Net radiation method

The energy balance equations for all the zones need to be established to solve this radiative exchange problem. This is done using the net-radiation method introduced by G. Poljak [5.49], This yields a system of linear equations that, when solved, deliver the unknown temperatures and heat flows. With simple... 

Enclosure with N Diffuse-Gray Surfaces—The Net Radiation Method.579... 

Net Radiation Method. A more powerful method for describing radiative transfer is the net radiation method. In this method, radiative energy balances are constructed for each surface, and the resulting set of equations is then solved. (Some equations as written may fail in the limit of black surfaces and must be slightly modified starting from the original relations.)... 

Surfaces with Nonuniform Radiosity. If the radiosity across a given surface does not meet the assumption of uniformity, then the surface may be subdivided into subsurfaces, each of which approximates the condition of uniformity. In the limit, this reduces to relations in the form of integral equations. In this case, the net radiation method can be extended. Note that Eqs. 7.72 and 7.73 still apply to every position on surface k, but Eq. 7.74 must be modified to remove the assumption of uniform radiosity. The third equation for the net radiation method is the relation for incident radiation onto a particular location on surface k from all other surfaces, each of which can have a variable radiosity. The resulting relations are... 

Figure 10.8. Presence of air pore in a repeat (a) Actual pore as in Case I (b) The air pore as an enclosed surface used for net radiation method [ Source Reference 8].

The net radiation method for diflfuse-gray areas [6] accounted for radiation exchange between the discretized channel wall elements themselves, and between each wall element and the inlet and outlet channel enclosures gas radiative emission and adsorption were not considered, given the small optical paths and large nitrogen content. 

Radiation heat transfer exchange between the discretized catalytic surface elements as well as between each surface element and the reactor inlet and outlet disk areas was accounted for by the net radiation method for diflfuse-gray areas [6]. The inlet, outlet, and channel-element emissivities were all equal and the radiation exchange temperatures for the entry and outlet were equal to the corresponding mean gas temperatures. 

Not Radiation Heal Transfer to or from a Surface 727 Net Radiation Heat Transfer betv.een Any Tv-o Surfaces 729 Methods of Solving Radiation Problems 730 Radiation Heal Transfer in Tv/o-Surface Enclosures 731 Radalion Heat Transfer in Three-Surface Enclosures 733... 

With the evaluation of the view factor, in addition to the concepts of radiosity, solid angle, intensity, and emissive power (the last three from Chapter 8), we complete the concepts needed for enclosure radiation problems. Now we proceed to the solution methods for these problems electrical analogy and net radiation. 

Having learned the method of electrical analogy and its application to a number of examples, we proceed now to the second method, the method of net radiation, for enclosure radiation problems. 

Thus, for each case, we end up with a set of N algebraic equations in terms of the unknown radiosities, B, B%,..., Bn. These equations can be solved by using a numerical iteration method as shown in the following example. For convenience, the solution procedure for enclosure radiation problems by the method of net radiation is summarized in Table 9.2 in terms of five steps. 

Next, we proceed to an example which illustrates the use of the method of net radiation for enclosure problems. 

Net-structured NiO was prepared via microwave radiation method with Ni(CH3COO)2 as precursor, followed by calcination at 500°C. The as-prepared NiO was dispersed into glucose solution and subsequently carbonized under hydrothermal condition at 180°C, and the net-structured NiO-C nanocomposites were obtained. TEM images show that the NiO network is homogenously filled with amorphous carbon. The electrochemical performance is improved... 

Attenuation of radiation as it passes through the sample leads to a transmittance of less than 1. As described, equation 10.1 does not distinguish between the different ways in which the attenuation of radiation occurs. Besides absorption by the analyte, several additional phenomena contribute to the net attenuation of radiation, including reflection and absorption by the sample container, absorption by components of the sample matrix other than the analyte, and the scattering of radiation. To compensate for this loss of the electromagnetic radiation s power, we use a method blank (Figure 10.20b). The radiation s power exiting from the method blank is taken to be Pq. 

Thermal radiation is electromagnetic radiation covering wavelengths from 2 to 16 p,m (infrared). It is the net result of radiation emitted by radiating substances such as HjO, CO2, and soot (often dominant in fireballs and pool fires), absorption by these substances, and scatter. This section presents general methods to describe... 

Fig. 8-25 Element representing "space resistance" in radiation-net-AiFi2 work method.

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. 

In Ihe radiation analysis of an enclosure, either the temperature or the net rate of heat transfer must be given for each of the surfaces to obtain a unique solution for the unknown surface temperatures and heal transfer rales. There are two methods commonly used to solve radiation problems. In the first method, Eqs. 13 32 (for surfaces with specified heat transfer rales) and 13-33 (for surfaces with specified temperatures) are simplified and rearranged as... 

Consider an enclosure consisting of two opaque surfaces at specified temperatures r, and T2, as shown in Fig. 13-24, and try to determine llie net rate of radiation heat transfer between the two surfaces with the network method. Surfaces 1 and 2 have emissivities c, and and surface areas /1 and A2 and are maintained at uniform temperatures T, and T, respectively. There are only two surfaces in the enclosure, and thus we can write... 

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