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)

Famous quotes containing the words circuit and/or analogy:

    “each new victim treads unfalteringly
    The never altered circuit of his fate,
    Bringing twelve peers as witness
    Both to his starry rise and starry fall.”
    —Robert Graves (1895–1985)

    “The analogy between the mind and a computer fails for many reasons. The brain is constructed by principles that assure diversity and degeneracy. Unlike a computer, it has no replicative memory. It is historical and value driven. It forms categories by internal criteria and by constraints acting at many scales, not by means of a syntactically constructed program. The world with which the brain interacts is not unequivocally made up of classical categories.”
    —Gerald M. Edelman (b. 1928)