Radiant heat transfer coefficient

In general, gas-to-particle or particle-to-gas heat transfer is not limiting in fluidized beds (Botterill, 1986). Therefore, bed-to-surface heat transfer coefficients are generally limiting, and are of most interest. The overall heat transfer coefficient (h) can be viewed as the sum of the particle convective heat transfer coefficient (h ), the gas convective heat transfer coefficient (h ), and the radiant heat transfer coefficient (hr). 

The radiant heat transfer coefficient becomes important above about 600°C, but is difficult to predict. Baskakov et al. (1973) report that depending on particle size, hr increases from approximately 8% to 12% of the overall heat transfer coefficient at 600°C, to 20 to 33% of h at 800°C. 

Overall bed-to-surface heat transfer coefficient = Gas convective heat transfer coefficient = Particle convective heat transfer coefficient = Radiant heat transfer coefficient = Jet penetration length = Width of cyclone inlet = Number of spirals in cyclone = Elasticity modulus for a fluidized bed = Elasticity modulus at minimum bubbling = Richardson-Zaki exponent... 

To convert the radiant heat transfer coefficient to a contribution to the effective bed conductivity, the particle diameter must be included, because this affects the path length for radiant energy transfer. Radiation between particles and conduction through the solid are accounted for in the model of Schotte [32] ... 

The radiant heat transfer coefficient, h, (W/m K), can be estimated using the following equation, among others [18] ... 

Simultaneous Loss by Radiation The heat transferred by radiation is often of significant magnitude in the loss of heat from surfaces to the surroundings because of the diathermanous nature of atmospheric gases (air). It is convenient to represent radiant-heat transfer, for this case, as a radiation film coefficient which is added to the film coefficient for convection, giving the combined coefficient for convection and radiation (h + hf In Fig. 5-7 values of the film coefficient for radiation are plotted against the two surface temperatures for emissivity = 1.0. 

A fire tube contains a flame burning inside a piece of pipe which is in turn surrounded by the process fluid. In this situation, there is radiant and convective heat transfer from the flame to the inside surface of the fire tube, conductive heat transfer through the wall thickness of the tube, and convective heat transfer from the outside surface of that tube to the oil being treated. It would be difficult in such a simation to solve for the heat transfer in terms of an overall heat transfer coefficient. Rather, what is most often done is to size the fire tube by using a heat flux rate. The heat flux rate represents the amount of heat that can be transferred from the fire tube to the process per unit area of outside surface of the fire tube. Common heat flux rates are given in Table 2-11. 

The wall of the duct and the gas stream are at somewhat different temperatures. If the heat transfer coefficient for radiant heat transfer from the wall to the thermometer remains constant, and the heat transfer coefficient between the gas stream and thermometer is proportional to the 0.8 power of the velocity, what is the true temperature of the air system Neglect any other forms of heat transfer. 

A small amount of heat will be transferred to the tubes by convection in the radiant section, but as the superficial velocity of the gases will be low, the heat transfer coefficient will be low, around 10 Wm-2oC-1. 

In preliminary design, the heat duty and furnace efficiency are the prime considerations. However, if the tube area needs to be specified, a preliminary estimate can be obtained from an assumed flux. In the radiant section, this usually lies in the range of 45,000 W m-2 to 65,000 W m 2 of tube surface, with a value of around 55,000 W m 2 most often used. The heat flux is particularly important if a reaction is being carried out in the furnace tubes. Overall heat transfer coefficients in the convection section are in the range 20 to 50 W m-2 K-1. 

Effect of pressure Figure 2.40 shows the heat transfer coefficients for film boiling of potassium on a horizontal type 316 stainless steel surface (Padilla, 1966). Curve A shows the experimental results curve B is curve A minus the radiant heat contribution (approximate because of appreciable uncertainties in the emissivities of the stainless steel and potassium surfaces). Curve C represents Eq. (2-150) with the proportionality constant arbitrarily increased to 0.68 and the use of the equilibrium value of kG as given by Lee et al. (1969). 

Summary of experimental data Film boiling correlations have been quite successfully developed with ordinary liquids. Since the thermal properties of metal vapors are not markedly different from those of ordinary liquids, it can be expected that the accepted correlations are applicable to liquid metals with a possible change of proportionality constants. In addition, film boiling data for liquid metals generally show considerably higher heat transfer coefficients than is predicted by the available theoretical correlations for hc. Radiant heat contribution obviously contributes to some of the difference (Fig. 2.40). There is a third mode of heat transfer that does not exist with ordinary liquids, namely, heat transport by the combined process of chemical dimerization and mass diffusion (Eq. 2-162). 

As can be seen from Equation 3.20, the short-time solution for the pyrolysis time, tPi is independent of the total heat-transfer coefficient term, hT = (h, + h,). Thus, the pyrolysis time tp is only a function of the energy absorbed aq" due to radiation from the radiant panel and the properties (k, p, Cp) of the solid fuel sample. 

A solar radiant heat flux of700 W/m2 is absorbed in a metal plate which is perfectly insulated on the back side. The convection heat-transfer coefficient on the plate is II W/m2 - °C, and the ambient air temperature is 3G"C. Calculate the temperature of the plate under equilibrium conditions. 

The emissivity depends on the characteristics of the emitting surface and, like the thermal conductivity and the heat-transfer coefficient, must be determined experimentally. Part of the radiant energy intercepted by a receiver is absorbed, and part may be reflected. In addition, the receiver, as well as the source, can emit radiant energy. 

A thin horizontal flat plate receives 1,200 W/m2 of radiant heat from the sun. The upward and downward heat transfer coefficients are 10 and 2.5 W/m2 -K. Determine the steady temperature of the plate if placed in ambient air at a temperature of 25 C... 

To represent the partially premixed turbulent combustion of a refinery gas in the heater, a combination of the flamelet formulations for premixed and nonpremixed combustion was used [16]. The standard k-e model was used for turbulent flow calculations. The effect of turbulence on the mixture fraction was accounted for by integrating a beta-PDF derived from the local mixture fraction and mixture fraction variance, which were in turn obtained by solving their respective transport equations. A relatively simple approach was used to compute radiant heat transfer—a diffusion model with a constant absorption coefficient (0.1 m i). 

The refractory wall also accounts for some heat transfer by indirect radiation to the convection section. From Figure 1-14, using an average tube wall temperature of 532° F, the heat transfer coefficient for the wall radiation, = 9.5 Btu/hr. sq. ft.°F. Expressing the radiant heat from the wall as a fraction of the heat directly transferred to the tubes, the factor 3 for wall radiation is... 

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