[m-fry]

Hi,
at the moment I'm writing an assessment and need some help. The problem is to calculate the steady state temperature using the finite volume method in a plate. In addition, the results of the finite volume method should be compared to the exact analytical solution.

The following chart shows the results of each calculation method and the difference between them:

Temperature on node Tx: T1 T2 T3 T4 T5
Finite Volume Method: 120°C / 160°C / 200°C / 240°C / 280°C
Analytic Method: 121,8°C / 164,2°C / 205°C / 244,2°C / 281,8°C
Differences: 1,8°C / 4,2°C / 5°C / 4,2°C /1,8°C

(T0= 100°C; T6=300°C = Known surface temperature)

The Chart shows that the values of the differences get some symmetrical characteristics (1,8; 4,2; 5; 4,2; 1,8). The highest difference is to find on temperature T3 with 5°C. On both sides the differences get smaller.

My question is: How can I explain this effect? Why is the highest difference on node T3 (5°C) and why get the differences smaller on the start T1 and end T5 node.

I hope somebody can help me!

Best regards,

m-fry

[kirilhs]

The reason is order of accuracy of the approximation
If You use more control volumes (close to infinity) two solution have to coinside.