The Radiation Heat-Transfer Coefficient

In Hie development of convection heat transfer in the preceding chapters, we found it convenient to define a heat-transfer coefficient by 

Since ratiation heat-transfer problems are often very closely associated with convection problems, and the total heat transfer by both convection and radiation is often the objective of an analysis, it is worthwhile to put both processes on a common basis by defining a radiation heat-transfer coefficient ft, as 

In many instances the convection heat-transfer coefficient is not strongly dependent on temperature. However, this is not so with the radiation heat-transfer coefficient. The value of ft, corresponding to Eq. (8-43), could be calculated from 

Obviously, the radiation coefficient is a very strong function of temperature. 

The reader may recall that we used a concept like Eq. (8-126) to obtain a radiation resistance for numerical examples in Chaps. 3 and 4. 

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Also, the radiation heat transfer coefficient is given by... 

We note that must be between 0°C and 22°C. but it must be closer to 0°C, since the heat transfer coefficient inside the tank is much larger. Taking Ti = 5°C = 278 K. the radiation heat transfer coefficient is determined to be... 

Analysis The body loses heat in sensible and latent forms, and the sensible heat consists of convection and radiation heat transfer. At lovy air velocities, the convection heat transfer coefficient for a standing man is given in Table 13-5 to be 4.0 W/m - C. The radiation heat transfer coefficient at typical indoor conditions is 4.7 W/m "C. Therefore, the surface heat transfer coefficient for a standing person for combined convection and radiation is... 

Radiation Correction Factor. Bromley [190] suggested a value of J = 0.75 as a multiplier for the radiation heat transfer coefficient in Eq. 15.155. Detailed analytical studies by Sakurai and Shiotsu [180] show that J can vary over a wide range they fitted the following expression to their analytical results for cylinders ... 

Calculate the radiation heat transfer coefficient corresponding to the fraction of time (1 —/) when there is no cluster at a given location on the heat transfer surface. It is assumed that the riser is large enough and the suspension dense enough that only suspension is seen by the bare portions of the wall during these intervals. We can then write... 

To the extent that radiation contributes to droplet heatup, equation 28 gives a conservative estimate of the time requirements. The parameter ( ) reflects the dependence of the convective heat-transfer coefficient on the Reynolds number ... 

Contact Drying. Contact drying occurs when wet material contacts a warm surface in an indirect-heat dryer (15—18). A sphere resting on a flat heated surface is a simple model. The heat-transfer mechanisms across the gap between the surface and the sphere are conduction and radiation. Conduction heat transfer is calculated, approximately, by recognizing that the effective conductivity of a gas approaches 0, as the gap width approaches 0. The gas is no longer a continuum and the rarified gas effect is accounted for in a formula that also defines the conduction heat-transfer coefficient ... 

Frequently, particularly in tray diying, heat arrives at the evaporating surface from the tray walls by condiiction through the wet material. For this case, in which both radiation and conduction are significant, the total heat-transfer coefficient is given by Shepherd,... 

The vial heat transfer coefficient is the sum of heat transfer coefficients for three parallel heat transfer mechanisms (1) direct conduction between glass and shelf surface at the few points of actual physical contact, Kc (2) radiation heat exchange, Kr, which has contributions from the shelf above the vial array to the top of the vials, Krt, and from the shelf upon which the vial is resting, Krb and (3) conduction via gas-surface collisions between the gas and the two surfaces, shelf and vial bottom, Kg ... 

All correlations based on ambient temperature data where thermal radiation is negligible should be considered to represent only the convective heat transfer coefficient hc. 

Hlavacek (1970) has shown that radiation between the solid catalyst and gas can significantly affect the temperature dynamics in packed bed systems operating in excess of 673 K. Since most packed bed systems usually operate well below these conditions, radiation terms are not explicitly included in the model. However, their effect can to some degree be accounted for in the overall heat transfer coefficients.4... 

Here, k is the effective thermal conductivity, A is the effective contact area between the adjacent cells, l is the characteristic conduction length scale, hconv is the convection heat transfer coefficient, Aext external surface area of the cell exposed to the ambient air, 7 x is the ambient temperature and P is the cell power. The characteristic conduction length is calculated as the volume of the bipolar plate divided by the cell normal area. Factor /3 is an empirical constant which is the ratio of the heat generated to the power produced by the cell, i.e. (1 - rj), rj being the efficiency. When radiation is considered, should be included in Equation (5.64). The heat transfer relationships between the gas channels and the solid regions are given by ... 

There are several possible mechanisms for the heat exchange between a reacting medium and a heat carrier radiation, conduction and forced or natural convection. Here we shall consider convection only. Other mechanisms are considered in the chapter on heat accumulation. The heat exchanged with a heat carrier (q ) across the reactor wall by forced convection is proportional to the heat exchange area (A) and to the driving force, that is, the temperature difference between the reaction medium and the heat carrier. The proportionality coefficient is the overall heat transfer coefficient (U) ... 

For example, for heat transfer through a flat wall, where heat is transferred by convection and radiation from the wall, the overall heat transfer coefficient is related to the individual coefficients by... 

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. 

The radiative heat transfer has been approximated and expressed to be similar to Newton s law of cooling, with a heat transfer coefficient due to radiation. The radiative heat transfer coefficient, like the convective heat transfer coefficient, is not a property of either bodies. The total heat transfer from body 1 is then expressed as... 

Problem For a body that is being considered, the convection heat transfer coefficient to the adjacent air is 33 W/(m2.°C), and the radiative heat transfer coefficient from this body to another body is approximately 36 W/(m2.°C). If the temperature of the first body is 188° C, that of the adjacent air is 22°C, determine the temperature of the second body so that the heat transferred by convection is equal in magnitude to the heat transferred by radiation. The area ratio Aconv Arad is 1 1.2. 

On a clear night the effective radiation temperature of the sky may be taken as -70°C. Assuming that there is no wind and the convection heat-transfer coefficient from the air to the dew which has collected on the grass is 28 W/m2 °C, estimate the minimum temperature which the air must have to prevent formation of frost. Neglect evaporation of the dew, and assume that the grass is insulated... 

Figure 4 plots, against suspension density, the heat transfer coefficients measured by Basu (1990) over a wide range of bed temperature for 296 pm sand, by Kobro and Brereton (1986) at a temperature of 850°C for 250 pm sand and by Grace and Lim (1989) at 880°C for 250-300 pm sand. The overall heat transfer coefficient is shown to increase with bed temperature. Before radiation becomes dominant in heat transfer, the observed rise in heat transfer coefficient with bed temperature may be explained as follows. The gas convective component is expected to decrease mainly because of the inverse dependence of gas density on temperature. On the other hand, the particles convective component will increase with temperature, thus leading to an increase in gas conductivity, because the latter is dominant for... 

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