Heat Transfer HW8a

6. Award: 2.43 out of 2.56 points You did not receive full credit for this question in a previous attempt 7. Award: 2.43 out of 2.56 points You received credit for this question in a previous attempt 8. Award: 2.43 out of 2.56 points You did not receive full credit for this question in a previous attempt How is hydraulic diameter defined in non-circular tubes? D h = 4 A c / p Hint #1 References Numeric Response Difficulty: Easy Previous attempt How is hydraulic diameter defined in non-circular tubes? D h = 4 A c / p Explanation: For flow-through non-circular tubes, the Reynolds number, as well as the Nusselt number and the friction factor, are based on the hydraulic diameter D h defined as D h = 4 A c / p , where A c is the cross-sectional area of the tube and p is its perimeter. Identify the fluid property responsible for the development of the velocity boundary layer and the kinds of fluids. References Section Break Difficulty: Easy What fluid property is responsible for the development of the velocity boundary layer? Viscosity of a fluid Mass density of a fluid Specific weight of a fluid Volume of a fluid The fluid viscosity is responsible for the development of the velocity boundary layer. Hint #1 References Multiple Choice Difficulty: Easy Previous attempt For the idealized inviscid fluids, there is no velocity boundary layer . True False The fluid viscosity is responsible for the development of the velocity boundary layer. For the idealized inviscid fluids(fluids with zero viscosity), there will be no velocity boundary layer. Hint #1 References True / False Difficulty: Easy Previous attempt ✓     ✓   Hints Hints Hints

14. Award: 2.43 out of 2.56 points L h = 0.05Re D L t = 0.05RePr D L t ≈ 10 D L h ≈ 10 D You received credit for this question in a previous attempt 15. Award: 2.43 out of 2.56 points You received credit for this question in a previous attempt Match the turbulent and laminar flows (in the left column) to their hydrodynamic and thermal entry lenghts (in the right column). 1. Thermal entry length of laminar flow 2. Hydrodynamic length of turbulent flow 3. Hydrodynamic entry length of laminar flow 4. Thermal entry length of turbulent flow The hydrodynamic and thermal entry lengths are given as L h = 0.05Re D and L t = 0.05RePr D for laminar flow, and L h ≈ L t ≈ 10 D in turbulent flow. Noting that Pr >> 1 for oils, the thermal entry length is larger than the hydrodynamic entry length in laminar flow. In turbulent, the hydrodynamic and thermal entry lengths are independent of Re or Pr numbers, and are comparable in magnitude. Hint #1 References Matching Difficulty: Easy Previous attempt Which of the following statements are true for laminar and turbulent flows? (Check all that apply.) Pr >> 1 for oils, the thermal entry length is larger than the hydrodynamic entry length in laminar flow. Pr << 1 for oils, the hydrodynamic entry length is larger than the thermal entry length in laminar flow. Pr << 1 for liquid metals, the thermal entry length is smaller than the hydrodynamic entry length in laminar flow. Pr << 1 for liquid metals, the hydrodynamic entry length is smaller than the thermal entry length in laminar flow. In turbulent, the hydrodynamic and thermal entry lengths are independent of Re or Pr numbers, and are comparable in magnitude. In turbulent, the hydrodynamic and thermal entry lengths are dependent of Re or Pr numbers, and are not comparable in magnitude. Pr >> 1 for oils, the thermal entry length is larger than the hydrodynamic entry length in laminar flow. Pr << 1 for liquid metals, the thermal entry length is smaller than the hydrodynamic entry length in laminar flow. In turbulent, the hydrodynamic and thermal entry lengths are independent of Re or Pr numbers and are comparable in magnitude. Hint #1 References Check All That Apply Difficulty: Easy Previous attempt  Correct: 3 ✓ 3  Correct: 1 ✓ 1  Correct: 4 ✓ 4  Correct: 2 ✓ 2 ✓  ✓  ✓  ✓  ✓  ✓  Hints Hints

Air enters an 18-cm-diameter, 12-m-long underwater duct at 50°C and 1 atm at a mean velocity of 7 m/s and is cooled by the water outside. If the average heat transfer coefficient is 65 W/ m 2 · K and the tube temperature is nearly equal to the water temperature of 7°C, determine the exit temperature of air and the rate of heat transfer. The properties of air at a bulk mean temperature of 30°C are ρ = 1.164 kg/m 3 and c p = 1007 J/kg·°C. Is this a good assumption? The exit temperature of air is 12.18 °C. The rate of heat transfer is 7.88 kW. 30°C is an appropriate temperature to evaluate the fluid properties. Hint #1 References Multi-Answer Difficulty: Medium Previous attempt Air enters an 18-cm-diameter, 12-m-long underwater duct at 50°C and 1 atm at a mean velocity of 7 m/s and is cooled by the water outside. If the average heat transfer coefficient is 65 W/ m 2 · K and the tube temperature is nearly equal to the water temperature of 7°C, determine the exit temperature of air and the rate of heat transfer. The properties of air at a bulk mean temperature of 30°C are ρ = 1.164 kg/m 3 and c p = 1007 J/kg·°C. Is this a good assumption? The exit temperature of air is 12.1976 ± 2% °C. The rate of heat transfer is 7.8913 ± 2% kW. 30°C is an appropriate temperature to evaluate the fluid properties. Explanation: The following assumptions have been made here: 1. Steady operating conditions exist. 2. The surface temperature of the duct is constant. 3. The thermal resistance of the duct is negligible. The mass flow rate of water is ˙ m = ρA c V avg = ρ π D 2 4 V avg ˙ m = 1.164 kg/m 3 π 0.18 m) 2 4 (7 m/s) ˙ m = 0.2073 kg/s A s = π DL = π 0.18 m) 12 m A s = 6.786 m 2 The exit temperature of air is determined from T e = T s − T s − T i e − hA s ˙ mc p T e = 7 − 7 − 50 e − (65 ) (6.786) (0.2073) (1007 ) T e = 12.1976°C The logarithmic mean temperature difference and the rate of heat transfer are ΔT lm = T e − T i ln T s − T e T s − T i ΔT lm = 12.1976 −50 ln 7 −12.1976 7−50 ΔT lm = 17.8904°C ˙ Q = hA s ΔT lm ˙ Q = 65 W/m 2 ·°C 6.786 m 2 (17.8904°C) ˙ Q = 7.8913 kW The bulk mean temperature here is ( 12.1976 +50 ) °C 2 = 31.1°C. This is close to 30ºC. Hence, the assumption made here is correct. ( ) ( ) ( ( ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) Hints