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

A hydraulic fluid preheater consists of a single tube with a diameter of D = 0.5 in and a length of L= 5 m. The tube surface is maintained at Ts = 200°F by hot combustion gases flowing past the outside surface. The hydraulic fluid enters at To = 80°F and a mass flow rate of 370 lbm/h. (a) Determine the convection heat transfer coefficient for the hydraulic fluid flowing through the tube. (b) Determine the hydraulic fluid exit temperature. (c) Determine the heat transfer rate to the hydraulic fluid. (d) Determine the power required to pump the hydraulic fluid through the tube.

Consider a 10 m length of 2 cm-I.D tube. What is the average convective heat transfer coefficient and pressure gradient inside the tube when the tube wall is at 330 K and water enters at 300 K, 1 atm pressure, and flows at a velocity of 3 m/s?

Air at 300 K flows across one side of a flat plate at a velocity of 15 m/s. The plate measures 2.0 m in the direction of flow and 1.0 m wide. If the surface temperature is 400 K, find the convective heat transfer. How much of the plate experiences laminar flow?

1) Consider the infinitely tall, annular mixing tank. The fluid to be mixed is Fluid between the inner cylinder and the outer wall. The fluid is mixed by a Fluid spinning the inner cylinder at an angular velocity of n (s-1). The tank has an inner radius of R (m) and the R. inner cylinder has a diameter of k (m). Fluid There is no net flow in the vertical or radial directions. Top view Answer the following questions about Side view this sytem:

2. Adjacent Flow of Two Immiscible Power Law Fluids Two immiscible fluids are contained in the space between two infinite parallel plates. The upper plate, at y = h, is in motion with a velocity U. Initially there is no pressure gradient in the x-direction. We have already solved for the velocity profile between the two plates for a number of different conditions, now we are going to make fluid II non-Newtonian. U Fluid II Interface Between Two Immiscible Fluids ah Fluid I d) Go back to your old assignment (b), but now let's let Fluid II be non-Newtonian. Specifically, model the fluid as a power law fluid with n =ky". Solve for the velocity profile across the channel and sketch the result for a shear thinning and shear thickening fluid as the velocity on the top plate is systematically increased. e) Now remove the velocity of the top plate and instead apply a pressure gradient. What is the velocity profile look like now?

According to nature of flow, convective heat transfer is classified into natural convection and forced convection. By taking specific examples, explain how the natural convection and forced convection arises in them.