mechanical engendering

ME 495 – Homework 9

Summer 2019

Submission Deadline: 19th July (Friday) midnight

Note: Write your name at the top right-hand corner of the first page of your homework.

Problem 1: A thermocouple is initially at room temperature of 20 0

C. The temperature-time

response of the thermocouple is observed by immersing the thermocouple in a hot liquid at 65 0

C.

What is the time constant of the thermocouple based on the temperature-time response given

below? What is the error fraction at 40s? Explain your work clearly.

Problem 2: A thermocouple bead in the shape of a sphere. The bead has a diameter of 0.2 mm

and is made of a material of density 8.9 × 103 kg/m³ and specific heat capacity (Cp) of 390

J/(kg·K). The heat transfer (h) between the bead and the fluid is 100 W/m2K. Show using excel

or matlab how the output would look like for an input temperatures of (a) 220 sin(0.5t); and (b)

220 sin(4t).

Problem 3: A thermocouple is used to measure a temperature of 220 sin(t). How would the

output look like if the time constant of the thermocouple 0.1s, 1s and 2s? Use excel or matlab.

Problem 4: A second order system behaves as follows:

1 y + a y + y = 100

Plot using excel or matlab how the input and the output will look like for a1 = 0.5; a1 = 2 and a1 =

3.

Problem 5: A second order system behaves as follows:

1 y + a y + y = 100 sin(t)

Plot using excel or matlab how the input and the output will look like for a1 = 0.5; a1 = 2 and a1 =

3.