Question

a rectangular shape Aluminum block (L=10mm, D=3mm) has well insulated top and bottom. The left surface has thermal boundary condition, and the right surface has convection boundary condition.

* the surface temperature Ts=100℃, the ambient air temperature Ta=20℃, heat transfer coefficient h=120 W/(m^2*K)

* thermal conductivity of Aluminum = 220 W/m*K, density of Aluminum= 2707kg/m^3, specific heat of Aluminum= 896J/kg*K

Assume Aluminum block in a two-dimensional shape. and find temperature on x-y plane as follows.

Question) Solve it by using numerical method(two- dimensional, finite difference equation). (Assumption: △x=△y=1mm)

p.s) I want to know the temperatures of each node.

what I want to know is finite difference equation for every nodal point and each temperature.

if possible, please add matrix notation as shown below.

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Answer 1

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