ME 303: Convection, Boiling, Condensation and Mass TransferAssignment #1 Last Date of Submission: 04 November, 2015 before 12.00pm Submission place: M413 Problem 1: A 6-cm diameter shaft rotates at 3000 rpm in a 20-cm long bearing with a uniform clearance of 0.2 mm. At steady operating conditions, both the bearing and the shaft in the vicinity of the oil gap are at 50°C, and the viscosity and thermal conductivity of lubricating oil are 0.05 N.s/m2 and 0.17 W/m.K. By simplifying and solving the continuity, momentum, and energy equations, determine (a) the maximum temperature of oil, and (b) the rates of heat transfer to the bearing and the shaft. Problem 2: The forming section of a plastics plant puts out a continuous sheet of plastic that is 1.2 m wide and 2 mm thick at a rate of 15 m/min. The temperature of the plastic sheet is 90°C when it is exposed to the surrounding air, and the sheet is subjected to air flow at 30°C at a velocity of 3 m/s on both sides along its surfaces normal to the direction of motion of the sheet. The width of the air cooling section is such that a fixed point on the plastic sheet passes through that section in 2 s. Determine the rate of heat transfer from the plastic sheet to the air. Problem 3: An array of power transistors, dissipating 6 W of power each, are to be cooled by mounting them on a 25-cm × 25-cm square aluminum plate and blowing air at 35°C over the plate with a fan at a velocity of 4 m/s. The average temperature of the plate is not to exceed 65°C. Assuming the heat transfer from the back side of the plate to be negligible and disregarding radiation, determine the number of transistors that can be placed on this plate. Problem 4: Atmospheric air at 375 K flows with a velocity of 4 m/s along a flat plate of 1 m long, maintained at a uniform temperature 325 K. The average heat transfer coefficient is determined to be 8 W/m2°C. Using the Colburn-Reynolds analogy, estimate the drag force acting on the plate over the width of 2 m. is estimated to be 0°C.2 Problem 10: Air flows across a 4 cm square cylinder at a velocity of 10 m/s. and the average temperature of the surfaces surrounding the pipe.Problem 5: During a plant visit.6 bar. The emissivity of the outer surface of the pipe is 0. The black side of the plate is insulated so that all the energy absorbed is dissipated to an air stream which blows across the plate at conditions of 25°C. Assume the tank surface to be at the same temperature as the water inside. What is the total heat transfer from the leading edge to a point 35 cm from the leading edge? Problem 7: Air flows across a 20 cm square plate with a velocity of 5 m/s. Estimate the temperature of the tank a 45-min period. Determine the amount of heat lost from the steam during a 10-h long work day. A heater in the plate surface furnishes a constant heat flux condition at the wall so that the average wall temperature is 100°C. The surface temperature is maintained at 85°C. The plate is 25 cm square. Problem 6: Air flows over a flat plate at a constant velocity of 20 m/s and ambient conditions of 20 kPa and 20°C. it was noticed that a 12-m long section of a 10-cm diameter stream pipe is completely exposed to the ambient air. Problem 8: A blackened plate is exposed to the sun so that a constant heat flux of 800 W/m2 is absorbed.5 cm from the leading edge. Calculate the surface heat flux and the value of h at an x position of 10 cm. 1 bar and 3 m/s. There are also light winds in the area at 10 km/h. Free-stream conditions are 10°C and 0. Estimate the average temperature of the plate. Use the following correlation proposed by Churchill and Bernstein (1977): RedPr > 0. The tank is placed horizontally