Question

Solve the 1D heat conduction equation with a source term.
The 1D heat conduction equation with a source term can be written as:

dr dr Using the Finite Volume Method, we use this equation to solve for the temperature T across the thickness of a flat plate of thickness L-2 cm. The thermal conductivity is k-0.5 W/Km, and the temperatures at the two ends are held constant at 100°C and 200°C, respectively. An electric current creates aAL constant heat source of a1000 kW/m The discretization is straightforward following the same principle as in the previous example, except that the source term is not zero, but q integrated over the volumeA5x The discretized equation can then be written as (compare with lecture notes): Th e constants aj and S, are then : Node aw t4 awt ae-S)p 2 to 4 awt aE- Sp qASr 0 awt aE-Sp The analytical solution is given by: 2k

Answer 1

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