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atio increases with increasing x .
II. 4 LANIMAR FLOW FOR Pr >> 1
In this case, the velocity distribution in the thermal boundary layer
must be considered. The velocity distribution near wall is given by Eq.(28)
in term of wall shear stress, T w,
u =u y (28)
When Prandtl number is very large, thermal boundary layer can be considered
to be located in the velocity field which is represented by Eq.(28).
Therefore, substituting Egs,(10) and (28) into Eq.(11), one obtains
6X6t(Stgw)+24pX ax(gwTwst) = Cp(29)
Considering q w = q0exp(wt), one obtains
we +a(62)+4}t ~x(Tw63) = 6a (30)
t
For laminar flow, the wall shear stress is given-:by
Tw = 0.332 pu. ^ u(31)
Substituting Eq.(31) into Eq.(30), and nondimensionaling by Eq.(14),
Eq.(30) becomes
S
*2 a ..21(
-1–)ast
t +=-(6t) atP + 0.083—() = 6 (32)
r ax T^
x Initial and boundary conditions are same as Eqs.(16) and (17). One of the solutions
of Eq.(32) which does not include t , can be considered to be a asymptotic
121
*3