Introduction to Computation and Modeling for Differential Equations by Edsberg Lennart

Author:Edsberg, Lennart
Language: eng
Format: epub
Publisher: Wiley
Published: 2013-05-27T04:00:00+00:00

and BCs

The only new variable and parameter introduced in this model compared to the model in example 4.1 is time t [s] and the initial value Tinit(z) [K]. We see that when steady state is reached (t → ∞), the first term drops out, the initial condition is not necessary and the PDE problem turns into the BVP (4.10).

FIGURE 6.2: 3D visualization of a solution u(x, t)of the heat equation

FIGURE 6.3: Hot flow in a cylindrical pipe

Example 6.2 (Time-dependent 2D flow in a pipe). Consider again the flow in a pipe model but now assume that heat is transported by diffusion both in the z-and in the r-direction. The model for the temperature T(z, r, t) [K] is modified to

(6.5)

with IC

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