Question

A flue passing hot exhaust gases has a square cross section, 300 mm to a side. The walls are constructed of refractory brick 150 mm thick with a thermal conductivity of 1.6 W/m·K. Calculate the heat loss from the flue per unit length when the interior and exterior surfaces are maintained at 350 and 25°C, respectively. Use a grid spacing of 75 mm. Assume the temperature in nodes 2 and 3 are given as T₂ = 108.3°C, T₃ = 162.2°C.

q^` (W/m) ?

150mm - KR TAWY y Symmetry 25 25 25 25 line 25 THEAFF Flue gas MITTUITM Air Air K +500mm van +300mm YA aned with ann en *ax-ay=75mm Symmetry line d

Answer 1

0 Solution Now, calculating the heat loss from the flue per unit length is By using nedal equations calculating the Unknown temperatupes Ta + 25 + To +350 - UT, = 0 T + 25 + T3 +350 - 4T2 =0 To + 25 + Tu-350 - 4T3 =0 Tz +25 + 25 + T3 - 4Tu co we have to = 108 300, T3 = 162.2°C substitute to the abole equation we get Eu 108.300 + 25 + 108.3 +350-4T=0 T 108.3 + 25 +108.3 +350 4 Ti = 147.9°C @ 147.990 + 25 + T3 + 350 -4 (108-3) =0 147.9 + 25 +350 - 433.2 - -T3 +T3 = +89.7 T3 - 89.7°C Then, the heat rate leaving the outer surface at this section is . q' = 2 + ab + ac + 2d tré - (4) 07-25) +(T-05) + (73e5) + (Tu-25) + o]

- 167/*(119.9-05) + (1083-as) + (1693-25) +(89.77-as)) 9' - 553:44 W/m Therefore, In this section is the total cross section, the heat loss tolar 28 al - 8x 553.44 - 4427.52 w/m 9 -4.427 kW/m qa qan geld qe 350 350