Radiation heat transfer radiosity

Equations similar to equation 9.158 may be obtained for each of the surfaces in an enclosure, 1 = 1,1 = 2, 1 = 3, 1 = n and the resulting set of simultaneous equations may then be solved for the unknown radiosities, qoi,qm- qun The radiation heat transfer is then obtained from equation 9.140. This approach requires data on the areas and view factors for all pairs of surfaces in the enclosure and the emissivity, reflectivity and the black body emissive power for each surface. Should any surface be well insulated, then, in this case, Qj — 0 and ... 

Surfaces emit radiation as well as rellecting it, and thus the radiation leaving a surface consists of emitted and reflected components, as shown in Fig. 12 21. The calculation of radiation heat transfer between surfaces involves the total radiation energy streaming away from a surface, with no regard for its origin. Thus, we need to define a quantity that represents the rate at which radiation energy leaves a unit area of a surface in all directions. This quantity is called the radiosity J, and is expressed as... 

The direction of the net radiation heat transfer depends on the relative magnitudes of 7, (the radiosity) and (, (the emissive power of a blackbody at the teinpeiature of the surface). It is from the surface if > 7,- and to the surface if 7f > ft),-. A negative value for ft indicates that heat transfer is to the surface. All of this radiation energy gained must be removed from the other side of the surface through some mechanism if the surface temperature is to remain constant. 

The equations above give AMincar algebraic equations for the deieiinination of the N unknown radiosities for an A -surface enclosure. Once Ihe radiosities J, fr , Jn 3te available, the unknown heat transfer rates can be determined from Eq. 13-34 while the unknown surface temperatures can be determined from Eq, 13-3, 5. The temperatures of insulated or reradiating surfaces can be delei mined from ffT/ 7,. A positive value for Qj indicates net radiation heal transfer from surface i to other surfaces in the enclosure while a negative value indicates net radiation heat transfer lo Ihe surface. 

The total radiation energy leaving a surface per unit time and per uuit area is called the radiosity and is denoted by J. The net rate of radiation heat transfer from a surface i of surface area A/ is expressed as... 

Radiation arrives at a grey surface of emissivity 0.75 al a constant temperature of 400 K, at the rate of 3 kW/m2. What is the radiosity and the net rate of radiation transfer to the surface What coefficient of heat transfer is required to maintain the surface temperature at 300 K if the rear of the surface is perfectly insulated and the front surface is cooled by convective heat transfer to air at 295 K ... 

Two 10 by 30 cm rectangular plates are spaced 10 cm apart and connected by four insulated and re-radiating walls. The plate temperatures are uniform at 1000 and 300°C, and their emissivities are 0.6 and 0.4, respectively. Using the numerical method, determine the net heat transfer under the assumptions that (a) the four re-radiating surfaces act as one surface and have uniform radiosity and (b) the four re-radiating surfaces have radiosities determined from the radiant balance with all other surfaces. Assume that the 1000 and 300°C surfaces have uniform radiosity. Also calculate the temperatures for the re-radiating surfaces for each case above. 

The thermal system model for radiant-tube continuous furnace involves integration of the mathematical models of the furnace enclosure, the radiant tube, and the load. The furnace enclosure model calculates the heat transfer in the furnace, the furnace gas, and the refractory walls. The radiosity-based zonal method of analysis [159] is used to predict radiation heat exchange in the furnace enclosure. The radiant-tube model simulates the turbulent transport processes, the combustion of fuel and air, and the convective and radiative heat transfer from the combustion products to the tube wall in order to calculate the local radiant-tube wall and gas temperatures [192], Integration of the furnace-enclosure model and the radiant-tube model is achieved using the radiosity method [159]. Only the load model is outlined here. 

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