Axial heat flux profile

All the references to burn-out have thus far been concerned with uniformly heated channels, apart from some of the rod bundles where the heat flux varies from one rod to another, but which respond to analysis in terms of the average heat flux. In a nuclear-reactor situation, however, the heat flux varies along the length of a channel, and to find what effect this may have, some burn-out experiments on round tubes and annuli have been done using, for example, symmetrical or skewed-cosine axial heat-flux profiles. Tests with axial non-uniform heating in a rod bundle have not yet been reported. 

Y = axial heat flux profile parameter Y = subchannel imbalance factor... 

Axial heat flux parameter Y The parameter Y, which replaces the heat flux shape factor in the CHF correlation, is not only a measure of the nonuniformity of the axial heat flux profile but also a means of converting from the inlet subcooling (AHin) to the local quality, X, form of the correlation via the heat balance equation. It is defined as... 

An approximate value of Yx at Z = Z, may be calculated by summing over a number of intervals of length. Thus, for a continuous axial heat flux profile, Yt is given by... 

The test section which will be used in the critical heat flux experiments can be seen in Figure 1. Its 3x3 geometry is a fair initial option used for CHF experiments once it can represent the reactor conditions. Rod diameter, rod height, and pitch are the same as in the reactor core. However, the first rod bundle will have a uniform axial heat flux profile. From a uniform power profile, it is still possible to... 

Figure A4.8 Regular and averaged Prandtl number and specific heat profiles for water along heated length of fuel channel. AHFP axial heat flux profile.

For a cluster with uniform axial heat flux, Y = 1 at all Z. For nonuniform heat flux, Y varies along the length. For example, with a chopped-cosine profile, Y < 1 over the first part of the channel, Y = 1 at about two-thirds of the length, and Y > 1 near the exit of the channel. 

Zero-order kinetics attracts special attention, due to its analytical simplicity and particular characteristics, especially when annulment of concentration at the solid surface is involved. Sellars et al. [61] and Siegel et al. [76] gave Graetz-type solutions for uniform axial heat flux, using the eigenfunction expansion method. Compton and Unwin [77] presented the Laplace s domain analytical solution of the mass transfer problem in a channel cell-crystal-electrode system under Leveque s assumptions. Rosner [78] wrote the solutions for the wall concentration profile as c att 1 -z/zb (z < Zo)> for several classes of boundary layer problems. 

Consider a fully developed steady-state laminar flow of a constant-property fluid through a circular duct with a constant heat flux condition imposed at the duct wall. Neglect axial conduction and assume that the velocity profile may be approximated by a uniform velocity across the entire flow area (i.e., slug flow). Obtain an expression for the Nusselt number. 

Imagine two solid bars brought into contact as indicated in Fig. 2-14, with the sides of the bars insulated so that heat flows only in the axial direction. The materials may have different thermal conductivities, but if the sides are insulated, the heat flux must be the same through both materials under steady-state conditions. Experience shows that the actual temperature profile through the two materials varies approximately as shown in Fig. 2-14b. The temperature... 

Here, ae is the effective thermal diffusivity of the bed and Th the bulk fluid temperature. We assume that the plug flow conditions (v = vav) and essentially radially flat superficial velocity profiles prevail through the cross-section of the packed flow passage, and the axial thermal conduction is negligible. The uniform heat fluxes at each of the two surfaces provide the necessary boundary conditions with positive heat fluxes when the heat flows into the fluid... 

A parametric study on the effects of axial heat conduction in the solid matrix has shown that i) such effects are negligible in ceramic monoliths (cordierite, kj = 1.4 w/m/K) but expectedly significant in metallic monoliths (Fecralloy, k i = 35 W/m/K) when a constant heat flux is imposed at the external matrix wall ii) however, the influence of axial conduction in metallic monoliths is much less apparent if a constant wall temperature condition is applied, since the monolith tends to an isothermal behavior. Metallic matrices exhibit very flat axial and radial temperature profiles, which seems promising for their use as catalyst supports in non-adiabatic chemical reactors. 

The desulfurized natural gas feed is mixed with steam and preheated to 500 °C before entering the reformer tubes. The heat for the reforming reaction is supplied by combustion of fuel in the furnace, which may contain up to 500 tubes with a length of 10 m and a diameter of 10 cm. Figure 6.2.31 shows axial profiles of the tube wall temperature and the heat flux. 

The axial profile of the hot-channel cladding surface temperature is next calculated by assuming a surface heat flux and employing empirical correlations for the surface heat transfer coefficient. The correlation Nu = 5 + 0.025(Pe) as developed for long tubes is often recommended. For purposes of fuel assembly design, this correlation appears conservative on the basis of data obtained by Dwyer and Kalish (7) for parallel flow through an equilateral-triangular array of rods. 

A main objective of the work of Hardt et al. was to study the influence of heat transfer on the achievable molar flux per unit reactor volume of the product species. They compared unstructured channels to channels containing micro fins such as shown in Figure 2.31. Heat transfer enhancement due to micro fins resulted in a different axial temperature profile with a higher outlet temperature in the reaction gas channel. Owing to this effect and by virtue of the temperature dependence... 

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