Cooling length of sheet products . Frequently in materials processing, a sheet o
ID: 1718559 • Letter: C
Question
Cooling length of sheet products. Frequently in materials processing, a sheet or slab of material is produced continuously and must be cooled after it leaves some processing device. This situation arises in polymer extrusion and in continuous casting of metals, for instance. The situation is sketched below. Assume that the sheet has a uniform temperature To as it leaves the upstream device, and that it moves with a constant velocity V. The thickness of the sheet is 2H. Cooling is accomplished by exposing the sheet to a coolant (usually air or water), and it may involve either free or forced convection. The cooling is characterized by a heat transfer coefficient h and a coolant temperature Tinfintiy. The goal of our analysis is to determine how the cooling length L depends on the other problem parameters.
(a) Write the energy equation, and simplify it by assuming a two-dimensional temperature distribution, steady-state behavior, constant properties, and no heat sources. Also write the boundary conditions.
(b) What are the physical parameters for this problem? Which parameter is initially unknown?
(c) Define appropriate dimensionless variables for this problem.
(d) Scale the energy equation, and simplify it by assuming that H <<L.
(e) Scale the boundary conditions. Identify a dimensionless group that describes whether the heat transfer coefficient h is small or large.
(f) Estimate the cooling length L in terms of known problem parameters, assuming that hH/k >> 1.
2H T-T T_T sheetExplanation / Answer
http://web.iitd.ac.in/~prabal/MEL806/(4-6)-heat-sink.pdf
Refer Slide no 8,9,10 from the link where it clearly shows the a) energy equation derivation and b) Parameters (h,p, K) along with c) dimensionless variable.
we have to use long fin condition i.e. H<<L and Tip temperature is To. d) scaling equation and e) Boundary Condition slide no. 15.
f) By assuming infinite long fin we will get Qf, then we will use this Qf in prescribed temperature condition to get the cooling length. Slide no 14