Conduction-convection contribution

It should be noted that without experimental data on the subcooled pool boiling crisis in liquid metals, the above equation cannot be verified. Another mechanism for estimating the subcooling contribution to the CHF was used for boiling with ordinary liquids (i.e., a conduction mechanism). The two mechanisms may operate simultaneously, along with the hydrodynamics and conduction-convection mechanisms (Dwyer, 1976). 

The energy flux consists of a conductive and a convective contribution. The general expression for the conductive flux is given by... 

The first term on the right-hand side of eq. (5) describes the heat conduction and the second term accounts for the Dufour effect. The convective contribution of the energy flux is given by... 

The paper by Haynes and Wepfer (2001) highlights the importance of heat exchange in SOFCs. To achieve an accurate temperature field, they propose a model that takes into account conduction, convection and radiation. The authors show how important the radiative heat exchange is. In particular, on heat transfer from the inner surface of the cell, radiation plays a much more important role than convection, which contributes for about 10%. 

In separation processes and chemical reactors, flow through cylindrical ducts filled with granular materials is important. In such systems conduction, convection, and radiation all contribute to the heat flow, and thermal conduction in axial ke x and radial ke r directions may be quite different, leading to highly anisotropic thermal conductivity. For a bed of uniform spheres, the axial and radial elements are approximated by... 

Figure 13B shows the calculated temperature differences for the same cases as considered before, but with catalyst beds diluted with silicon carbide to one third of the original catalyst concentration. It can be seen that the temperature differences are appreciably smaller than in the undiluted case (note the differences in temperature scale between Figures 13A and 13B). The dilution with good thermally conducting material is particularly effective at the low velocities in short beds because the convective contribution to the effective heat conductivity is then relatively small. It can be inferred that in microflow reactors (D = 1 cm L = 10 cm) and in bench-scale reactors (D = 2 cm L = 1 m) with diluted beds radial temperature differences are less than 1-2 °C for the considered cases, which is quite acceptable. 

However, Eq. (3-248) is just Fourier s law, with an effective thermal conductivity k(azUz/48k2). Further, because there is no net convection contribution to the cross-sectionally averaged heat flux calculated with respect to the moving axis z, we see that the convective transport rate down the tube is just that due to the mean velocity U. Both of these results may at first seem surprising. For example, the maximum rate of transport that is due to convection acting alone is the centerline velocity 2 U, and it is not immediately obvious why the actual convective transport rate is slower. In addition, the effective thermal diffusivity is seen in (3-246) to be inversely proportional to the molecular thermal diffusivity k, and this may also seem to be counterintuitive. 

It is clear that Nuo, which is the dimensionless overall heat flux in the pure conduction limit, will depend on the geometry of the body. However, once Nuq is known (either by theoretical calculation or, perhaps, by experiment), we can calculate the first convective contribution in (9-138) by means of (9-141), with no extra work, so that... 

The first term in this expression is, of course, the familiar result for pure conduction from a heated sphere and is the same for all flows. The second term represents the first contribution of convection and should be compared with the second term in Eq. (9 60), which is the Nusselt number for forced convection heat transfer at low Pe when the flow is uniform streaming. The most important observation is that the dependence on Pe is different in the two cases, being O(Pe) in the uniform streaming flow and 0(Pe1/2) in simple shear flow. The two results, (9-60) and (9-191), are plotted in Fig. 9-8. Evidently, the Nusselt number for simple shear flow exceeds the value for uniform streaming flow for Pe< 1 where the two asymptotic predictions are valid. Although the numerical difference between the two results is small, the most important conclusion from the analysis is not the numerical magnitude of corrections to the conduction heat flux but rather the fact that the asymptotic form of the convection contribution clearly depends on flow type. In general, heat transfer correlations developed for one type offlow will not carry over to some other type offlow. 

For a temperature difference of lOOK, an ambient temperature of 300K, and a particle diameter of D = 3 p,m (at which size high temperatures are reached for a typical beam), Nu = 2 + 3x10 for water and Nu = 2 + 7x10 for kerosene, values which are very close lo Nu = 2 for pure conduction. The convective contribution to the cooling is therefore negligible. 

Knowledge of the heat transfer characteristics and spatial temperature distributions in packed beds is of paramount importance to the design and analysis of the packed-bed catalytic or non-catalytic reactors. Hence, an attempt is made in this section to quantify the heat transfer coefficients in terms of correlations based on a wide variety of experimental data and their associated heat transfer models. The principal modes of heat transfer in packed beds consist of conduction, convection, and radiation. The contribution of each of these modes to the overall heat transfer may not be linearly additive, and mutual interaction effects need to be taken into account [23,24]. Here we limit our discussion to noninteractive modes of heat transfer. 

Investigator Type of correlation Phases involved Model associated Yagi and Kunii [31] Effective thermal conductivity of packed bed Fluid-solid Accounting the fluid motion (convective contribution) Applicable to heat transfer in the direction normal to fluid flow... 

The energy flux is related to conductive and convective contributions as follows... 

Heat transfer in gas-fluidized bed can occur by conduction, convection, and radiation depending on the operating conditions. The contribution of the respective modes of heat transfer to the coefficient of heat transfer depends on particle classification, flow condition, fluidization regimes, type of distributor, operating temperature, and pressure. Heat transfer between a single particle and gas phase can be defined by the conventional equation of heat transfer ... 

VIP and VG offer outstanding thermal resistance because evacuation of the porous core material or the glazing cavity, respectively, results in a drastic reduction of heat transport by gas molecules. Aerogels on the contrary are nonevacuated superinsulators. Their low thermal conductivity is correlated with the pore structure of these materials. Before we briefly touch on the effect of the unique structural features of aerogels on heat transport, let us recapitulate the basics. Generally, heat is transferred by conduction, convection, and radiation. In porous materials there are five possible contributions to the total heat transfer, namely ... 

Heat management in monoUth reactors via external heating or cooling is not as effective as in PBRs due to lack of convective heat transport in the radial direction. At this point, the material of construction of the monolithic structure affects the overall performance. Monolith reactors can be made of metals or ceramics. In case of nonadiabatic reactions, metallic monoliths are preferred due to their higher thermal conductivity which partially eliminates the lacking convective contribution. Ceramic monoliths, on the other hand, have very low thermal conductivities (e.g., 3 W/m.K for cordierite [11]) and are suitable for use in adiabatic operations. 

In this heat transport model, the radial heat transfer is represented by a Fourier-like law, using an equivalent radial thermal conductivity of the medium with flowing fluids 4r = A dT/dr. The bed radial effective thermal conductivity was expressed as sum of two terms—conductive contribution and convective contribution A -Aso+ gf In Hashimoto et al. [94] and Mat-suura et al. s [95] approach, the theory of single-phase gas flow... 

The temperature of the catalyst is derived from various contributions of an energy balance at the interface. The conductive, convective, and diffusive energy transport from the gas phase adjacent to the surface as well as the chemical heat release at the surface, the thermal radiation and a possible external heating (here resistive heating) of the catalyst are included. This results in... 

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