A key step in the production process of

100mm

thick steel plates is "annealing", which consists of repeated heating and cooling of the plates in order to make the steel less brittle.\ The heating step occurs in a gas-fired furnace, in which combustion gases at a temperature of

700\\\\deg C

are blown against both surfaces of the steel plate, thus creating a convective heat transfer coefficient of

hh=500(W)/(m^(2))*K

.\ The cooling step takes place by hanging the plates in a cooling room, where air at a temperature of

50\\\\deg C

is slowly blown across the plates, generating a convective coefficient

h_(c)=50(W)/(m^(2))*K

.\ Proper annealing requires that the maximum temperature in the plate after cooling is no more than

200\\\\deg C

, while the minimum temperature of the plate after the heating cycle is

550\\\\deg C

. The steel properties can be assumed as follows:

\\\ ho =8000k(g)/(m^(3)),c_(P)=550(J)/(k)g*K,k=48(W)/(m)*K

.\ A) What do you know about the temperature distribution in the plates during the heating and cooling cycles, respectively?\ B) Determine how long the heating cycle takes, if the plates enter the furnace with a uniform temperature of

200\\\\deg C

.\ C) How long does the cooling cycle last if the plates arrive in the cooling room at a uniform temperature of

550\\\\deg C

?\ D) How large are the temperature variations in the steel plate when it leaves the furnace?

A key step in the production process of 100mm thick steel plates is "annealing", which consists of repeated heating and cooling of the plates in order to make the steel less brittle. The heating step occurs in a gas-fired furnace, in which combustion gases at a temperature of 700C are blown against both surfaces of the steel plate, thus creating a convective heat transfer coefficient of hh=500W/m2K. The cooling step takes place by hanging the plates in a cooling room, where air at a temperature of 50C is slowly blown across the plates, generating a convective coefficient hc=50W/m2K. Proper annealing requires that the maximum temperature in the plate after cooling is no more than 200C, while the minimum temperature of the plate after the heating cycle is 550C. The steel properties can be assumed as follows: =8000kg/m3,cP=550J/kgK,k=48W/mK. A) What do you know about the temperature distribution in the plates during the heating and cooling cycles, respectively? B) Determine how long the heating cycle takes, if the plates enter the furnace with a uniform temperature of 200C. C) How long does the cooling cycle last if the plates arrive in the cooling room at a uniform temperature of 550C ? D) How large are the temperature variations in the steel plate when it leaves the furnace