CANKAYA UNIVERSITY FACULTY OF ENGINEERING MECHANICAL ENGINEERING DEPARTMENT ME 313 HEAT TRANSFER

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Domenic Flowers
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1 CANKAYA UNIVERSITY FACUTY OF ENGINEERING MECHANICA ENGINEERING DEPARTMENT ME 313 HEAT TRANSFER CHAPTER-3 EXAMPES 1) Cnsider a slab f thicness as illustrated in figure belw. A fluid at temperature T 1 with heat transfer cefficient h1 flws ver the surface at = 0, and anther fluid at temperature T 2 with a heat transfer cefficient h2 flws ver surface at = f plate. Find the heat flw thrugh area A. A = 1 m 2, T 1 = 130 C, h1 = 250 W/m 2. C, h2 = 500 W/m 2. C, = 4 cm, = 20 W/m C, T 2 = 30 C. h2, T 2 h1, T 1 2) An irn plate f thicness with thermal cnductivity is subjected t a cnstant unifrm heat flu q (W/m 2 ) at the bundary surface = 0. Frm the ther bundary '' surface = heat is dissipated by cnvectin int a fluid at T with heat transfer cefficient h. T1 '' q T2 Develp epressins fr the determinatin f surface temperatures T1 and T2 at the surfaces = 0 and = respectively. Calculate T1 and T2 fr = 2 cm, = 20 W/m.K, '' 5 2 q 10 W / m, T = 50 C, h = 5000 W/m 2. C.

2 3) A wall is cnstructed by several layers. Bric Mrtar imestne Plaster A B C D E Ti, hi T, h = 0.25 m, 2 = m, 3 = 0.1 m, 4 = m, 1 =0.66 W/m.K, 2 = 0.7 W/m.K, 3 = 0.66 W/m.K, 4 = 0.7 W/m.K, hi = 5.8 W/m 2.K, Ti = 26 C, h = 11.6 W/m 2.K, T = - 7 C. Find; a) verall heat transfer cefficient b) verall thermal resistance c) heat flw rate thrugh cmpsite wall d) temperature at the inter face f mrtar and limestne 4) A square plate heater (15 cm 15 cm) is inserted between tw slabs. Heater at T1 T A B TR T, ha A B T, hb A B A= 2 cm, B = 1 cm, A = 50 W/m.K, B = 0.2 W/m.K, ha = 200 W/m 2.K, hb = 50 W/m 2.K, T = 25 C, Q = 1 W = 1000 W, A = 15 cm 15 cm = m 2. Find; a) maimum temperature f the system b) uter surface temperatures n bth slabs

5) Cnsider the cmpsite f tw materials cmbined in parallel paths with the ends maintained at unifrm temperatures as illustrated in the figure belw. Ta A1 1 Tb A2 2 Varius quantities are specified.

3 5) Cnsider the cmpsite f tw materials cmbined in parallel paths with the ends maintained at unifrm temperatures as illustrated in the figure belw. Ta A1 1 Tb A2 2 Varius quantities are specified. A1 = 0.2 m 2, 1 = 20 W/m.K, A2 = 0.4 m 2, 2 = 15 W/m C, = 0.5 m, Ta = 150 C, Tb = 30 C. Calculate the rate f heat transfer, q acrss cmpsite material. 6) Cnsider a cmpsite wall that includes an 8 mm thic hardwd siding, 40 mm by 130 mm hardwd studs n 0.65 m centers with glass fiber insulatin (paper faced, 28 g/m 3 ), and a 12 mm layer f gypsum (vermiculite) wall bard. What is the thermal resistance assciated with a wall that is 2.5 m high by 6.5 m wide (having 10 studs, each 2.5 m high)? 7) Tw large aluminum plates ( = 240 W/m.K), each 1 cm thic with 10 µm surface rughness are placed in cntact under a pressure f 1 bar in air ( = W/m.K). The temperature at inside and utside surfaces are 400 C, and 150 C. Calculate; a) heat flu b) temperature drp due t cntact resistance 8) A hllw cylinder with inner cylinder radius r = a and uter radius r = b is heated at '' 2 the inner surface at a rate f q (W / m ), and dissipates heat by cnvectin frm the uter surface int a fluid at temperature T with a heat transfer cefficient h. There is n energy generatin and thermal cnductivity is cnstant. Develp epressins fr the determinatin f temperatures at T1 and T2 f inner and uter surfaces f the cylinder. Calculate T1 and T2 fr a = 3 cm, b = 5 cm, h = 400 W/m 2. C, T = 100 C, = 15 '' 5 2 W/m.K, q 10 W / m.

