1. By Jayde Kowallis and Jordan Rhoads

2. Introduction A copper pipe wrapped with heated tape is needed to direct blow-by gasses from the engine crank case to a centrifuge pump. Our Tube Objective: To find the length needed (L) to heat gas from 25°C to 130°C and from 190°F to 230°F.

3. Problem Setup: assumptions Assumptions: Heat tape creates a constant heat flux (q s ”) Tube is perfectly insulated with a fiberglass coating. (no heat is lost)

4. Problem Setup Conservation of energy (with perfect insulation) Using and you get Solving for L:

5. Solution and Procedure Known Values Properties of Air at 372.03 K ρ = 0.94827 kg/m 3 c p = 1.0112 x 10 3 J/kg*K Other known values q s ” = 2055 W/m 2 mdot varies from 0.0009 to 0.005 kg/s Inside Diameter = 1 in Case 1: T o,air = 25°C, T f,air =130°C Case 2: T o,air = 190°F, T f,air = 230°F Use the following equation to find the length of pipe for each mass flow rate using the temperatures in Case 1 and in Case 2.

6. Results Case 1: (T o,air = 25°C, T f,air = 130°C) For mdot = 0.0009 kg/s: L = 0.545m For mdot = 0.005 kg/s: L = 3.079m Case 2: (T o,air = 190°F, T f,air = 230°F) For mdot = 0.0009 kg/s: L = 0.115m For mdot = 0.005 kg/s: L = 0.545m

7. Conclusion and Recommendations Using this analysis and given assumptions, heating a fluid, flowing at these velocities, using a typical heat tape is a plausible solution for this application. For the majority of constant flow conditions, a recommended length of minimum 0.545 m is needed to eliminate condensation.

8. Appendix Sources: Dr. Soloviev’s assistance in setting up the problem Fundamentals of Heat and Mass Transfer (7 th edition)