Equation 1.7 is subject to several restrictions, such as the surroundings being isothermal and large relative to the smaller surface. Consider the small and large surfaces to be isothermal concentric spheres of radii \(r_{1}\) and \(r_{2}\), respectively.

(a) Calculate the radius ratio, \(r_{2} / r_{1}\) for which Equation 1.7 yields a radiation heat rate that is within \(1 \%\) of the heat rate given by Equation 13.26 for the following cases. The opaque surfaces are diffuse and gray.

(b) Plot the required radius ratio versus the emissivity of the larger sphere for the two emissivities of the smaller sphere.

Equation 1.7 and 13.26:-

Transcribed Image Text:

Case 1: & = 0.9, 2 = 0.9 Case 2: =0.9, & = 0.1 Case 3: = 0.1, = 0.9 Case 4: & = 0.1, = 0.1