Radial heat flux

Shape of axial and radial heat flux distributions... 

Effective Thermal Conductivities of Porous Catalysts. The effective thermal conductivity of a porous catalyst plays a key role in determining whether or not appreciable temperature gradients will exist within a given catalyst pellet. By the term effective thermal conductivity , we imply that it is a parameter characteristic of the porous solid structure that is based on the gross geometric area of the pellet perpendicular to the direction of heat transfer. For example, if one considers the radial heat flux in a spherical pellet one can say that... 

Hollow Cylinder. Radial heat flux, qr, through the wall of a long cylinder of length L and inner radius rl held at temperature 7). and outer radius ra held at temperature Ta. e.g. the wall of a pipe or tube in a heat exchanger, is given by... 

Considering the models in Table I, it follows that the response of model III-T will be more close to reality due to (i) the correct way the transfer phenomena in and between phases is set up, and (ii) radial gradients are taken into account. Therefore, the responses of the different models will be compared to that one. It is obvious that the different models can be derived from model III-T under certain assumptions. If the mass and heat transfer interfacial resistances are negligible, model I-T will be obtained and its response will be correct under these conditions. If the radial heat transfer is lumped into the fluid phase, model II-T will be obtained. This introduces an error in the set up of the heat balances, and the deviations of type II models responses will become larger when the radial heat flux across the solid phase becomes more important. On the other hand, the one-dimensional models are obtained from the integration on a cross section of the respective two-dimensional versions. In order to adequately compare the different models, the transfer parameters of the simplified models must be calculated from the basic transfer... 

These equations permit the correct evaluation of the radial heat flux when the interfacial temperature gradients are negligible. Even when these gradients are important, the error introduced by the use of Equations 5 and 6 is not as significant as that due to the inexact calculation of the reaction rate (1). 

Equation (11.1) is essentially a solution of Eq. (11.7) and is based on a few assumptions and simplifications, e.g., no axial heat conduction, constant average heat conductivity and specific heat, constant heat source, steady-state heat transfer, one-dimensional (radial) heat flux, cylindrical geometry in the waste and in the surrounding material, e.g., salt, and no heat source in the salt. 

Boiling Limitation. At very high radial heat fluxes, nucleate boiling may occur in the wick-ing structure and bubbles may become trapped in the wick, blocking the liquid return and resulting in evaporator dryout. This phenomenon, referred to as the boiling limit, differs from the other limitations previously discussed in that it depends on the evaporator heat flux as opposed to the axial heat flux [7],... 

In a one-dimensional model of a tubular reactor, the radial heat flux is expressed using an overall coefficient and an average driving force ... 

The enthalpy equation, (12.7), is obtained by writing the heat flux as q = —+ /tpjUj. Assuming a uniform radial heat flux <75 = n to the droplet,... 

Nu = 5.0 + 0.025(Pe) Uniform axial wall temperature and uniform radial heat flux... 

Figure 6.11.23 Influence of internal tube diameter on the radial heat flux from the bed to cooling medium per unit volume feooNng) tid heat produced by the FT reaction (per unit volume).

Ratio of the average axial heat flux in a channel to the average heat flux in the core (radial heat flux distribution)... 

All the limitations discussed earlier depend upon the axial heat transfer. The boiling limit, however, depends upon the evaporator heat flux (radial). Boiling limit occurs when the radial heat flux into the heat pipe causes the liquid in the wick to boil and evaporate causing dryout. It also occurs when the nucleate boiling in the evaporator creates vapor bubbles that partially block the return of fluid. The presence of vapor bubbles requires both (1) the formation of bubbles and also (2) the subsequent growth of these bubbles. Let us imagine a spherical vapor bubble that is very close to the heat pipe surface. At equilibrium, we have... 

During crucible erosion, the water temperature in the annulus increased with a constant rate of 0.043 K/s from 15°C at 300 s to 90 C at 2050 s, and then subcooled boiling of the water did occur. The constant rate of temperature rise and of steam production throughout the experiment until failure of the cylinder wall shows that the radial heat flux is only little affected when the metal melt approaches the cylinder surface, and confirms the observation of constant radial erosion rates. The heat transferred into the water is 28 kW, corresponding to 21% of the induction heating rate. 

For the stability of the concrete cylinder the radial heat flux from the melt to the concrete wall is important. If the same heat flux is realized, the type of melt, oxidic or metallic, is of no more importance. Calculations with the WECHSL code for the experiment and the accident are given in Table. 1. The comparison shows that the heat flux in the experiment and the freezing temperature of the melt meet reasonably well the conditions of the oxidic melt in the accident under consideration. Similarly, the measured erosion velocity in this test with 0.027 mm/s=9.7 cm/h meets the desired conditions. Therefore, the result of wall failure is transferable to the accident condition, although in the accident under consideration, because of geometrical reasons, only the oxidic melt would penetrate the cylinder. 

The failure of the concrete can be understood from heat conduction estimates. To transfer the radial heat flux to the water without melting, the residual concrete layer must have a thickness s not exceeding... 

Shase. Indeed, the radial attack of the biological shield in the real accident would be oimnated by the oxidic melt progression. Therefore, to allow a representative experimental simulation, the internal heat generation in the BETA test is adjusted to give the same radial heat flux firom the melt to the cylinder as in reality 8 hours into tiie accident situation. With this condition fulfilled, the metallic melt can be used for simulation. The necessary heating rate of 120 kW was determined by WECHSL calculations comparing BETA and accident conditions. 

Demonstration of water heat pipes for heat rejection systems with operation at greater than 550 K and greater than 10 W/cm radial heat flux and development of heat pipe coolants for operation above 550 K. 

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