Consider the geometry of Figure 6.5. Total energy flux is supplied to two of the three surfaces at rates [latex]q_1, q_2, [/latex] and [latex]T_3 [/latex] is known. Determine [latex]q_3[/latex] and the unknown surface temperatures.

The equations are the same as in Example 6.3 . Now, however, the prescribed boundary conditions have made the solution much more difficult. Because two of the surface temperatures are unknown, the [latex]F_{ΔλT}[/latex] and [latex]ϵ_{Δλ}[/latex] are unknown because they depend on temperature. The solution is carried out as follows: A temperature is assumed for each surface with unknown temperature, and [latex] q_{Δλ,k}(T)[/latex] for each surface is computed. This is done for each of the wavelength bands. The [latex] q_{Δλ,k}(T)[/latex] values are then summed over all the Δλ to find to find [latex]q_1[/latex] and [latex]q_2,[/latex] which are compared to the specified boundary values. New temperatures are chosen and the process repeated until the computed [latex]q_k[/latex] values agree with the specified values. The new temperatures for successive iterations are guessed on the basis of the [latex]F_{ΔλT}[/latex] and [latex]ϵ_Δλ[/latex] variations and the trends of how changes in [latex]T_k[/latex] produce changes [latex]q_k[/latex] throughout the system.

Question 6.4: Consider the geometry of Figure 6.5. Total energy flux is su...

Thermal Radiation Heat Transfer

Consider the geometry of Figure 6.5. Total energy flux is supplied to two of the three surfaces at rates $q_1, q_2,$ and $T_3$ is known. Determine $q_3$ and the unknown surface temperatures.

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

The equations are the same as in Example 6.3. Now, however, the prescribed boundary conditions have made the solution much more difficult. Because two of the surface temperatures are unknown, the $F_{ΔλT}$ and $ϵ_{Δλ}$ are unknown because they depend on temperature. The solution is carried out as follows: A temperature is assumed for each surface with unknown temperature, and $q_{Δλ,k}(T)$ for each surface is computed. This is done for each of the wavelength bands. The $q_{Δλ,k}(T)$ values are then summed over all the Δλ to find to find $q_1$ and $q_2,$ which are compared to the specified boundary values. New temperatures are chosen and the process repeated until the computed $q_k$ values agree with the specified values. The new temperatures for successive iterations are guessed on the basis of the $F_{ΔλT}$ and $ϵ_Δλ$ variations and the trends of how changes in $T_k$ produce changes $q_k$ throughout the system.