Question

To enhance heat rejection from a spacecraft, an engineer proposes to attach an array of rectangular fins to the outer surface of the spacecraft and to coat all surfaces with a material that approximates blackbody behavior. Consider the U-shaped region between adjoining fins and subdivide the surface into components associated with the base (1) and the side (2). Obtain an expression for the rate per unit length at which radiation is transferred from the surfaces to deep space, which may be approximated as a blackbody at absolute zero temperature. The fins and the base maybe assumed to be isothermal at a temperature T. Comment on your result. Does the engineer's proposal have merit

Answer 1

Answer:

Attached below is the required diagram related to the question

answer :

q'3 = WбT^4

engineer's proposal has merit

Explanation:

Let : A'3 represent the deep space

      A'1 represent the surface area , F13 and  F23  represent the view factors

      T1 , T2, T3 ; represent temperatures

      q'3 represent net rate of heat radiation

 Derive the expression for the rate per unit length at which radiation is transferred from the surfaces to deep space

derived expression ; q'3 = WбT^4

attached below is a detailed solution

Given that The emission is proportional to the area of the opening and the surfaces ( 1 and 2 ) have the same temperature hence this problem can be treated as a two surface enclosure. hence the engineer's proposal have merit .

attached below is a prove ( b )