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, Ez = 0.5 A4, T1 = 1000 K, £z = 0.33- -A3, T3 , £z = 0.8 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 £3 on the net radiation transfer from surface A1

Answer 1

3] A., Taloook & -0.33 Az, Tz = 7ook Ex=0.5 im Assumptions (is Surfacon are diffuse gray and are (i) Puct is very long end effects negligible Az , 73, 8:08 Insul Insulared Surface b) The three Surface enclose for duct approximates third Surface (As) is which de Racinting The ner Radiation transferi is given by Eni - Em 9,=-/ + + E 41 (1 - E.) (1-2) Al fiz & CLAIF, & YAZfa)" EzAz fi2 = F = f₂ =0.5 A = Az = wol t - length roomal poze Foi = out for to To to the By Symmetry fiz r fi fosos wam a = avile (A/A) w q (567 700 – 13614) oist (%o-s +%s) -0.5 1 1-0.33 + 0.33 qiz 9874 W/m

J Radiation Balance, Ғь, - J, + 990 (A3 foi) E b3 - (Agf32) Eba - Juta 2 To Find J. and Ja, Jo - Ebi - 9 q: (LEO Ai T, 86700 (9876) 1-0-33 36, 653 W/m² ET 2 0.33 Is = 13614 (~9874) 1-os 23488 W/m2 os &bg= o Tor To - (Em) J, + J./20) T Vy TB - 8536 36653+ 23488 2 (SLTX10-) adiabatic, 4 d) Since, Az is J3 = fb3 Hence, The value of Ez is having influence Radiation exchange rempenhure T3 on the