KURENAI : Kyoto University Research Information Repository

Equation (79) was derived based on above equation, Eq.(80) . Substituting
Eq.(78) into Eq.(79) and taking into consideration of q w = q0 exp(wt),one
finally obtains a differential equation for boundary layers in dimensionless
form,
*t 8/7 * 9t 8/7 7 a *t 9/7
x(s)+x—*(S)+9*{x()}= 0.623(81)
vat vaxv
* *
Here, x and t are given by Eq.(14) and intial and boundary conditions are
given by
* *
St( x',0 ) = 0 for x > 0
• t( 0,t ) = 0 for t < 0
For small time, the convection term in Eq.(79) can be neglected and Eq.(79)
reduces to
x*(st)8/7+ x*a*(st)8/7= 0.623(83)
v ax v
This differential equation is easily solved and the solution is given by
St 0 .623{ 1 - exp(-t*)}7/8
(
T)_[*7(84)
vx
For large time, St/6 v will be independent of time and given by the solution
of following differential equation
x+*(t)8/77 S9*{x
vaxv
a *t (S) 9/7 } = 0.623
* *
Figure 10 shows the numerical solution of Eq.(85) in (S t/6v)x vs. x plot•
This solution can be approximated by the simple analytic function which is
analogous to Eq.(84)
132
,(85)
(8,2)