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Finite Difference

BRANCH-E&TC ENGINEERING

SEM – 3^rd

SUBJECT- Engg math-iii

CHAPTER– 7 – finite difference

TOPIC- finite difference

Ay-2021-2022 , winter-2021

FACULTY- Tapas si (faculty Mathematics)

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FINITE DIFFERENCE

In numerical analysis, two different approaches are commonly used: The finite difference and the finite element methods. In heat transfer problems, the finite difference method is used more often and will be discussed here. The finite difference method involves:��⮚ Establish nodal networks�⮚ Derive finite difference approximations for the governing� equation at both interior and exterior nodal points�⮚ Develop a system of simultaneous algebraic nodal equations�⮚ Solve the system of equations using numerical schemes�

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The Nodal Networks

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Finite Difference Approximation

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Finite Difference Approximation cont.

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Finite Difference Approximation cont.

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A System of Algebraic Equations

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Matrix Form

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Numerical Solutions

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Iteration

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Example

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Example (cont.)

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Example (cont.)

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Summary of nodal finite-difference relations for various configurations:

Case 1 Interior Node

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Case 2 �Node at an internal corner with convection

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Case 3 �Node at a plane surface with convection

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Case 4 �Node at an external corner with convection

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Case 5 �Node at a plane surface with uniform heat flux

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Thank You