Question

It's a heat transfer question

Consider a long duct constructed with diffuse and gray walls. The width of each wall is 1 m. Heat transfer is from surface 1 to surface 2, while surface 3 is completely insulated and cannot absorb heat (which means 93 = 0). Az, T2 = 700 K, Ey = 0.5 Aj, T = 1000 K, E1 = 0.33 A - Ag, T3, Ez = 0.8 IRI a. Provide a sketch and state your assumptions b. Determine the net radiation transfer from surface A1 per unit length of the duct. c. Determine the temperature of the insulated surface A3. d. Use 1 sentence to describe the effect of changing the value of 83 on the net radiation transfer from surface A1

Answer 1

Solution Given Wz 1m surface-3 is completely insulated Q=0 4 (1) Assumption ① surface are diffuse grey ② Duct is very long end effects are negligisse calculate the net & radiation transfer from sustace A, per unit dengan to of the duct view factor A, on a Fir = -0.5 from Symmety FiR - Fax = fir A,.= we A₂ = ad net sadiaton on per unit length 6. (7,² – T) - a = 2 21 1-6 Ei 7:))+(13) + figt (the (10007_7007) 5.67x108 I-0.5 1 q 1-0.33 0.35

9 9875 W/m Ans (c) Calculate the teme of the insulated surface A for radiation balance (2. = 2 = 0) F63-J. Foz - J - Az for Az F22 .J+J 2.8b3 J+ Je Ebo 0 2 Where J = {to - 2. (10) Ji = (5.67X164) (10004) – 9875 (1–0.23 0.33 J = 36651 W/m2 - E Jp = Ebat 92 AL Er 1-0.5 - (5.67% 17%)x (7004) - (-3875) "[ Je = 23489 W/ml from er we get 36651 +23489 30070 Ebz

4. 5 T3 - 30070 =) 3007 o To J) 5-67 X 16-8 T = 853k Ans (d) + Since the third way is completely insulated (870) So there is no effect of of emissivity. Change