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  3. 4 hot wire method one popular method to measure the...

Question: 4 hot wire method one popular method to measure the...

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4. Hot Wire Method. One popular method to measure the heat transfer coefficient h for natural convection of a fluid is the so-called hot wire method. To conduct the measurement, a long and thin metal wire is immersed in a fluid bath. The diameter of the wire is 1 mm. The bulk fluid temperature is To - 20 °C. Initially the metal wire is at the same temperature as the bulk fluid. For the measurement, an electrical current is passed through the metal wire to heat it up through joule heating, with a heat generation rate of 10-2 W/mm3 inside the metal wire. The temperature rise of the metal wire can be calculated by measuring the change of its electrical resistance (typically platinum is used because its electrical resistance changes linearly with temperature within a large temperature range). The thermal conductivity of the metal wire is 71 W/m-K. The density and the specific heat of the metal wire are 2.1 x 104 kg/m3 and 126 J/kg-K, respectively. (a) First assume the temperature of the wire is uniform. If the measured steady-state temperature rise of the metal wire is 5 °C, what is the heat transfer coefficient h between the wire surface and the fluid? (b) How can we make sure the assumption made in part (a) (uniform temperature of the wire) is reasonable? (c) In analogy to the lumped capacitance model discussed in class, write down a differential equation that describes the temperature rise of the metal wire as a function of time. Solve for the time evolution of the wire temperature. (Recall the solution of a 1st-order inhomogeneous ODE)

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