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Raquel Riera Homework 1 ⑪ The thermal conductivity of a sheet of rigid extruded insulation is reported to be 1 = 0.029 N/m.K. The measured temp. diference across a 20mm-thick sheet of the materials is T1 - Tz = 10 a) What is the heat flox through a 2x2[m) sheet of the insulation ? - I A = 2x2m g = 41 1 11 DT 10 C - - =0.029 N/m.K x4m2 x 10 C L 20mm - 1 ↓ 1000mm 20mm =58 [N] b) What is the rate of heat transfer through the sheet of insulation ? 9" = 1 A q g" = - = W = 14.5 [ A

D A wall has inner & outer surface imperature of 162 and 62 respec tivel f the interior and exterior air Emperatures are 20C &S2 respecti- rely. Calculate the heat tx from the interior air to the wall, from the wall to the exterior air, from the wall to the interior air. -s the I wall under steady-state conditions ? T, = 12 g," Ty, = 5 -> To = 20C I Tz = 62 convection * n = 5W/m2k ↑ h= = 20W/m2K I heat flux from interior air to the wall q" = h,.(T - Ti) = 5x (20-16) =20 mm heat flux from the wall to the exterior air q " = nz (Tz - Toc) 2 - 20(6 - 5) =20 W/m2 heat flox from the wall to the interior air: g" = - G, = - 20w m2 is the wall under steady-state conditions 0 Steady-state Ein- Fort +1 -Est Ig - d = 0 g,-q,"Est Este e e dt 20 -20 = Est = 0 The wall is under steady-state

⑫ An overhead 25m long, uninsulated industrial steam pipe of 100mm diameter is routed through a building whose walls and air are at 25C. Pressurized stam maintains a pipe surface temperature of 150 and the coefficient associated w natural convection is n = 10W/m2K The surface emissitivity is E = 0.8 a) what is the rate of heat loss from the steam line ? Tw= 252 T h = to L = 2Sm - = 25C q = fcur + grad a 4 Ts = 130 t = 298k q = n.A.(Ts - 5) + do [s" - TwY) - D = 1m 2 = 0.8 Ts = 423R ~ A = π D.2 = 1047.85(423 - 298) + (0.8x5.67x108*(42322984) q = 18405W b) If the steam is generated is a gas-fired boiler operating at - an efficiency, of f=0.90 a natural gas is priced at Cg= $ 0.02 per M5 what The annual cost of heat loss from the line ? E = Q A t 18405*(3654244360075 = 5.8842x10" Et = = 4x"= 6.449/IX 2 = 2y x Ef = 6.449/IX10"

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1.66 A vertical slab of wood's metal is joined to a substrate one one surface on the opposite surface. The metal is initialle as its fusion temp of if=722 and the melt runs off by gravity as soon as its formed. The absorptivity of metal to the laser rad. is as = 0.4 and latent neat of fusion is hd= 33K5/Rg a) Neglecting heat transfer from the irritated surface by convect. or rad exchage w the surroundings determine the instantaneous rate of melting if the irradiation is SRW/m2 How much material is removed if [kgIs. m2] - 1m2 G = 5000 irradiation is maintained fores ? 12C a - 2G -> 55 = 722 di = 0.4 nst 35 2.G = m" Ast 0.41 5000 M" * 33 m" = 60.6x183 me q " A b) My 2G = Ein Ein- Route Eg= Est & ↓ g"rad a G- (qco" - grad") = mil. Ast q cr" = h. (Tf. To) Arad = 3 o (If4-50") q con" = 15(72 - 20) S q con" = 15x52 (3454 - 2934) W qun" = 780 m2 0.4650880 - 780 - 0.455.67x1581.4167x101 - 7.370051X109 - haf m" m" = 32.3 x10-3ky/sm2

1.79 A rectangular forced air heating duct is suspended from 0 the ceiting of a basement whose air and walls are at a temp of To = SC = Tsur The duct is 15m long and its cross-section is Tsur = 52 ↑ To = SC 350mmx 200mm ⊥ I ⊥ Ts = 50C a) For an unisulated duct whose arg. surface tmp is soc estimate the rate of hat loss from the dust. The force emissivity and convection coeficient are approx 0.5 and 4 Wink respectively floss = 4 awio.soy te eso tetas 2 =5268W b) If heated air enters the duct at ssic and a velocity of 4m/s and the heat los corresponds to the result of part cal what's the outlet temp ? = 1.10 Kg/n specf. heat --- glos inlet (p = 10085/rg-K - in Cp Tin me eri exiti pt te q con: in up (Tin-Fort) in = p-u. A = 0.308.1008. (582 -4(() in = 1.10.4 m.S 1.350m2.200m) 9 loss = 5277.88 = 0.308

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Answer correctly and quickly as possible please.

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