4 T2 T1 " q r = a r = b 9) A hllw sphere f inside radius r = a and utside radius r = b is electrically heated at ' ' the inner surface at a cnstant rate f q (W/m 2 ). At the uter surface it dissipates heat by cnvectin int fluid at temperature T with a heat transfer cefficient h. Thermal cnductivity f slid is cnstant. T2 T1 " q r = a r = b Develp epressins fr the determinatin f the inner and uter surface temperatures T1 and T2 f sphere. Calculate the inner and uter surface temperatures fr a = 3 cm, b = 5 cm, h = 400 W/m 2. C, T = 100 C, = 15 W/m. '' 5 2 C and q 10 W / m. 10) A pressure vessel fr a nuclear reactr is apprimated as a large flat plate f thicness. The inside surface f the plate at = 0 is insulated, the utside surface at = is maintained at a unifrm temperature T2, and the gamma-ray heating f the plate can be represented as a heat generatin term in the frm q ( ) = g0 e -γ W/m 3

5 where g0 and γ are cnstants q T2 insulatin a) develp an epressin fr temperature distributin in the plate b) develp an epressin fr the temperature at = 0 f the plate c) develp an epressin fr heat flu at the uter surface 0 11) Cnsider a slab f thicness and cnstant thermal cnductivity in which energy is 3 generated at a cnstant rate f q ( W / m ). insulated 0 The bundary at = 0 is insulated and that = dissipates heat by cnvectin with a heat transfer cefficient h int a fluid at a temperature T. Develp epressins fr temperature T () and heat flu q '' () in the slab. Calculate temperatures at = 0 and = under the fllwing cnditins. = 1 cm, = 20 W/m.K, W/m. C, T = 100 C. 7 3 q = 8 10 W / m, h = ) Cnsider a slid cylinder f radius r = b in which energy is generated at a cnstant rate f g (W/m 3 ), while the bundary surface at r = b is maintained at cnstant temperature Ts. Develp an epressin fr ne dimensinal, radial, steady state temperature distributin T(r) and heat flu q '' (r). Calculate the center temperature T(0) 8 3 and the heat flu at the bundary surface r = b fr b = 1 cm, g = 2 10 W / m, = 20 W/m. C, Ts = 100 C.

6 b Ts 13) 250 A current flws thrugh a cpper cable (as shwn in the figure) epsed t cnvective air. d = 30 mm a) Find maimum temperature in the wire b) Find surface f temperature in the wire h = 25 W/m 2. C T = 20 C 14) Develp an epressin fr the steady state temperature distributin T (r) in a lng, q r g 1 Ar W/m 3 hllw cylinder, a r b, in which heat generatin at a rate f where g and A are cnstants, while the bundary surfaces at r = a and r = b are ept at zer temperatures. r = a r = a T = 0 r = b T = 0 r = b 15) A very lng fin ( = 380 W/m.K) has a diameter f 25 mm. Fin etends frm a surface at 120 C. The temperature f the surrunding air is 25 C and the heat transfer cefficient ver the rd is 10 W/m 2.K. Calculate: a) heat lss frm the rd b) hw lng the rd shuld be in rder t be cnsidered infinite?

7 Tb 16) A steel rd f diameter D = 2 cm, length = 25 cm, and thermal cnductivity = 50 W/m. C is epsed t ambient air at T = 20 C with a heat transfer cefficient h = 64 W/m 2. C. If ne end f the rd is at temperature f 120 C, calculate heat lss frm the fin. 17) Cnsider a stainless steel spn ( = 15.1 W/m.K) partially immersed in biling water at 95 C in a itchen at 25 C. The handle f the spn has a crss sectin 0.2 cm 1 cm and it etends 18 cm in the air frm the free surface f water. If the lcal heat transfer n the epsed surface f spn is 15 W/m 2.K, calculate the temperature difference acrss epsed surface f the spn handle. State yur assumptins, if any.

Problem 1 Known: Dimensions and materials of the composition wall, 10 studs each with 2.5m high

Problem 1 Known: Dimensions and materials of the composition wall, 10 studs each with 2.5m high Prblem Knwn: Dimensins and materials f the cmpsitin wall, 0 studs each with.5m high Unknwn:. Thermal resistance assciate with wall when surfaces nrmal t the directin f heat flw are isthermal. Thermal resistance