Question

After fermentation, a mixture of ethanol and water is sent to a small distillation column. At the top of the distillation column, a 95% ethanol solution at 65°C is produced at a flow rate of 3.5 kg/s. Your job is to design a double-pipe heat exchanger that will cool the 95% ethanol mixture to 40°C by using cooling water that is available at 10°C. Assume an outlet temperature of the cooling water of 55°C, and only use Schedule 40 pipe from the table below. Do not do viscosity corrections for heat transfer coefficients and the 95% ethanol solution will be pumped to the inside pipe. Assume that the heat capacity for the ethanol mixture is 2.55 kJ/kg.K and the heat capacity of the coolant is 4.18 kJ/kg.K. The density of the 95% ethanol solution is 0.804 g/mL Assume that the velocity of ethanol solution as 1 m/s as the initial guess. Check the accuracy of this calculation once you select the size of the pipe (the area should agree with the area required to achieve the desired heat transfer). The viscosity of the solution is given as 9.72 × 10–4 kg/(m · s) and the thermal conductivity is 0.175 W/(m · K).

1. Draw a schematic for the given system and define all the given information. List all assumptions. (5 points)
2. Find heat transfer required for the hot fluid. With this heat transfer required calculate the mass flow rate of coolant needed to achieve the desired outcome. (10 points)
3. Estimate the area of the pipe by assuming a velocity of 1 m/s and using the mass flowrate of ethanol solution. Find an estimated diameter. (5 points)
4. Use estimated values to find a pipe that meets the criteria using the table (schedule 40 is a requirement). (5 points)
5. With the chosen pipe, recalculate velocity for the inner pipe. (5 points)
6. Select a Schedule 40 pipe as the outer pipe and estimate the area of the annulus section and estimate the velocity of the coolant. (10 points)
7. Using the velocities find the Re number for each fluid and the corresponding convection coefficients. (10 points)
8. To finalize the design, we need the length of the pipes and number of bends. Limiting the length of the pipe to 6 m, calculate the surface areas for each of the pipes. With this areas and the corresponding convection coefficients, find the overall heat transfer coefficient, U. (10 points)
9. Determine the LMTD for your system. Use the relationship q=UA∆T_LMTD to find the necessary heat transfer area. Based on this, estimate the number of bends needed using the ratio of heat transfer area and surface area of the selected pipe for your design. (10 points)
10. What factors will be needed to provide a better design? (5 points)

Answer 1

Assumptions:

1. The fluid specific heats do not vary with temperature.

2. The overall heat transfer coeff is constant throughout the heat exchanger

3. Heat exchange with ambient air is negligible

4. The flow is steady

5. The fouling factors are neglected.

        

You can also use the estimated dia of outer pipe = 5 inches.

The convective heat transfer coefficients for both the fluids can be calculated. After calculating the h's, the values of U, heat transfer area (A) and number of bends can be calculated.