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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