Miscellaneous Exercises 293
h convection coefficient (W/m^2 K)
κ thermal conductivity of steel (W/mK)
L length of cooling line
T(x,y) temperature in the strip
Ta temperature of coolant
T 0 temperature of the strip at entry to cooling line
v strip speed (m/s)
k thermal diffusivity of steel (m^2 /s)
B Biot number (dimensionless)
Table 1 Table of Notation.Figure 5 Exercise 40.d.Condition at entry to cooling line (atx=0):
T( 0 ,y)=T 0 , −b<y<b.The author treats the strip as infinite. In fact, typical dimensions are
100 m in thex-direction and 2 cm in they-direction,sotheratioof
xtoylengths is on the order of 10^4.
Next, these dimensionless variables are introduced:θ=TT−Ta
0 −Ta, Y=yb, X=xb,and these dimensionless parameter combinations appear in the equa-
tions:
γ=bkv, B=hbκ.