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Method of Chasing 36 The second boundary condition is written in the usual way when the solid surface is in contact with a fluid at a different temperature with negligible radiation: x = I: - k dT (l) / dx = h[ T (l) - Too] where k is the heat conductivity, h is the convective heat transfer coefficient, Too is the temperature of the fluid away from the surface of the plate, and I is half the thickness of the plate. Introducing the dimensionless quantities _ x x= I ' 0= T- T 00 qJ2/k Eq. 13) subject to the boundary conditions x = 0: dO(O)/ dx = 0 x = 1: - dO(I)/ dx = NbiO(I), where N bi is the Biot number.

29040, respectively. 4. 25 X 10- 6 F). The initial charge in the circuit is zero and a constant emf of 24 V is applied at t = O. 001 sec is 0,031 A, it is desired to find the current at t = O. 25 Q X 10- 6 =24 ' Q(O) = 0 . 031 Answer: i(O) = dQ(O)/ dt = 5 A. REFERENCES l. 2. 3. 4. 5. 6. 7. , "The Numerical Treatment of Differential Equations," pp. 184-186, Springer-Verlag, New York, 1966. Lee, E. , Quasilinearization, nonlinear boundary value problems and optimization, Chern. Eng. , 21, 183-194 (1966).

8) Finally, the solution of Eq. 3) since It is now a known constant. 9) subject to the boundary conditions: yeO) = 0, dy(O) - - =0 dx ' y(l) =0 Comparison with Eq. 1) shows that fl(x) = 0, f2(x) = -7, f3(x) = 6, rex) = 6 22 2. Integration of Eqs. 8007 which can be substituted into Eq. 6871 The solution of the given differential equation can therefore be calculated by using Eq. 3) since now YI(X), h(x), and the constant J-t are known. Because of its simplicity, no details will be given. 1 Three-Point Third-Order Differential Equations It should be noted that the form of Eqs.

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