convection coefficient. The different property values of water at 20 C are given by: u W/m K, h=8062 W/m K

Transcription

1 Practice rblems fr Cnvective Heat Transfer 1. Water at 0 C flws ver a flat late 1m 1m at 10 C with a free stream velcity f 4 m/s. Determine the thickness f bndary layers, lcal and average vale f drag cefficient and cnvectin cefficient. The different rerty vales f water at 20 C are given by: = m /s, Pr= 7.02, k = K. Ans ê êë Cf = = - : dx = mm, C fx = , , hx K, h=8062 K ú ú 2. In a certain glass making rcess, a sqare late f glass 1 m 2 area and mm thick heated nifrmly s 90 C is cled by air at 20 C flwing ver bth sides arallel t the late at 2 m/s. Calclate the initial rate f cling the late. Neglect temeratre gradient in the glass late and cnsider nly frced cnvectin. Take fr glass: r = 2500 kg/m, = 0.67 kj/kgk c Take the fllwing rerties f air: r = kg/m, c = 1008 J/kgK, k = C, and m = N-s/m. ëans : C/s. A flat late 1m wide and 1.5 m lng is t be maintained at 90 C in air with a free stream temeratre f 10 C. Determine the velcity with which air mst flw ver flat late alng 1.5 m side s that the rate f energy dissiatin frm the late is.75 kw. Take the fllwing rerties f air at 50 C: m =. -5 = kg/m-s and Pr 0.7 r = 1.09 kg/m, k = C, c = kj/kgk, [ Ans : 100 m/s] 4. Air at 0 C flws with a velcity f 2.8 m/s ver a late 1000 mm (length)x 600 mm (width) x 25 mm (thickness). The t srface f the late is maintained at 90 C. If the thermal cndctivity f the late material is 25 C, calclate : i. Heat lst by the late, ii. Bttm temeratre f the late fr the steady slate cnditin. The therm-hysical rerties f air at mean film temeratre (90 + 0)/2 = 60 C are: r = k = c = = = 1.06 kg/m, C, kj/kgk, m /s, Pr ëans i :. 25 W, ii C 1

2 5. Air at 20 C and at a ressre f 1 bar is flwing ver a flat late at a velcity f m/s. If the late is 280 mm wide and at 56 C, Calclate the fllwing qantities at x= 280 mm, given that rerties f air at the blk mean temeratre r = = æ ö ç = è 2 ø 8 C kg/m, k c = = i. Bndary layer thickness, ii. Lcal frictin cefficient, iii. Average frictin cefficient, iv. Shearing stress de t frictin, v. Thickness f the thermal bndary layer, vi. Lcal cnvective heat transfer cefficient, vii. Average cnvective heat transfer cefficient, viii. Rate f heat transfer by cnvectin, ix. Ttal drag frce n the late, x. Ttal mass flw rate thrghh the bndary. (Sitable velcity rfile may be assmed) 2 [Ans : 6.26 mm, , , N/m, 7.05 mm, are: m C, 1.005kJ/kgK, m /s, Pr= W/ m C, W/ m C, 6.29 W, N, 0.015kg/s] 6. Cnsidering the data f rblem 1, determine the average vale f cnvectin cefficient and C f vales, taking int cnsideratin the laminar regin. Cmare with the rblem 4. Plate length = 1 m, velcity = 4 m/s, late temeratre = 10 C, Water temeratre = 0 C.Film temeratre= 20 C. The rerty vales are = m /s, Pr = 7.02 and k = K. ëans : C f = Engine il at 60 C flws ver a flat srface with a velcity f 2 m/s, the length f the srface being 0.4m. If the late has a nifrm heat flx f 10 k 2, determine the vale f average cnvective heat transfer cefficient. Als find the temeratre f the late at the trailing edge. We have the kinematic viscsity = m 2 /s, Pr = 1050, k = W/ /mk. Use the fllwing data frm the rerty tables: - 2 ëans : h = 48.6 K, T = C 2

3 8. A thin cndcting late searatess tw arallel air streams. The ht stream is at 200 C and 1 atm ressre. The free stream velcity is 15 m/5. The cld stream is at 20 C and 2 atm ressre and the free stream velcity is 5 m/s. Determine the heat flx at the midint f the late f 1 m length. [Ans: Heat flx: 172 W] 9. In an indstrial facility, air is t be reheated befre entering a frnace by gethermal water at 120 C flwing thrgh the tbes f a tbe bank lcated in a dct. Air enters the dct at 20 C and 1 atm with a mean velcity f 4.5 m/s, and flws ver the tbes in nrmal directin. The ter diameter f the tbes is 1.5 cm, and the tbes are arranged in-line with lngitdinal and transverse itches f S L = S T = 5 cm. There are 6 rws in the flw directin with 10 tbes in each rw, as shwn in the figre belw. Determine the rate f heat transfer er nit length f the tbes, and the ressre dr acrss the tbe bank. The rerties f air at 60 C are: k = W / m K,r = 1.06 kg/m -5, C = kj/kg K, Pr = , m = kg/m s, Pr = = ëans Q& 4 : = W, D = 21Pa 10. Water enters a 2.5-cm-internal-diameter thin cer tbe f a heat exchanger at 15 C at a rate f 0. kg/s, and is heated by steam cndensing tside at 120 C. If the average heat transfer cefficient is C, determine the length f the tbe reqired in rder t heat the water t 115 C (see figre belw). Als determine the rate f steam cndensatin. The secific heat f water at 65 C is 4187 J/kg C. The heat f cndensatin f steam at 120 C is 220 kj/kg.

