Heat flux equation

The value of the integral in the energy balance (equation 11.55) is again given by equation 11.60 [substituting (6S - 8o) for 0 ]. The heat flux q0 at the surface is now constant, and the right-hand side of equation 11.55 may be expressed as (—qa/Cf,p). Thus, for constant surface heat flux, equation 11.55 becomes ... 

For the second item ignition to lead to flashover, the area involved must equal or exceed the total critical area needed for the second item. The time for ignition depends inversely on the exposure heat flux (Equation (11.51)). Figure 11.21 shows the behavior for ignition of the second item, where Af,i is the fixed area of the first item and AF c is the critical area needed. The energy release rate of both fuels controls the size of the jump at criticality and depends directly on AFAhc/L. No flashover will occur if the jump in energy for the second item is not sufficient to reach the critical area of fuel, AFjc- The time to achieve the jump or to attain flashover is directly related to the fuel property,... 

Although relatively flat leaves can be described by the boundary layer considerations just presented (Fig. 7-6 and Eq. 7.10), many plant parts, such as stems, branches, inflorescences, fruits, and even certain leaves (e.g., the tubular leaves of onion, Allium cepa), represent three-dimensional objects. Airflow is intercepted by such bluff bodies and forced to move around them. Here we will consider two shapes, cylinders and spheres. In the next subsection we will present heat flux equations for objects of cylindrical and spherical symmetry as well as for flat leaves. 

All of tlie recoimnended heat flux equations in API 520 and NFPA Codes tliat are used to design relief valve assmne tliat tlie liquids are not self-reactive or subject to runaway reaction. If tliis situation arises, it is necessary to include tlie heat of reaction and tlie rate of the reaction into account in sizing the relief device. 

Dibular Reactors (FFR/PBR). When the heat flow varies along the length of the reactor, such as would be the case in a tubular flow reactor, we must integrate the heat flux equation along the length of the reactor to obtain the total heat added to the reactor. 

For cocurrent operation (case 3a in Figure 3.1) both the case design and simulation are simple. The four balance equations (3.18 through 3.21) supplemented by a suitable drying rate and heat flux equations are solved starting at inlet end of the dryer, where all boundary conditions (i.e., all parameters of incoming streams) are defined. This situation is shown in Figure 3.4. 

Because of the low vapor pressures of DOP, DBP, and DBS the prediction of droplet evaporation rates for these species does not require simultaneous solution of the mass flux and heat flux equations. For more volatile species evaporating in the Knudsen regime, (15.4), (15.21), and (15.24) must be satisfied. 

During the study of phenomenon of thermo-osmosis, major difficulty in encountered in testing the validity of ORR. According to Eq. (3.79), formerly discussed in Section 3.3, the heat flux equations can be written as... 

The quantity F from Equation 67 differs from that in Equation 2.3-56 owing to the appearance of a contribution of diffusion and to the mutual influence of diffusion and heat flux. Equation 66 does not comprise negligible non-Lorentzian terms like those in Ekjuation 2.3-3. 

Manipulation of these three heat flux equations gives ... 

Most of the chemical engineering flows are chemically reactive. Therefore, the net heat flux equation (6.53) needs to be expanded to include heat fluxes into the fluid element due to thermal conduction, diffusion of all species, and thermal radiation. The extended net heat flux equation, where heat fluxes in x, y, and z directions due to thermal conduction are replaced by Fourier s law of heat conduction, is written as... 

By replacing the net heat flux equation (6.53) in Equation 6.58 with Equation 6.72 and substituting the substantial derivative of the kinetic energy in Equation 6.71 by Equation 6.69 and substituting the substantial derivative of the total energy in the same Equation 6.71 by Equation 6.58, we finally get... 

Introducing the net heat flux equation (6.72) into Equation 6.77, we get the nonconservation form of the energy equation for chemically reactive flows in terms of enthalpy in the 3D space of the Cartesian coordinate system for time-dependent, compressible, and viscous flow as... 

The heat transport due to conduction and that due to radiation are not readily separable from the experimental data. Curve A of Fig. 4 shows the measured temperature distribution through a typical sample containing 29 shields per inch. Curve B shows the temperature distribution expected if each sheet of aluminum foil were a floating radiation shield. These results were obtained from Fig. 1. Curve C shows the temperature distribution througji an ideal sample, whose thermal conductivity would be independent of temperature. The observed result is probably a combination of radiation heat transfer and the change in thermal conductivity of the insulation with temperature. The thermal conductivity of most disordered dielectrics is approximately proportional to the first power of the temperature, but the temperature dependence of multiple contacts is not well understood. The fact that the temperature distribution for a sample of this type can be accounted for by a temperature-dependent thermal conductivity is sufficient justification for using Eq. (3), a particular solution of the Fourier equation, rather than Eq. (1), the heat flux equation for radiant heat transport, to represent our results. 

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