Lumped Thermal Model for ThermocoupleWe wish to estimate the dynamics of a cold thermocouple probe suddenlyplaced in a hot flowing fluid stream for the purpose of temperaturemeasurement. The probe consists of two dissimilar metal wires joined bysoldering at the tip, and the wires are then encased in a metal sheath andthe 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 specificheat Cp. Denote the transfer coefficient as h.(a) If the effects of thermal conductivity can be ignored, show that thetemperature response of the probe is described byMCp dT/dt = hA (Tf-T)where A denotes the exposed area of probe tip, and T(t) is itstemperature.
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