A long, heated, cylindrical steel rod is removed from a heat treatment furnace and has to be cooled to complete the process. If the surface temperature of the rod is at 150°C and the cooling fluid temperature is maintained at 25°C, what is the minimum diameter of the rod to produce turbulent natural convection heat transfer if it is held in a horizontal position in (a) air and (b) water? Also, determine the initial heat transfer rate by natural convection from a 10-cm diameter rod in each of the two fluids.

Question

GIVEN

• Long heated cylindrical steel rod, cooled by natural convection.

• Surface temperature of rod (Ts=1500C

• Fluid temperature (T?) = 250C

FIND

(a) Minimum diameter of rod to produce turbulent natural convection in (i) Air (ii) water

(b) Initial heat transfer rate by natural convection from 10 cm diameter rod in each fluids.

ASSUMPTIONS

• Radiation is negligible

SKETCH



PROPERTIES AND CONSTANTS

for dry air at the mean temperature of 87.5°C

Thermal expansion coefficient (?) = 0.00277 1/K

Thermal conductivity (k) = 0.0298 W/(m K)

Kinematic viscosity (?) = 22.55 × 10–6 m2/s

Prandtl number (Pr) = 0.71

for water at the mean temperature of 87.5°C

Thermal expansion coefficient (?) = 0.000678 1/K

Thermal conductivity (k) = 0.6765 W/(m K)

Kinematic viscosity (?) = 0.33 × 10–6 m2/s

Prandtl number (Pr) = 67.8

Answer 1

(a) The Grashof number when the fluid is air at 250C is



For Turbulent flow in Natural convection the criterion





Thus the required diameter to produce turbulent natural convection in air is 59.5 cm.

The Grashof number when the fluid is water at 250C is



For Turbulent flow in Natural convection the criterion



Thus the required diameter to produce turbulent natural convection in water is 1.25 cm



For a horizontal cylinder in natural convection, the Nusselt number is given by



Thus heat transfer rate is



For a 10 cm diameter rod in water,



For a horizontal cylinder in natural convection, since turbulent Nu equation for natural convection in

horizontal cylinders is not available,

The Nusselt number with Sin?= 0.



Thus heat transfer rate is