentry into the atmosphere. It is of interest to investigate the thermal effects quantitatively. For this purpose, calorimeters are used to determine the heat flux and enthalpy flows in a plasma atmosphere that is created by an arcjet. Heat fluxes on the order of 50 MW rrT and enthalpy flows of about 20 MJ kg have to be measured at temperatures around 10 000 K. This can only be accomplished using transient techniques. To do so, the calorimeter, or the heat flux meter, is traversed through the arc and exposed to the plasma for only a fraction of a second, and the temperature increase of a thermocouple is measured. The calorimeter usually consists of a conical-shaped axisymmetric body of 25-50 mm diameter with a central bore in which a thermocouple is embedded close to the surface. Typical exposure times are 30 ms, resulting in temperature increases of several hundred kelvin. Traditionally, the measured temperature and the geometric parameters of the sensors are used to calculate the heat flux under the assumption of linear one-dimensional heat conduction. 

In towers with inert packing, both radial and axial gradients occur, although conduction in the axial direction often is neglected in view of the preponderant transfer of sensible enthalpy in a flow system. 

In these equations x and y denote independent spatial coordinates T, the temperature Tib, the mass fraction of the species p, the pressure u and v the tangential and the transverse components of the velocity, respectively p, the mass density Wk, the molecular weight of the species W, the mean molecular weight of the mixture R, the universal gas constant A, the thermal conductivity of the mixture Cp, the constant pressure heat capacity of the mixture Cp, the constant pressure heat capacity of the species Wk, the molar rate of production of the k species per unit volume hk, the speciflc enthalpy of the species p the viscosity of the mixture and the diffusion velocity of the A species in the y direction. The free stream tangential and transverse velocities at the edge of the boundaiy layer are given by = ax and Vg = —ay, respectively, where a is the strain rate. The strain rate is a measure of the stretch in the flame due to the imposed flow. The form of the chemical production rates and the diffusion velocities can be found in (7-8). 

Although the formation of ionic hydrides is usually exothermic, the formation of interstitial hydrides may have positive enthalpy values. Physical characteristics of interstitial hydrides are determined by the fact that hydrogen atoms in interstitial positions cause some expansion of the lattice but contribute very little mass. Consequently, the interstitial hydrides always have lower densities than the metal itself, even though the crystal structure is normally the same. When interstitial positions contain hydrogen atoms, the flow of electrons in conduction bands within the metal is impeded, so the... 

To overcome thermal entry effects, the segments may be virtually stacked with the outlet conditions from one segment that becomes the inlet conditions for the next downstream section. In this approach, axial conduction cannot be included, as there is no mechanism for energy to transport from a downstream section back to an upstream section. Thus, this method is limited to reasonably high flow rates for which axial conduction is negligible compared to the convective flow of enthalpy. At the industrial flow rates simulated, it is a common practice to neglect axial conduction entirely. The objective, however, is not to simulate a longer section of bed, but to provide a developed inlet temperature profile to the test section. 

Looking at a little slice of the process fluid as our system, we can derive each of the terms of Eq. (2.18). Potential-energy and kinetic-energy terms are assumed negligible, and there is no work term. The simplified forms of the internal ener and enthalpy are assumed. Diffusive flow is assumed negligible compared to bulk flow. We will include the possibility for conduction of heat axially along the reactor due to molecular or turbulent conduction. 

The quantity, h, in Equation 5 is not likely to be greatly different from its value in a plane adiabatic combustion wave. Taking x as the coordinate normal to such wave, h becomes the integral of the excess enthalpy per unit volume along the x-axis, so that the differential quotient, dh/dx, represents the excess enthalpy per unit volume in any layer, dx. Assuming the layer to be fixed with respect to a reference point on the x-axis, the mass flow passes through the layer in the direction from the unbumed, w, to the burned, 6, side at a velocity, S, transporting enthalpy at the rate Sdh/dx. Because the wave is in the steady state, heat flows by conduction at the same rate in the opposite direction, so that... 

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