Heat Transfer

A counter-flow heat exchanger with inlet fluid temperature at 120°C and leaves at temperature 310°C. Hot side inlet temperature is 500°C, outlet temperature is 400°C, find the LMTD.

Two finned surfaces with very long fins are identical, EXCEPT that the convection heat transfer coefficient for the first finned surface is TWICE that of the second one. What statement below is accurate for the efficiency and effectiveness of the first finned surface relative to the second one?

A 1.6-cm-diameter, very long cylindrical fin made of aluminum (k-156 W/m.K) is attached to a surface at 117°C. The surface is exposed to ambient air at 22 °C with a heat transfer coefficient of 19 W/m².K. Determine the rate of heat transfer from the fin in (W)

AL=2.6-cm-long, W-2.4-mm width, and t-1.0-mm thickness rectangular fin is manufactured from metal of K-401 W/m.K and is attached to a surface. The fin efficiency is 64%. Determine the effectiveness of this single fin. Use, respectively, the following equations for surface and cross-sectional areas:

An infinite circular fin of diameter D is attached to wall with surface temperature of 393°C. The thermal conductivity of the fin is 424 W/m K The fin is exposed to an ambient air condition of 20°C and 205 W/m2K. The rate of heat transfer loss from the fin is 277 W Find the diameter of the fin, in Cm.

3. (15 pts) You are going to boil an egg in water for breakfast. The egg can be approximated as a sphere with a diameter of 4 cm. Initially, the egg was at room temperature of 20 °C. What is the corresponding Fourier number F. (dimensionless time), if the egg temperature everywhere needs to be at least 65 °C? Indicate how you obtain the F. in the figure.

4. (1 pt) Heating of a Product in Parallel Flow or Counterflow Heat Exchanger: NTU Method Consider a concentric-tube heat exchanger that is 3 m in length. The inside diameter of the inner tube is 0.01 m and the inside diameter of the outer tube is 0.02 m. The wall thickness of the inner tube can be neglected. A fluid enters the inner tube at 10 °C and flows at an average velocity of 0.3 m/s. Water enters the annular region between the tubes at 50 °C and flows at an average velocity of 0.1 m/s. The overall heat- transfer coefficient is 350 W/m²-K. Properties of the fluid: p = 1300 kg/m³, c = 2500 J/kgK. Properties of water: p = 1000 kg/m³, c = 4200 J/kgK. Using the NTU method, determine the temperature of the fluid exiting the tube if: A. It is a counterflow heat exchanger. B. It is a parallel-flow heat exchanger. C. Which type of heat exchanger provides a higher heat-transfer rate and by what %?

Question 5 In a polymeric pipe (50 W/m/K of thermal conductivity) 13 m long, the temperature measured at the outermost radius is 11°C. The temperature at the innermost pipe surface is 57°C and the heat flux at outermost surface is one quarter of the heat flux at innermost surface of the pipe. Evaluate the whole heat transfer (absolute value) through the pipe thickness to the nearest kW. Note: use pi=3.1415

C. Which type of heat exchanger provides a higher heat-transfer rate and by what %? 5. (6 pts) Numerical Solution for a Counter-flow Heat Exchanger (by Daisy Fuchs) A countercurrent, shell-and-tube heat exchanger with an effectiveness of 54.3% uses a coolant fluid to cool hot oil. You know that there is one shell pass and four tube passes. Unfortunately, some of the temperature probes and flow meters have broken. The outlet temperature of the oil, flowing at 15 kg/s, is 60 °C, although the inlet temperature is unknown. The coolant enters the shell side of the heat exchanger at 15 °C and exits the heat exchanger at 45 °C. Although the exact flow rate of coolant is unknown, you do know that it is 1 greater than 9 kg/s. The specific heat of the oil is 2.2 kJ/m²-K and the specific heat of the coolant is 4.2 kJ/m²K. The overall heat-transfer coefficient (based on the outside surface area of the tubes) is 1200 W/m²-K and the outside heat-transfer area of the tubes with the correction factored applied is 26.3 m². A. What are two different methods that you can use to solve for parameters in a shell-and-tube heat exchanger? When would you use one method over the other? B. What is the temperature of the hot oil at the inlet of the heat exchanger? Solve the non-linear equation for this temperature using both the secant method in Excel and a built-in solver in Excel. Include a PDF of your spreadsheet. Your spreadsheet should be easy to follow, have all variables labeled (including units), and your name should be on the spreadsheet. Hint: You may need to combine the two methods from Part A to generate an equation for the unknown entrance temperature of the oil. C. What is the exact mass flow rate of the coolant? D. What is the correction factor for this system? What is the outside surface area of the tubes? E. What is the number of transfer units of this heat exchanger? F. If the heat exchange was co-current and had the same number of transfer units, what would the effectiveness be?

Question # 3 a) Discuss main challenges and limitations in the design and operation of heat exchangers. b) How the performance of heat exchanger can be enhanced.