Heat transfer external resistance

The bath is normally at a temperature in the range 620-710°C, depending on whether the coating material is an aluminium-silicon alloy (for use in high-temperature conditions) or pure aluminium (for corrosion prevention). It is heated by inductors, by resistance heaters or by an external flame. The pot will usually be refractory lined unless cast-iron pots are needed to ensure adequate heat transfer from an external flame. As molten aluminium is extremely aggressive towards ferrous metals, replacement of cast-iron pots is fairly frequent. Refractory-lined pots obviously do not have this drawback, although the bath hardware, in particular the sinker roll and support mechanism, will still be attacked and need replacement at intervals. 

The Biot number is essentially the ratio of the resistance to heat transfer within the particle to that within the external fluid. At first sight, it appears to be similar in form to the Nusselt Number Nu where ... 

Catalyst pellets often operate with internal temperatures that are substantially different from the bulk gas temperature. Large heats of reaction and the low thermal conductivities typical of catalyst supports make temperature gradients likely in all but the hnely ground powders used for intrinsic kinetic studies. There may also be a him resistance to heat transfer at the external surface of the catalyst. 

The micro heat transfer module (Figure 3.15) comprises a stack of micro structured platelets which are irreversibely bonded [29, 30]. The module is heated by external sources, e.g. by placing it in an oven or by resistance heating. The single parallel flows are all guided in the same direction on the different levels provided by the platelets. Before and after, distribution and collection zones are found, connected to inlet and outlet connectors. 

Dimensionless numbers in mixing, 16 685 used in convection heat-transfer analysis, 73 246-247 Dimensionless parameter, external mass transfer resistance and, 25 290-292 Dimensionless reactor design formulation, 21 350... 

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

When the effects of heats of adsorption cannot be ignored—the situation in most industrial adsorbers—equations representing heat transfer have to be solved simultaneously with those for mass transfer. All the resistances to mass transfer will also affect heat transfer although their relative importance will be different. Normally, the greatest resistance to mass transfer is found within the pellet and the smallest in the external boundary film. For heat transfer, the thermal conductivity of the pellet is normally greater than that of the boundary film so that temperatures through a pellet are fairly uniform. The temperature... 

When a fluid is heated, the hot less-dense fluid rises and is replaced by cold material, thus setting up a natural convection current. When the fluid is agitated by some external means, then forced convection takes place. It is normally considered that there is a stationary film of fluid adjacent to the wall and that heat transfer takes place through this film by conduction. Because the thermal conductivity of most liquids is low, the main resistance to the flow of heat is in the film. Conduction through this film is given by the usual relation (74), but the value of h is not simply a property of the fluid but depends on many factors such as the geometry of the system and the flow dynamics for example, with tubes there are significant differences between the inside and outside film coefficients. 

The effects of non-uniform distribution of the catalytic material within the support in the performance of catalyst pellets started receiving attention in the late 60 s (cf 1-4). These, as well as later studies, both theoretical and experimental, demonstrated that non-uniformly distributed catalysts can offer superior conversion, selectivity, durability, and thermal sensitivity characteristics over those wherein the activity is uniform. Work in this area has been reviewed by Gavriilidis et al. (5). Recently, Wu et al. (6) showed that for any catalyst performance index (i.e. conversion, selectivity or yield) and for the most general case of an arbitrary number of reactions, following arbitrary kinetics, occurring in a non-isothermal pellet, with finite external mass and heat transfer resistances, the optimal catalyst distribution remains a Dirac-delta function. 

The last term on the left-hand side of eq. (3.301) corresponds to the heat transfer to the external fixed-bed wall. The overall heat transfer resistance is the sum of the internal, external, and wall resistances. In an adiabatic operation, the overall heat transfer coefficient is zero so the corresponding term in the energy balance expression drops out, while in an isothermal operation this coefficient is infinite, so that 7 f 7 s 7W. 

Although resistance to heat transfer goes up as the thickness of pipe insulation is increased, the external surface also increases a thickness may be reached at which the heat transfer becomes a minimum and then becomes larger. In accordance with this kind of behavior, heat pickup by insulated refrigerated lines of small diameters can be greater than that of bare lines. In another instance, electrical transmission lines often are lagged to increase the rate of heat loss. An example worked out by Kreith (Principles of Heat Transfer, Intext, New York, 1973, p. 44) reveals that an insulated 0.5 in. OD cable has a 45% greater heat loss than a bare one. 

External transfer transfer of energy from the surface of the particle into the fluid stream. The properties of flowing fluids are such that the resistance to heat transfer can be larger than that for mass transfer, so that a negligible concentration difference may exist between bulk fluid and particle surface and yet the corresponding temperature difference will be significant. 

The inactivation of heat-resistant spores appears lo follow first-order kinetics. Thus if the rate of inactivation of a spun population is knuwn at several temperatures, and the rate or heating of the slowest point in u package can be determined or calculated from heat-transfer principles, then the time needed to sterilize the package can be calculated for any external healing condition. 

For the nonisothermal catalyst pellet with negligible external mass and heat transfer resistances, i.e., with Sh —> 00 and Nu —> 00 and for a first-order reaction, the dimensionless concentration and temperature are governed by the following couple of boundary value differential equations... 

Non-Isothermal Mass and Heat Balance Model of the Catalytic Pellet BVP with Finite External Mass and Heat Transfer Resistance... 

In this section we consider the case where external mass and heat transfer resistances are not negligible, i.e., when both Sh and Nu are finite. In this case we need to solve the nonlinear material and energy balance equations simultaneously and this must be done for a coupled BVP in four dimensions. 

Compute the r — d> diagram for negligible external mass and heat transfer resistances. Also compute the yield yu of B versus dq diagram. 

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