A thermocouple is made up of a spherical bead bimetallic junction at the end of two very thin wires of different materials. For example, in a type-T thermocouple, a copper wire and a constantan wire, with wire diameters ranging from 0.5 mm to 0.025 mm, are fused together to make a spherical bead that is also of a similar order-of-magnitude diameter. For such a thermocouple, determine the appropriate diameter of the spherical bead junction so as to ensure a response time of less than 2 s (?t ? 2 s) in water, which is at 40°C and has a convective heat transfer coefficient of 80 h = W/m2 K. Consider the bead junction to have properties of Cu, and to be initially at 150°C. Also, for the calculated bead diameter, what would be the response time in air at 40°C and 10 h = W/m2 K?
GIVEN
• Copper and constanton wire with diameter range from 0.5 mm to 0.025 mm fused together
• Response time ?t ? 2 s
• Water bath temperature (T?) = 40°C
• Convective heat transfer coefficient ( ch ) = 80 W/(m2 K)
• Initial temperature of bead junction (T0)=1500
FIND
• Appropriate diameter of spherical bead junction to ensure response time of less than 2 seconds.
• Response time in air at 40°C and 10 h = W/m2 K for calculated bead diameter.
ASSUMPTIONS
• Constant thermal conductivity
• End effects are negligible
PROPERTIES AND CONSTANTS
we get for Copper ks =391 W/m K c = 383 J/kg K ?=8930 kg/m3
The surface area and volume of the junction beads are
The surface area and volume of the junction beads are
As Bi is <<< 0.1, internal resistance can be neglected and system can be considered as lumped capacitance.
Considering 2 s as time constant we get
You might also like to view...
A light ray goes through two thick rectangular slabs of glass, each of the same uniform thickness. The first slab has index of refraction n1 and the second n2 . If n1< n2. How does the original angle of incidence 
into the first slab compare to the final angle of refraction where the ray leaves the second slab going back into air?
A. 
B. 
C. 
D. 
E. more information is needed
If you want to stop a car without anti-lock brakes as quickly as possible on an icy road, you should
A. Jam on the brakes as hard as you can. B. Push on the brakes as hard as you can without locking the car’s wheels and thus making the car skid. C. Pump the brakes. D. Do something else (specify).
Compare two diverging lenses similar except that lens B is rated at 20 Diopters, whereas lens A is rated at 10 Diopters. The focal length of lens B is
A) twice the focal length of lens A. B) one-fourth of the focal length of lens A. C) one-half of the focal length of lens A. D) 1/ of the focal length of lens A. E) four times the focal length of lens A.
Copper atoms have a greater tendency to be reduced than iron atoms do. Was this good news or bad news for the Statue of Liberty, whose copper exterior was originally held together by steel rivets?
A) This was good news since the steel rivets prevented the copper from eroding. B) Electrons will preferentially flow from the iron to the copper and then onto oxygen. Corrosion is thus accelerated around the interface of these two metals. C) This combination of metals have no effect on each other and that is why engineers chose to use them together. D) This combination of metals caused the copper to oxidize and turn green.