Time-averaged heat transfer coefficient

The above equations for heat transfer apply when there is no heat generation or absorption during the reaction, and the temperature difference between the solid and the gas phase can be simply defined tliroughout the reaction by a single value. Normally this is not the case, and due to the heat of the reaction(s) which occur tlrere will be a change in the average temperature with time. Furthermore, in tire case where a chemical reaction, such as the reduction of an oxide, occurs during the ascent of tire gas in the reactor, the heat transfer coefficient of the gas will vary with tire composition of tire gas phase. 

It may be used, the relation of the time-averaged heat transfer coefficients on the top and bottom, as a criterion for determination of dryout. It was assumed that the relation he/hi < 1 indicates dryout, i.e., the surface superheat Tw -7f is greater than that, when the surface contacts single-phase water only (hg is the heat transfer at the bottom of the channel). This method can be applied to connect dryout with hydraulic conditions, if the value of he may be associated with intermittent flow parameters. 

The first type of model considers the heat transfer surface to be contacted alternately by gas bubbles and packets of closely packed particles. This leads to a surface renewal process whereby heat transfer occurs primarily by transient conduction between the heat transfer surface and the particle packets during their time of residence at the surface. Mickley and Fairbanks (1955) provided the first analysis of this renewal mechanism. Treating the particle packet as a pseudo-homogeneous medium with solid volume fraction, e, and thermal conductivity (kpa), they solved the transient conduction equation to obtain the following expression for the average heat transfer coefficient due to particle packets,... 

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... 

For an immersed cylindrical surface, the solution of Eq. (6) yields the following time-averaged heat transfer coefficient ... 

Two-fluid simulations have also been performed to predict void profiles (Kuipers et al, 1992b) and local wall-to-bed heat transfer coefficients in gas fluidized beds (Kuipers et al., 1992c). In Fig. 18 a comparison is shown between experimental (a) and theoretical (b) time-averaged porosity distributions obtained for a 2D air fluidized bed with a central jet (air injection velocity through the orifice 10.0 m/s which corresponds to 40u ). The experimental porosity distributions were obtained with the aid of a nonintrusive light transmission technique where the principles of liquid-solid fluidization and vibrofluidization were employed to perform the necessary calibration. The principal differences between theory and experiment can be attributed to the simplified solids rheology assumed in the hydrodynamic model and to asymmetries present in the experiment. 

Eq. (2) can also be used to calculate the heat-up time for nonisothennal heating (such as hot-water jacketing), provided that the difference between the outlet and inlet jacket temperatures is not greater than 10% of the difference between the batch and average jacket water temperature [21 The heat transfer area, reaction mass and heat capacity of the vessel contents are generally known. The overall heat transfer coefficient, however, is a function of five resistances and can be difficult to estimate. 

A long 20H m-diameter cylindrical shaft made of stginless steel 304 comes out of an oven at a uniform temperature of 600 C (Fig. 4- 3). The shaft is then allowed to cool slowly in an environment chamber at 200°C with an average heat transfer coefficient o( ft 80 W/m C. Determine the temperature at the center of the shaft 45 min after the start of the cooling process. Also, determine the heat transfer per unit length of the shaft during this time period. 

Layers of 23-cm-thick meal slabs (k = 0.47 W/m °C and a — 0.13 X 10 mVs) initially at a uniform temperature of 1°C are to be frozen by refrigerated air at —SO C flowing at a velocity of 1.4 m/s. The average heat transfer coefficient between the meat and the air is 20 W/m °C. Assuming the size of the meal slabs to be large relative to their thickness, determine how long it will take for the center temperature of the slabs to drop to -18°C, Also, determine the surface temperature of the meal slab at that time. 

SOLUTION A hoi stainless steel ball is cooled by forced air. The average convection heat transfer coefficient and the cooling time are to be determined. 

The heat-loss terms describe both the loss via the flow of gases leaving the reactor and via Newtonian cooling through the walls where f es is taken to be the average residence time of the reactor. is the ambient temperature, V the volume, 5 the reactor surface area and x the heat transfer coefficient. Cp is the heat capacity per unit volume which is assumed to be independent of temperature, and qj the exothermicity of the yth reaction step. 

Our discussions on the film model for heat transfer showed an exact parallel with the corresponding mass transfer problem. The same parallel holds for unsteady-state transfer. Thus, for Fo = Xt/pC rl 0 (short contact time), the time-averaged heat transfer coefficient is given by... 

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