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3 | P a g e F i n i t e V o l u m e M e t h o d [ N o t e 1 ]
Finite Volume Method for one-dimensional Steady State Diffusion
4 | P a g e F i n i t e V o l u m e M e t h o d [ N o t e 1 ]
STEP 1: GRID GENERATION
STEP 2: DISCRETISATION
6 | P a g e F i n i t e V o l u m e M e t h o d [ N o t e 1 ]
Example-1 : 1-D steady state conduction without heat source
Solution:
7 | P a g e F i n i t e V o l u m e M e t h o d [ N o t e 1 ]
Rearranging,
Discretised equation for node 1
For node 5
9 | P a g e F i n i t e V o l u m e M e t h o d [ N o t e 1 ]
EXAMPLE – 2: CONDUCTION WITH HEAT GENERATION L=2cm, k=0.5W/m/K, q=1000kW/m3, TA=100oC, TB=200oC
Solution:
12 | P a g e F i n i t e V o l u m e M e t h o d [ N o t e 1 ]
EXAMPLE 3: CONVECTION-DIFFUSION PROBLEM