Question

In a planned experiment, a thermocouple is to be exposed to a step change in temperature. The response characteristics of the thermocouple must be such that the thermocouple's output reaches 98% of the final temperature within 5 s. Assume that the thermocouple's bead (its sensing element) is spherical with a density equal to 8000 kg/m3, a specific heat at constant volume equal to 380 J/(kg.K), and a convective heat transfer coefficient equal to 210 W/(m2.K). Determine the maximum diameter [] that the thermocouple can have and still meet the desired response characteristics. The unit is millimeter.

Answer 1

max Diameter = 0.530 mm

Step-by-step explanation:

Calculate the maximum Diameter that the thermocouple should have

applying this formula : e =
`(SvCv)/(hA)` ------ ( 1 )

mass = density * volume

Time constant = mc / hA

attached below is the detailed solution

r ( diameter ) = 0.530 mm