Estimate the equilibrium temperature rise and estimate the

Question

Problem 1:

Figure shows the results of a laboratory experiment. A current of 90A was applied to an Copper cylindrical conductor for more than a half hour. The points represent the temperature rise measurements; the continuous line represents a mathematical approximation found by the students who did the test using the first order model described in class. The ambient temperature was approximately kept at an average of 25 C.

a. Estimate the equilibrium temperature rise.

b. Estimate the time constant

c. Write an expression for the estimated curve (theta as a function of time) using the numerical results obtained in parts a and b.

d. The wire diameter is 4.5 mm, approximately. Estimate a value for the equivalent convection factor, h in W/(m².K).

e. Your task is to predict the theta vs t curve using the same and laboratory set-up but with a current of 120 amps. Write an equation like the one you wrote in Part c for the new conductor assuming that h has the same value determined in Part d. Plot the estimate theta as a function of time.

Note: You do NOT have to use MATLAB to do Part e. You can do it with your calculator and plot the curve on a linear-scaled plot paper, or EXCEL, or any other method you have.

Figure 1: Results of a wire heating experiment (notice the temperature reaches burning levels)

Problem 2:

a) A metallic wire of certain secret new alloy has a resistivity ρ = 1.2 -10^-8 ohm-m and a coefficient alpha α= 0.003 1/K both given at 20°C. The density and specific heat of the metal are unknown. The wire has circular section with a diameter of 4 mm and is used to build a cable with a rated temperature of 65°C and a damage temperature of 150°C. The damage l²t = K_d was found experimentally using no initial current and an ambient temperature of 25°C. The result was:

K_d = 3.5.10⁶ amp².s

Find Kd using the rated temperature as initial value.

b) Find K_d for a wire with the same characteristics as the wire in a) but with a diameter of 2 mm (use the same rated temperature and the initial temperature value)

c) Plot the three damage curves using a log-log scale, indicating which curve corresponds to each case.

Problem 3:

a. Determine the HV-side fuses needed to protect a transformer bank with a total three-phase capacity of 475kVA, 13800/208 in connection Y_Ny_nO. Show and explain step by step the procedure you employ to solve this question. Choose between the type K and type T fuse curves given in class. Assume the transformer has a damage curve as the one given in class.

b. Plot both, the fuse curves and the transformer damage curve on the same log-log graphic. Use the log-log curve posted in the class web page. You do NOT need to use MATLAB to do this problem. You can do it with your calculator and plotting the curve with pencil on the given log-log sheet. The current must be referred to HV side of the transformer bank.