Autumn 2005 THERMODYNAMICS. Time: 3 Hours

Transcription

1 CORK INSTITUTE OF TECHNOOGY Bachelor of Engineering (Honours) in Mechanical Engineering Stage 3 (Bachelor of Engineering in Mechanical Engineering Stage 3) (NFQ evel 8) Autumn 2005 THERMODYNAMICS Time: 3 Hours Answer any FIVE questions. All questions carry equal marks. Examiners: Dr. S.F. Cassidy Prof. J. Monaghan Mr. J. Hegarty 1. a) Derive the expressions given is Table 1 for the temperature distribution within and heat transfer through a fin with convection from the fin tip. b) It is proposed to introduce a 1cm square stainless steel fin per 25 sq. cm of a heat exchanger wall. Hot exhaust gases flow over the wall at 650 C and the heat exchanger wall is maintained at 65 C by an oil cooling system. The convection coefficient between the gases and the wall is estimated to be 100 W/m 2 K. The thermal conductivity of the fin is 55 W/mK. If the maximum operating temperature of the fin is to be 400 C, calculate: i) The optimum fin length ii) The percentage increase in heat transfer performance by incorporating the fins into the heat exchanger wall. 2. a) Describe three methods for determining the transient temperature distribution within a solid. Illustrate your answer with suitable examples. (9 marks) b) The heat transfer coefficient for air flowing over a sphere is to be determined by observing the temperature-time history of a sphere fabricated from pure copper. The sphere, which is 12.7 mm in diameter, is at 66 ºC before it is inserted into an airstream having a temperature of 27 ºC. A thermocouple on the outer surface of the sphere indicates 55 ºC after the sphere has been inserted in the airstream for 69 seconds. Assume, and then justify, that the sphere behaves as a spacewise isothermal object and calculate the heat transfer coefficient. Copper properties: k=400 W/mK c p =383 J/kgK ρ=8933 kg/m 3 (11 marks)

2 3. a) Describe the effect of boundary layer development on heat transfer to a flat plate. b) A steel strip emerges from the hot roll section of a steel mill at a speed of 20m/s and a temperature of 1200 K. Its length and thickness are 100m and respectively. Accounting for heat transfer from both the top and bottom surfaces and neglecting radiation and strip conduction effects, determine the initial time rate of change of the strip temperature at a distance 1m from the leading edge and at the training edge. Determine the distance from the leading edge at which the minimum cooling rate is achieved. Steel Properties: c p =640 J/kgK ρ=7900 kg/m 3 Air Properties: k=0.0549w/mk υ=76.4x10-6 m 2 /s Pr= a) Describe the concept of developing flow as found in internal flow in a pipe. Detail when a flow may be assumed to be fully developed. b) Engine oil flows through a 25mm diameter, 10m long tube at a rate of 0.5kg/s. The oil enters the tube at 25ºC, while the tube is maintained at 100ºC. i) Determine the total heat transfer to the oil and the oil outlet temperature. ii) Repeat part (i), subject to the assumption of fully developed conditions throughout the tube. Comment on the results obtained. Engine oil Properties: k = W/mK c p = 2076 J/kgK ρ = 860 kg/m 3 Pr = 793 µ = 5.31x10-2 kg/sm 5. a) Describe with the aid of suitable sketches heat transfer between a heated vertical wall and still air. Your discussion should include a review of the critical parameters which influence this heat transfer. b) An experimental procedure to determine the free convection coefficient for a vertical plate involves suspending a 200mm square thin slab of ice in a large enclosure that allows for slight air movement. The ambient air and walls of the enclosure are at a temperature of 27 C. Considering both convection and radiant heat transfer, estimate the mass of water that melts from the slab in a two hour period. The latent heat of fusion of ice is kj/kg and its emissivity is Note : σ = 5.67 x 10-8 W/m 2 K 4

