A 0.6-cm-diameter mild steel rod at 38°C is suddenly immersed in a liquid at 93°C with ch = 110 W/(m2 K). Determine the time required for the rod to warm to 88°C.

Question

GIVEN

• A mild steel rod is suddenly immersed in a liquid

• Rod diameter (D) = 0.6 cm = 0.006 m

• Initial temperature of the rod (To) = 38°C

• Liquid temperature (T?) = 93°C

• Heat transfer coefficient ( ch ) = 113.5 W/(m2 K)

FIND

• The time required for the rod to warm to 88°C

ASSUMPTIONS

• The rod is 1% carbon steel

• Constant thermal conductivity

• End effects are negligible

• The rod is very long compared to its diameter

• There is radial conduction only in the rod

SKETCH



PROPERTIES AND CONSTANTS

For 1% carbon steel at 20°C:

Thermal conductivity (k) = 43 W/(m K) Specific heat (c) = 473 J/(kg K) Density (?) = 7801 kg/m3 Thermal diffusivity (?) = 1.172 × 10–5 m2/s. [? = k/?c].

Answer 1

(a) The Biot number is calculated first to check if the internal resistance is negligible



Therefore, the internal resistance of the rod is negligible.

The temperature-time history of the rod,





Solving for the time



The time required to reach 88°C is