Derive an expression for the net radiation exchange between the two uniform concentric spheres shown in Figure P15.27. You may assume each sphere is a diffuse graybody with emissivity \(\varepsilon_{1}^{r}\) and \(\varepsilon_{2}^{r}\). The outer sphere is insulated.

If \(\varepsilon_{1}^{r}=0.5, \varepsilon_{2}^{r}=0.8, T_{1}=500 \mathrm{~K}, T_{2}=1000 \mathrm{~K}, r_{1}=0.5 \mathrm{~m}\), and \(r_{2}=1.5 \mathrm{~m}\), what is the net rate of heat exchange between the two objects?

Transcribed Image Text:

FIGURE P15.27 T T, r 1 1 E