5. Liquid lithium flows at 5 m/s in a 1 cm-I. D. tube. Calculate the Nusselt number and heat transfer coefficient. Evaluate the properties at 800 K. (liquid metal has very low Pr number. Review 4.3.1 for instructions). a. If the wall temperature is uniform b. If the wall heat flux is uniform

a) Nusselt number=17.97

b) heat transfer coefficient=58870 W/m^2

Explanation:

For liquid lithium at 800 K, density ρ = 482 kg/m3, thermal conductivity k = 48.75 W/m-K, Kinematic viscosity, ν = 7.469*10-7 m2/s, Prandtl number, Pr = 0.03.

Reynolds no., Re = Vd/ν = 5 * (1*10-2) / (7.469*10-7) = 66943 (Flow is turbulent since Re>2300)

For turbulent flow of liquid metals in circular pipe with uniform wall heat flux, Nusselt no, Nu = hd/k = 7+0.025 * (RePr) 0.8

Putting values, we get, for uniform heat flux, Nu = hd/k = 17.97

This gives, h = 17.97*48.75 / (1*10-2) = 87604 W/m2K

For turbulent flow of liquid metals in circular pipe with uniform wall temperature, Nusselt no, Nu = hd/k = 3.3+0.02 * (RePr) 0.8

Putting values, we get, for uniform heat flux, Nu = hd/k = 12.076

This gives, h = 12.076*48.75 / (1*10-2) = 58870 W/m2K