on the roof of a house. Free-stream air conditions are 20°C and 0. The tank is then exposed to windy air at 18°C with an average velocity of 40 km/h during the night. What is the plate temperature at the trailing edge? Problem 9: Consider a 50-cm diameter and 95-cm long hot water tank. and the heat transfer coefficient on the top and bottom surfaces to be the same as that on the side surface. Calculate the heat loss from the cylinder per meter of length.2 atm. starting at a distance of 7. The temperature measurements indicate that the average temperature of the outer surface of the stream pipe is 75°C when the ambient temperature is 5°C. The plate is heated to a constant temperature of 75°C. including the sky. .8. The water inside the tank heated to 80°C by a flat-plate solar collector during the day. x = 0.074Re −1 / 5 L − 1742Re L All Prandtl number (Churchill and Ozoe): Pex ≥ 100 ξ = unheated starting length C f .037Re 4L/ 5 Pr1/ 3 Nu L = 0.453Re1x/ 2 Pr1/ 3 Laminar: Rex < 5 × 105 .037Re Nu x = 4/ 5 L − 871) Pr 1/ 3 0.664Re−x 1/ 2 Laminar: Rex < 5 × 105 . 0.x = 0. 0.35 × 106 Re−L6 / 5 Nu x = 0.6 ≤ Pr ≤ 60 ξ = unheated starting length Laminar: ReL < 5 × 105.6 < Pr < 50 Laminar: ReL < 5 × 105 .6 ≤ Pr ≤ 60 Recr = 5 × 105 C f = 1.664Re−x 1/ 2 Nu x = 0.3387Re1x/ 2 Pr1/ 3 0.680Re1L/ 2 Pr1/ 3 C f . 0.0308Re 4x / 5 Pr1/ 3 C f = 0.0468 1 + Pr 2 / 3 1/ 4 0. 0.6 ≤ Pr ≤ 60 Partly Laminar.Type Local Average Local Average Average Local Local Local Average Summary of Correlation for Forced Convection Flow over Flat Plates Properties evaluated at Film temperature Heat Transfer Restrictions Fluid Flow Isothermal (Tw = constant) Isoflux (qw = constant) C f .037Re 4L/ 5 Pr1/ 3 Nu L = 1 + 12. Partly Turbulent: 5 × 105 ≤ ReL ≤ 107 . 0.x = 0.6 < Pr < 50 Turbulent: 5 × 105 ≤ Rex ≤ 107 .037Re 4L/ 5 Pr1/ 3 C f = 0.074Re−L1/ 5 Nu L = 0. 0.332Re1x/ 2 Pr1/ 3 Nu x = 0. 0. p = 2 Turbulent: 5 × 105 ≤ ReL ≤ 107.059Re−x 1/ 5 Nu x = 0.0207 2 / 3 1 + Pr ξ 3 / 4 Nu x = Nu x( for ξ =0) 1 − x −1 / 3 ξ 9 / 10 Nu x = Nu x( for ξ =0) 1 − x L Nu L = Nu L( for ξ =0) L −ξ −1 / 9 ξ 1 − x p +1 p+2 p p +1 1/ 4 .664Re1L/ 2 Pr1/ 3 Nu L = 0.6 ≤ Pr ≤ 60 Turbulent: 5 × 105 ≤ ReL ≤ 107 . p = 8 Nu L = ( 0.x = 0.328Re −L1/ 2 Nu L = 0.4637Re1x/ 2 Pr1/ 3 0.0296Re 4x / 5 Pr1/ 3 Nu x = 0.059Re−x 1/ 5 Turbulent: 5 × 105 ≤ Rex ≤ 107 .6 < Pr < 50 ξ = unheated starting length C f . 000 40.148Re0.000–400.330 0.683Re0.612 Pr1/3 5 5 5 5 5 D Square (tilted 45°) D Hexagon D Hexagon (tilted 45°) Vertical plate D D Ellipse D . 1972.258Re0.4–4 4–40 40–4000 4000–40.618 0.638 Pr1/3 Gas 5200–20.700 Nu 5 0.911Re0. and Sparrow et al. TABLE 7–1 Empirical correlations for the average Nusselt number for forced convection over circular and noncircular cylinders in cross flow (from Zukauskas.027Re0.989Re0.197Re0.039Re0.466 0. 2004) Cross-section of the cylinder Fluid Circle D Square Range of Re Nusselt number 0.000 Nu Nu Nu Nu Nu Gas 3900–79.094Re0.443 CHAPTER 7 The characteristic length D for use in the calculation of the Reynolds and the Nusselt numbers for different geometries is as indicated on the figure.000 Nu 5 0.000 Nu 5 0. Note that the values presented in Table 7–1 for non-circular geometrics have been updated based on the recommendations of Sparrow et al.638 Pr1/3 Nu 5 0.600 Nu 5 0.588 Pr1/3 Gas 4500–90. (2004).400 20.782 Pr1/3 Gas 6300–23.731 Pr1/3 Gas 1400–8200 Nu 5 0. All fluid properties are evaluated at the film temperature.162Re0..385 0.193Re0.805 Pr1/3 Pr1/3 Pr1/3 Pr1/3 Pr1/3 Gas or liquid 0. Jakob 1949.257Re0.000 Nu 5 0.675 Pr1/3 Gas 5600–111.400–105. 