1 | 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

2 | 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 ]

CONTROL VOLUME NOTATIONS

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

5 | 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 ]

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

8 | 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 ]

TA = 100 TB = 500

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:

10 | 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 ]

11 | 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 ]

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

13 | 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 ]

Solution:

14 | 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 ]

15 | 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 ]