2. Consider a thin metal plate where the temperature (in degree Celsius) around the boundary is known. Introduce a grid

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2 Consider A Thin Metal Plate Where The Temperature In Degree Celsius Around The Boundary Is Known Introduce A Grid 1 (61.49 KiB) Viewed 25 times

2. Consider a thin metal plate where the temperature (in degree 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 flow in the direction perpendicular to the plate. Let T₁, T2,..., To 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. 3 20⁰ 1 20° 2 20⁰ 10 40° 10° 10° 40 20° 20° 20⁰ (a) (3 marks) Formulate a system of equations for T₁, T2,..., T6. (b) (1 mark) Express the system in the form Az = b. (c) (1 mark) The solution for the system is T₁ 120/7, T₂ 150/7, T3 190/7, T₁ = 120/7, T5 = 150/7, T6 = 190/7. Explain how to solve the equation in (b) to obtain the answers for T₁, T2,..., T6. = = =