Question

A thick steel slab ( 7800 kg/m3 , c 480 J/kg K, k 50 W/m K) is initially at 300 C and is cooled by water jets impinging on one of its surfaces. The temperature of the water is 25 C, and the jets maintain an extremely large, approximately uniform convection coefficient at the surface. Assuming that the surface is maintained at the temperature of the water throughout the cooling, how long will it take for the temperature to reach 50 C at a distance of 25 mm from the surface

Answer 1

1791 secs ≈ 29.85 minutes

Step-by-step explanation:

( Initial temperature of slab ) T1 = 300° C

temperature of water ( Ts ) = 25°C

T2 ( final temp of slab ) = 50°C

distance between slab and water jet = 25 mm

Determine how long it will take to reach T2

First calculate the thermal diffusivity

∝ = 50 / ( 7800 * 480 ) = 1.34 * 10^-5 m^2/s

next express Temp as a function of time

T( 25 mm , t ) = 50°C

next calculate the time required for the slab to reach 50°C at a distance of 25mm

attached below is the remaining part of the detailed solution