294 Chapter 4 The Potential Equation
The problem in terms of dimensionless variables and parameters is:γ∂θ
∂X=∂^2 θ
∂X^2 +∂^2 θ
∂Y^2 ,^0 <X,^0 <Y<^1 ,
∂θ
∂Y(X,^0 )=^0 ,^0 <X,
∂θ
∂Y(X,^1 )=−Bθ(X,^1 ),^0 <X,
θ( 0 ,Y)= 1 , 0 <Y< 1.
SolvetheproblemforthecaseofahighBiotnumber,B→∞,which
means thatθ(X, 1 )=0, 0<X.
41.(Continuation) Solve the problem in Exercise 40 for the case of a low
Biot number,B≈0, which means that∂∂θY(X, 1 )=0, 0<X.