3 6 a) Explain the following terms as they apply to radiative heat transfer: emissivity, grey, diffuse and opaque. b) A drying oven consists of a long semicircular duct of diameter 1m. Materials to be dried cover the base of the oven while the wall is maintained at 1200 K. What is the drying rate per unit length of the oven if a water covered layer of material is maintained at 52 º C during the drying process? Blackbody behaviour may be assumed for the water surface and for the oven wall. Water Properties: h fg = 2.378x10 6 J/kg 7. a) Discuss the terms grey and diffuse as they apply to radiative properties of real surfaces. Illustrate your answer with suitable sketches. (4 marks) b) A vertical flat plate, insulated on its edges and backside, is suspended in still air at 27 C. The convection coefficient between the plate and the still air is estimated to be 10W/m 2 K. The exposed surface is painted with a special diffuse coating having the prescribed absorptivity distribution shown in Figure 1. The plate is irradiated by solar-simulation lamps that provide a spectral irradiation distribution, G λ. characteristic of the solar spectrum. Under steady state conditions, the plate reaches a temperature of 127 C. i) For the prescribed conditions, determine the plate emissivity ε, the plate absorptivity α and the plate irradiation G. ii) If the irradiation G found in part (i) were increased ten-fold, what steady state temperature would the plate now reach? Assume convection losses are negligible in this case. Is this assumption reasonable? Note: The sun may be treated as a blackbody at temperature 5800K. (16 marks) 0.9 α λ λ (µm) Figure 1 Spectral absorptivity of coating

4 Fin Tip Condition Temperature Distribution Fin Heat Transfer Rate Convection Heat Transfer hsinh( m( x) ) + kmcosh( m( x) ) Adiabatic ( ) Prescribed Temperature ( ) ( ) Infinite fin ( ) hsinh( m) + kmcosh( m) h cosh( m) + sinh( m) M mk h sinh( m) + cosh( m) mk cosh( m x ) cosh( m) Mtanh ( m ) mx ( m x ) sinh + sinh cosh m b M b sinh( m) sinh( m) e mx ϑ = T T 2 hp where m = k A M = h P k A ϑ b Table 1 Temperature Distribution and Heat oss for Fins of Uniform Cross-section Correlation Nu x = Re x Pr aminar, local, T f, 0.6 < Pr < Nu x = Rex Pr aminar, average, T f, 0.6< Pr < Nu x = Re x Pr Turbulent, local, T f, Re x < 10 8, 0.6 < Pr < Nu = ( Rex 871) Pr Mixed,average, T f, Re crit =5x10 5, Re <10 8,0.6 <Pr < 50 Table 2 Convection correlations for external flow over a flat plate Correlation = 436. aminar, fully developed, uniform heat flux, Pr > 0.6 = 366. aminar, fully developed, uniform T s, Pr > ( D/ ) ReD Pr aminar, thermal entry length, uniform T s NuD = / [( D/ ) ReD Pr] n = Re D Pr Turbulent, fully developed, Re D > 10000, n = 0.4 for T s > T m, n = 0.3 for T s < T m M Table 3 Convection correlations for flow in a circular tube Temperature k ρ c p ν α Pr (K) (W/mK) (kg/m 3 ) (kj/kgk) (m 2 /s) (m 2 /s) Table 4 Thermophysical properties of Air

5 Correlation 2 16 / Vertical Plate, T Ra f Nu = / [ 1+ ( / Pr) ] 827 / 14 / Nu = 054. Ra Upper surface of heated plate or lower surface of cooled plate, 10 2 < Ra < / Nu = 015. Ra Upper surface of heated plate or lower surface of cooled plate, 10 7 < Ra < / Nu = 027. Ra ower surface of heated plate or upper surface of cooled plate, 10 5 < Ra < / Ra Horizontal Cylinder, Ra D D <10 12, T f = /16 8 / 27 [ 1+ ( / Pr) ] Table 5 Free convection empirical correlations for immersed geometries λt (µm. K) F (0 λ) Table 6 Blackbody Radiation Functions