Question

Annealing is a process by which steel is reheated and then cooled to make it less brittle. Consider the reheat stage for a 100-mm-thick steel plate ( 7830 kg/m3 , c 550 J/kg K, k 48 W/m K), which is initially at a uniform temperature of Ti 200 C and is to be heated to a minimum temperature of 550 C. Heating is effected in a gas-fired furnace, where products of combustion at T 800 C maintain a convection coefficient of h 250 W/m2 K on both surfaces of the plate. How long should the plate be left in the furnace

Answer 1

T = 858.25 s

Step-by-step explanation:

Given data:

Reheat stage for a 100-mm-thick steel plate ( 7830 kg/m3, c 550 J/kg K, k 48 W/m K),

initial uniform temperature ( Ti ) = 200 c

Final temperature = 550 c

convection coefficient = 250 w/m^2 k

products combustion temp = 800 c

calculate how long the plate should be left in the furnace ( to attain 550 c )

first calculate/determine the Fourier series Number ( Fo )

`(T_(0)-T_(x) )/(T_(1)-T_(x) ) = C_(1) e^{(-0.4888^(2)*Fo )}`

= 0.4167 =
`1.0396e^(-0.4888*Fo)`

therefore Fo = 3.8264

Now determine how long the plate should be left in the furnace

Fo =
`((k)/(pc_(p) ) ) ( (t)/((L/2)^2) )`

k = 48

p = 7830

L = 0.1

Input the values into the relation and make t subject of the formula

hence t = 858.25 s