Celsius) around the boundary is known. Introduce a grid as shown in
the figure below, so that the metal plate is a collection of 20
point masses (14 of these are on the boundary of the plate and 6
(labelled 1, 2, 3, 4, 5 and 6) are in the interior of the plate).
You may assume that there is negligible heat ow in the direction
perpendicular to the plate. Let T1, T2, . . . , T6 denote the
temperatures at the six interior nodes of the grid in the figure.
The temperature at a node is approximately equal to the average of
the four nearest nodes.
- Consider A Thin Metal Plate Where The Temperature In Degree Celsius Around The Boundary Is Known Introduce A Grid A 1 (19.16 KiB) Viewed 39 times
T6.
(b) Express the system in the form Ax = b.
(c) The solution for the system is T1 = 120/7, T2 = 150/7,
T3 = 190/7, T4 = 120/7, T5 = 150/7, T6 = 190/7. Explain how to
solve the equation in (b) to obtain the answers for T1, T2, . . . ,
T6.
10° 10° 20⁰ 1 20° 20⁰ 2 5 20° 20° 3 6 20° 40° 40°