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Lumped Thermal Model for Thermocouple We wish to estimate the dynamics of a cold thermocouple probe suddenly placed in a hot flowing fluid stream for...

Lumped Thermal Model for Thermocouple
We wish to estimate the dynamics of a cold thermocouple probe suddenly
placed in a hot flowing fluid stream for the purpose of temperature
measurement. The probe consists of two dissimilar metal wires joined by
soldering at the tip, and the wires are then encased in a metal sheath and
the tip is finally coated with a bead of plastic to protect it from corrosion.
Take the mass of the soldered tip plus plastic bead to be m, with specific
heat Cp. Denote the transfer coefficient as h.
(a) If the effects of thermal conductivity can be ignored, show that the
temperature response of the probe is described by

MCp dT/dt = hA (Tf-T)

where A denotes the exposed area of probe tip, and T(t) is its
temperature.
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