Answer Happy

3 Lumped Convection a A nickel cylinder is exposed to a flow of air at Too = 400 °C. The cylinder is initially at T; = 20 °C. The cylinder has a diameter of d = 15 mm, a length of L = 15 cm, a thermal conductivity of kni. = 80 W m-1 k-1, a density of Pni. = 8900 kg m-', and a specific heat of cni. = 444 J kg-4k-1, The Nusselt number for flow over a cylinder is given by the Hilpert Correlation: Nud = C Rey Pr1/3 where: Red С m 0.4 - 4 0.989 0.333 4 – 40 0.911 0.385 40 - 4000 0.683 0.466 4000 - 40000 0.193 0.618 40000 - 400000 0.027 0.805 The viscosity of air is Vair = 0.000 035 m2 s-1, the thermal conductivity is kair = 0.024 W m-1k-1 and the Prandtl number is Prair = 0.7. The characteristic length of a sphere is Lc = d/6. If the air flows at 5 ms-1, determine: - whether lumped capacitance is reasonable. Yes, the lumped capacitance is reasonable assuming lumped capacitance is reasonable, the time for the cylinder to reach 3000