PROBLEM BACKGROUND The most common heat exchanger used in industry is a 'shell-and-tube' heat exchanger as illustrated in the figure. One fluid is fed into a set of tubes around which a second fluid is circulated. In the example shown, complex flow patterns illustrated by arrows show the flow may be partially parallel flow and partially crossflow. PROBLEM STATEMENT For this problem, we will consider a single tube in a crossflow configuration as shown. Air is to be heated to the desired temperature to feed a bioreactor. The air is feed flows normal to the outside of the center tube. Saturated steam is flows through the inside of the tube to provide the heat. The air is being fed at an average velocity of 15 m/s though the outer pipe of the heat exchanger at 27 °C and 1 atm. It heated by using saturated steam which condenses at 107°C over the surface of the inner tube. The tube is 5 m long with an outer diameter of 0.015 m and an inner diameter of 0.014 m. For simplicity in answering this problem, assume the bulk air temperature does NOT rise significantly above 27 °C in a single pass through the heat exchanger. a) Determine the convective heat transfer coefficient for the air flowing normal to the inner tube accurate to two significant figures. Tube Shell Outlet Inlet Baffles Shell Outlet Tube Crossflow b) Determine the overall heat transfer coefficient from the steam-side to the air-side of the inner tube, noting that the heat transfer coefficient of condensing water vapor is 5000 W/m²-K over the surface of the tube. Neglect radiation. The inner tube is copper and so thin and conductive that it has a negligible heat transfer resistance and the inner and outer surface areas are effectively equal: Ao-Ai. c) Determine the overall heat transfer coefficient if the radiation heat transfer coefficient is 5.2 W/m-K. d) Extra credit (2 pts):-Determine the radiation heat transfer coefficient from the surface of the tube (unpolished copper) to the air. Physical Properties of copper p = 1250 kg/m³ k = 0.285 W/m-K Copper emissivity (unpolished) = 0.57 Stefan-Boltzmann constant: 5.676x10-8 W/m²-K4 Note: Values are all at 1 atm. In the headings, x 10+ means that the values have been reduced by a factor of 10 x10m is listed in the table of values, this means that the values should be multiplied by 10". For example, C, of air at 300 °C is 1.0063 x 10°, and the value of the lumped parameters in the rightmost column for air is 1.327 x 10". T (K) (kg/m³) 5px 10-3 (J/kg xK) *x 10³ (Pax s) vx 105 (m²/s) kx 10² (W/m x K) ax 10³ (m²/s) Pr (1/K m³) Air 250 1.4133 1.0054 1.5991 1.1315 2.2269 1.5672 0.722 4.638 x 10 260 1.3587 1.0054 1.6503 1.2146 2.3080 1.6896 0.719 2.573 280 1.2614 1.0057 1.7503 1.3876 2.4671 1.9448 0.713 1.815 300 1.1769 1.0063 1.8464 1.5689 2.6240 2.2156 0.708 1.327 320 1.1032 1.0073 1.9391 1.7577 2.7785 2.5003 0.703 0.9942 340 1.0382 1.0085 2.0300 1.9553 2.9282 2.7967 0.699 0.7502 360 0.9805 1.0100 2.1175 2.1596 3.0779 3.1080 0.695 0.5828 400 0.8822 1.0142 2.2857 2.5909 3.3651 3.7610 0.689 0.3656