Radiosity (heat Transfer) - Circuit Analogy

Circuit Analogy

For an enclosure consisting of only a few surfaces, it is often easier to represent the system with an analogous circuit rather than solve the set of linear radiosity equations. To do this, the heat transfer at each surface, is expressed as

\dot{Q_i} = \frac{A_i \epsilon_i}{1-\epsilon_i}(E_{bi}-J_i) = \frac{E_{bi} - J_i}{R_i} \qquad \text{where} \quad R_i = \frac{1-\epsilon_i}{A_i \epsilon_i}

and is known as the surface resistance. Likewise, is the blackbody radiation minus the radiosity and serves as the 'potential difference.' These quantities are formulated to resemble those from an electrical circuit .

Now performing a similar analysis for the heat transfer from surface to surface ,

\dot{Q_{ij}} = A_i F_{ij} (J_i - J_j) = \frac{J_i - J_j}{R_ij} \qquad \text{where} \quad R_{ij} = \frac{1}{A_i F_{ij}}

Because the above is between surfaces, is known as the space resistance and serves as the potential difference.

Combining the surface elements and space elements, a circuit is formed. The heat transfer is found by using the appropriate potential difference and equivalent resistances, similar to the process used in analyzing electrical circuits.

Read more about this topic:  Radiosity (heat Transfer)

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