4 [ Ans : 61m] 11. Water is t be heated frm 15 C t 65 C as it flws thrgh a -cm-internal-diameter 5- m-lng tbe (see figre belw). The tbe is eqied with an electric resistance heater that rvides nifrm heating thrght the srface f the tbe. The ter srface f the heater is well inslated, s that in steady eratin all the heat generated in the heater is transferred t the water in the tbe. If the system is t rvide ht water at a rate f 10 L/min, determine the wer rating f the resistance heater. Als, estimate the inner srface temeratre f the ie at the exit. The rerties f water at C = 4179 J/kg C, k = C and 1 atm ressre are: C, Pr = 4.2, = m /s. r = 992.1kg/m, ë Ans : 4.6 KW,115 C 12. Ht air at atmsheric ressre and 8000 enters an 8 m-lng ninslated sqare dct f crss sectin 0.2 m x 0.2 m that asses thrgh the attic f a hse at a rate f 0.15 m /s (figre belw). The dct is bserved t be nearly isthermal at 60 C. Determine the exit temeratre f the air and the rate f heat lss frm the dct t the attic sace. The rerties f air at k = C and 1 atm ressre are: C, Pr = , -5 2 = m /s. r = kg/m, C = 1008J/kg C, 4

5 ë Ans : 71. C, -11 W 1. Water at 25 C enters a ie with cnstant wall heat flx q = 1 k. The flw is // 2 s hydrdynamically and thermally flly develed. The mass flw rate f water is and the ie radis is m= & 10 g/s r = 1 cm. Calclate (a) Reynlds nmber, (b) the heat transfer cefficient, and (c) the difference between the lcal wall temeratre and the lcal mean (blk) temeratre. Prerties f water at 25 C : dynamic viscsity kf = C. m -4 = kg/ms, thermal cndctivity ë 2 Ans : 709,1. K, 7.5 K 14. Fr thermally and hydrdynamically flly develed laminar flw thrgh a circlar tbe with nifrm velcity rfile, shw that N D = 8.0. Assme nifrm wall heat flx and als determine the temeratre rfile. 15. The dr f a ht ven is 0.5 m high and is at 200 C. The ter srface is exsed t atmsheric ressre air at 20 C. Estimate the average heat transfer cefficient at the ter srface f the dr. Assme the fllwing rerties at thermal cndctivity -1 b = K. Tf 110 = C : kinematic viscsity n = m /s, k = K, Pr= 0.704, vlmetric exansin cefficient [ Ans :5.99 K ] 5

6 16. Water at 20 C and 1 atm flws ver a flat late at a seed f 0.5 m/s. The width f the late is 1 m. The entire late is entirely heated t a temeratre f 60 C. Calclate the heat transfer in the first 40 cm length f the late sing the Reynlds-Clbrn analgy. Prerties f water at r = kg/m ressre at cnstant ressre 40 C : dynamic viscsity, thermal cndctivity c kf = kj/kg C. m -4 = kg/ms, density = C, Pr 4.4 [ Ans :15.04 kw ] = and secific 17. Cnsider a 0.6-m x 0.6-m thin sqare late in a rm at 0 C. One side f the late is maintained at a temeratre f 90 C, while the ther side is inslated, as shwn in figre belw. Determine the rate f heat transfer frm the late by natral cnvectin if the late is (a) vertical, (b) hrizntal with ht srface facing, and (c) hrizntal with ht srface facing dwn. The rerties f air at -5 2 = m /s, 1 T f 1 K 60 C and 1 atm ressre are: k = b = =. [ Ans : 115W,128 W,64.2 W] C, Pr = , 18. A 12-cm-wide and 18-cm-high vertical ht srface in 0 C air is t be cled by a heat sink with eqally saced fins f rectanglar rfile shwn in the figre belw. The fins are 0.1 cm thick and 18 cm lng in the vertical directin and have a height f 2.4 cm frm the base. Determine the timm fin sacing and the rate f heat transfer by natral cnvectin frm the heat sink if the base temeratre is 80 C. The rerties f air at 55 C and 1 atm ressre are: k = , = m /s, b = 1 = 1 28K. T f C, Pr = 6

7 7 [ Ans : m, 1.0 W]