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
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