625 3.920 3.0283 1.671 2.214 1.139 0.131 0.583 2.765 3.69 20.1602 0.7833 0.574 1.710 0.715 6.0090 1.8 138.100 0.482 1.540 7.251 2.705 0.0856 1.105 0.1951 1.22160 0.75 99.5 229.17 5.1682 0.1538 0. and Pr are not strongly pressure-dependent and may be used over a fairly wide range of pressures T .248 1.3760 0.111 0.705 0.1 205.175 0. Stand.230 1.5 0.3675 1.0782 0.332 3.0551 1.0057 1.3524 0.3097 1.7512 0.02501 0.1858 0.93 5.372 1.018 3.4405 0.9980 0.04038 0.705 0.34 51.04953 0.1774 0.04659 0.02227 0.708 0.2947 0.6010 2.5510 1.06279 0.29 6.3204 0.658 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services .07 6.923 4.692 0.4271 1.31 15.05230 0.707 0.4709 0.338 1.3716 0.03707 0.0053 1.770 0.03365 0.0 543.0392 1.4128 1.6779 1.91 82.020 7.286 2.699 0.609 3.680 0.705 0.7684 1.63 5.02624 0.4149 0. # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg.† The values of µ.023 4.683 0.441 0.718 0.5879 0. (U.689 0.1 182.7048 0.707 0.684 0.811 5.696 0.160 1.93 7.124 0. 1955.1 338.0140 1.06752 0.730 † From Natl.0295 1.0 399.50 6.0099 1.075 2.90 44.6 432.2 117.197 1.013735 0.5030 0.69 4.739 0.2211 0.5990 1.177 3.6 159. No.57 1.0891 0.179 1.702 0.) Circ.03003 0.1321 1.90 31.0061 1.06525 0.704 0.2707 0.0266 1.1762 0.700 0.8826 0.260 5.0207 1.6532 0.76 25. 564.34 58.2983 0. k.3 108.0774 1.686 0.K 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 ρ kg/m3 cp kJ/kg · ◦ C µ × 105 kg/m· s ν × 106 m2 /s k W/m · ◦ C α × 104 m2 /s Pr 3.05509 0.06028 0.4222 0.0946 0.309 1.680 0.71 37.490 11.8578 0.753 0.969 2.2082 0.1095 1.481 3. Bur. cp .1970 0.35 7.0837 0.152 4.419 1.5 308.120 6.72 6.484 2.14 7.704 0.1417 1.0 504.1212 1.379 4.3289 1.15675 0.85 6.25 73.05745 0.6924 1.688 0.697 0.267 1.1394 1.705 0.149 0.1 254.Hol29362_appA 658 11/7/2008 14:57 A P P E N D I X A Tables Table A-5 Properties of air at atmospheric pressure.51 66.0752 1.5564 0.689 0.977 4.117 0.04360 0.S.262 3.5 369.1458 0.0635 1.682 0.5430 0.343 7.009246 0.10165 0.8462 2.9672 1.0732 0.44 4.680 0.29 90.704 0.5 280.40 5.01809 0.6423 0.2355 0.05779 0.6 464.899 4.161 0.722 0.2515 0.0978 1.287 1.848 3.702 0.3925 0. 250 4.67 32.179 4.179 4.8 994.616 Pr 13.2 928.36 1.644 0.271 4.6 997.68 0.630 0.678 0.174 4.44 2.174 4.71 4.6 gβρ 2 cp µk x 3 T cp ρ µ k kJ/kg · ◦ C kg/m3 kg/m · s W/m · ◦ C 4.685 0.90 1.6 126.2 955.78 93.216 4.47 3.33 2.1 946.88 6.665 0.51 1.91 × 1010 2.7 983. 1958.7 204.8×10−4 8.6 988.649 0.575 0. No.585 4.53 4.34 × 109 1.66 1.5 678.62 5.79×10−3 1.204 4.2 966.179 4.7 315.04 3.8 999.89 54.33 104.659 0.07 9.179 4.675 0.30 3.64 3.35 9.84 × 1010 9.06 2.67 82.72 3.731 5.8 999.186 4.13 4.22 87.208 4. New York: McGraw-Hill.8 148.2 735.01 2.40 7.19 × 1010 4.0 990.654 0.20 1.22 37.4 115.17 1.44 10 15.024 5. M.11 76.199 4.83 gβρ 2 cp µk 1/m3 · ◦ C 1.19 1.78 5.684 0.614 0.08 × 1010 1.0 890.85 × 1010 1.48 × 1010 7.66 × 1010 6.8 985.† Note: Grx Pr = ◦F ◦C 32 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 220 240 260 280 300 350 400 450 500 550 600 0 4.12 4.12 9.02 1.665 0.4 995. # 101675 Cust: McGraw-Hill Au: Holman Server: Title: Heat Transfer 10/e Pg.36 1.191 4.595 0.9 176.7 1.9 993.01 3. Introduction to Heat Transfer.7 970.25 11.174 4.662 K/PMS 293 Short / Normal / Long DESIGN SERVICES OF S4CARLISLE Publishing Services .371 4.09 × 1011 †Adapted to SI units from A. 3rd ed.46 × 1010 1.65 6.11 26.55 1.623 0.24 1.3 × 1010 4.4 825.86 1. Brown and S.604 0.4 859.33 48.56 21.668 0.195 4.55 71.57 1.53 2.6 7.4 232.16 5.195 4. Marco.98 1.67 2.7 963.673 0.00 0.467 4.78 43.16 2.85 0.646 0.566 0.44 60 65.03 1.637 0.7 937.89 × 1010 5.685 0.3 973.296 4.703 999.183 4.27 3.48 × 1010 3.677 0.51×10−5 8.82 6.62 × 1010 8.3 977.3 980.2 260 287.Hol29362_appA 662 11/7/2008 14:57 A P P E N D I X A Tables Table A-9 Properties of water (saturated liquid).684 0.585 0.2 998.7 137.1 918.225 4.31 1.73 2.174 4.186 4.91 × 109 6.3 4.7 785.229 4.85 5. I.685 0.