Conductive heat flux

Sum of the superficial gas and liquid velocities Thermal conductivity Heat flux... 

The spheroidal modulus (So) is defined as the ratio of conduction heat flux through the vapor film to the evaporation heat flux ... 

These authors numerically solved the system of equations with appropriate boundary conditions to derive the time-averaged radiant and conductive heat fluxes between the fluidized bed and the heat transfer surface. Using... 

The other mode of heat transfer is conduction. The conductive heat flux is, by Fourier s law,... 

For laminar conditions of slow flow, as in candle flames, the heat transfer between a fluid and a surface is predominately conductive. In general, conduction always prevails, but in the unsteadiness of turbulent flow, the time-averaged conductive heat flux between a fluid and a stationary surface is called convection. Convection depends on the flow field that is responsible for the fluid temperature gradient near the surface. This dependence is contained in the convection heat transfer coefficient hc defined by... 

Ps/u.i gas-vapour pressure of component i, N/m q conductive heat flux, J/m s... 

It is expected that as the strain rate increases, the overall coupling between the surface and the gas-phase increases, since the flame is pushed toward the surface. Figure 26.6a shows the wall heat flux that can be extracted from the system, and the fuel mole fraction near the surface vs. the inverse of the strain rate for 28% inlet H2 in air, at two surface temperatures. The end points of the curves in Fig. 26.6, at high-strain rates, are the extinction points. The conductive heat flux exhibits a maximum as the strain rate increases from low values, which is at first counterintuitive. In addition, with increasing strain rate the fuel mole fraction increases monotonically, while the mole fractions of NOj, decrease, as seen in Fig. 26.66. The species mole fractions show sharper changes with strain rate near extinction, as the mole fractions of radicals decrease sharply near extinction. 

Fig. 5.25 Temperature gradient, conductive heat flux, convective heat flux, and heat flux by chemical reaction as a function of distance from the burning surface at 3 MPa (initial temperatures 243 K and 343 K) for BAMO/ THF = 60 40 copolymer.

Fig. 3.9 A cylindrical differential control volume showing conductive heat fluxes.

While solving Equation 19.2, one can construct numerically the conduction heat flux on the surface of the unpyrolyzed material (i.e., -kdT/dx[r=ll) and thus the actual heat flux transferred into the unpyrolyzed material can be found by considering the energy balance at the surface of the unpyrolyzed material as shown in Figure 19.28 ... 

Fig. 3.25. Heat flux histories following an ELM of 1MJ/m2 with a power flux triangular waveform (curve 1) with ramp-up and ramp-down phases lasting 300 ds each on a 10mm thick W target under an inter-ELM power flux of 10MWm 2. Curves. (1) incident heat flux load (2) conducted heat flux into the material (3) heat flux spent in melting of the material (the evaporation and black-body radiation heat fluxes are comparatively small and not shown). Curve (4) shows the surface target temperature and (5) shows the temperature of the melt layer. Curve (6) shows the vaporized thickness (amplified of a factor of 1000) and (7) the melt layer assuming that no losses of molten material occur during the ELM [3]...

Note that the standard temperature (77°F or T0 = 298.15 K) is used in this definition. cp i is the specific heat and Ah p is the enthalpy of formation at the standard state, both for species i. The heat flux, q, includes contributions from conduction, radiation, differential diffusion among component species, and concentration gradient-driven Dufour effect. For combustion applications, the most important contributions come from conduction and radiation. As discussed in Section 4.3, conduction heat flux follows Fourier s law (Equation 4.27) and radiation heat flux is related to the local intensity as... 

For diffusion in isothermal multicomponent systems the generalized driving force was written as a linear function of the relative velocities (m/ — My). In the general case, we must allow for coupling between the processes of heat and mass transfer and write constitutive relations for and q in terms of the (m — My) and V(l/r). With this allowance, the complete expression for the conductive heat flux is... 

Recall our earlier analysis of the mass transfer process in Section 8.1 when we found that the were constant through the film.) The energy flux E is related to the conductive heat flux by Eq. 11.1.4 which, when combined with Eq. 11.2.8, simplifies to... 

Equation 11.4.22 can be differentiated to obtain the conductive heat flux at the wall... 

Equations 11.4.26-11.4.30 allow the calculation of the conductive heat flux Qq the total energy flux Eq is the sum of the conductive and the bulk flow enthalpy contributions... 

If we neglect subcooling of the liquid condensate, the conductive heat flux in the condensed liquid film will also equal the heat flux through the wall and into the coolant. Thus, we may write... 

Conductive heat flux [W/m ]. Also, integer parameter [-]... 

While the film and surface-renewal theories are based on a simplified physical model of the flow situation at the interface, the boundary layer methods couple the heat and mass transfer equation directly with the momentum balance. These theories thus result in anal3dical solutions that may be considered more accurate in comparison to the film or surface-renewal models. However, to be able to solve the governing equations analytically, only very idealized flow situations can be considered. Alternatively, more realistic functional forms of the local velocity, species concentration and temperature profiles can be postulated while the functions themselves are specified under certain constraints on integral conservation. Prom these integral relationships models for the shear stress (momentum transfer), the conductive heat flux (heat transfer) and the species diffusive flux (mass transfer) can be obtained. 

By comparing the given conductive heat flux relation with the corresponding definition of the heat transfer coefficient, it is customary to define the heat transfer coefficient by ... 

The governing equation to determine the temperature distribution in the tube is the thermal energy equation, (2-110). To solve this equation, we need to know the form of the velocity distribution in the tube. We have already seen that the steady-state velocity profile for an isothermal fluid, far downstream from the entrance to the tube, is the Poiseuille flow solution given by (3-44). In the present problem, however, the temperature must depend on both r and z, and hence the viscosity (which depends on the temperature) will also depend on position. The dependence on z is due to the fact that heat is added for all z > 0, and thus the temperature must continue to increase with the increase of z. The dependence on r is due to the fact that there must be a nonzero conductive heat flux in the fluid at the tube wall to match the prescribed heat flux through the wall, and thus the temperature must have a nonzero r derivative. It follows that the velocity field will generally differ from Poiseuille flow. 

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