Discuss the below:
Q: The density and specific heat of a particular material are known (p = 1200 kg/m3 · c p = 1250 J/kg · K), but its thermal conductivity is unknown. To determine the thermal conductivity, a long cylindrical specimen of diameter D = 40 mm is machined, and a thermo couple is inserted through a small hole drilled along the centerline.
The thermal conductivity is determined by performing an experiment in which the specimen is heated to a uniform temperature of Tj = 100°C and then cooled by passing air at T8 = 25°C in cross flow over the cylinder. For the prescribed air velocity, the convection coefficient is h = 55 W/m 2 · K.
(a) If a centerline temperature of T (0, t) = 40°C is recorded after t = 1136 s of cooling, verify that the material has a thermal conductivity of k = 0.30 W/m · K.
(b) For air in cross-flow over the cylinder, the prescribed value of h = 55 W/m2 · K corresponds to a velocity of V = 6.8 m/s. If h = CV0.618, where the constant C has units of W · s 0.618/m2.618 · K, how does the centerline temperature at t = 1136 s vary with velocity for 3 < v="">< 20="" m/s?="" determine="" the="" centerline="" temperature="" histories="" for="" 0="">< t="">< 1500="" s="" and="" velocities="" of="" 3,="" 10,="" and="" 20="">
