E5.6 Forced Convection through Annulus

Example 5.6: Water is flowing through an annulus formed by two tubes 1.5 in and 2 in OD, having thickness rating of 14 BWG. The fluid is cooled from 160 °F to 100 °F. The viscosity at the wall temperature is 1.406 lb/(ft·°F. Find the Nusselt number if w = 50 lb/hr, L = 10 ft. Use the following data:

Specific heat = 0.9989 Btu/(lb·°F); density = 61.55 lb/ft³;

Absolute viscosity = 1.24 lb/(ft·hr); thermal conductivity = 0.375 Btu/(hr·ft·°F);

Wall temperature = 117 °F; bulk temperature = 130 °F.

Solution: The fluid is flowing through an annulus, so we need to find the equivalent diameter for the annulus. It is important to note that the equivalent diameter for heat transfer is different from that calculated for pressure drop.

Outside diameter of the smaller tube, d_o = 1.5 in = 0.125 ft.

Inner diameter of the outer tube, D_i = 1.834 in = 0.1528 ft.

Equivalent diameter for heat transfer, d:

Annulus area, a:

Velocity of fluid, V

Reynolds number, Re = (Vdρ)/μ = 410.7

Prandtl number, Pr = (cμ)/k = 3.3

Nusselt number, Nu: We can see that Re is less than 2100 and the following correlation is applicable.

Coefficient of thermal expansion, β (Use steam tables):

Driving force, ΔT = T_b - T_w = 13 °F.

Grashof number, Gr (5.10):

Viscosity correction factor, φ:

Nusselt number, Nu: