In a metal alloy manufacturing and heat treatment plant and in its immersion quenching process, steel plates are first heated in a furnace and then quenched (or cooled) in a coolant bath to obtain the desired steel properties and surface hardness. In one such process a flat stainless steel plate 0.6-cm-thick, 7.5-cm-wide and 0.3-m-long is immersed horizontally at an initial temperature of 980°C in a large water bath at 100°C and at atmospheric pressure. Determine how long it will take this plate to cool to 540°C.

Question

GIVEN

? A flat stainless steel plate is immersed horizontally in water

? Plate thickness (s) = 0.6 cm = 0.006 m

? Plate width (w) = 7.5 cm = 0.075 m

? Plate length (L) = 0.3 m

? Initial plate temperature (Tpi) = 980°C = 1253 K

? Pressure = 1 atm

? Water bath temperature (Tb) = 100°C (saturation) = 373 K

FIND

? Time for plate to cool to Tpf = 540°C = 813 K

ASSUMPTIONS

? The heat fluxes from the bottom and top of the plate are equal

? The plate is polished

SKETCH



PROPERTIES AND CONSTANTS

From Appendix 2, Table 13, for water at the pool temperature of 100°C



From Appendix 2, Table 35, for steam at 100°C



From Table 9.2, The surface tension, o, for water @ 100°C = 0.0589 N/m

From Table 9.1, The coefficient, Csf, for water on mechanically polished stainless steel = 0.0132

From Table 11.3, the emissivity of polished stainless steel at the average temperature of

(980°C + 540°C)/2 = 760°C (g) = 0.22

Answer 1

As the plate cools, the heat flux from the plate will diminish. Therefore, the heat flux will be assumed to be constant over a small time step, then the plate temperature will be updated. This procedure will be repeated until the plate temperature drops to 540°C.

The initial excess temperatures,??Tx = Tpi – Tsat = 980°C – 100°C = 880°C.

Assuming nucleate boiling, the heat flux is given by Equation (9.2)



The critical heat flux for nucleate boiling is given be Equation (9.4)





Since q" > q"c, The nucleate boiling assumption is invalid and film boiling will occur. Note that at the final plate temperature, Tb,f = 540°C, ?Tx = 440°C, and q" = 1.12 x 1010 > q"c . Therefore, film boiling will occur during the entire cooling period.

For film boiling on flat horizontal surfaces, the conduction heat transfer coefficient is given by Equation (9.7)





For a flat plate, D ??, therefore A/D ? 0



Initially



The radiation heat transfer coefficient is given by Equation (9.9)



Initially



The total heat transfer coefficient is given by Equation (9.8)



The initial rate of heat transfer is



The initial Biot number is



Therefore, the internal resistance of the steel is negligible. The change in the plate temperature is given by



For ?t = 5 s



Therefore, after 5 s



Repeating this procedure: for ?t = 5 s



The plate will cool to 540°C in approximately 50 seconds.