Two-Dimensional Conduction: Shape Factors and Dimensionless Conduction Heat Rates

1. Two-Dimensional Conduction:Shape Factors andDimensionless Conduction Heat Rates Chapter 4 Sections 4.1 and 4.3 Lecture 7

2. 2-D Heat Diffusion Equations Steady-state, 2-D conduction, No heat generation

3. 2-D Heat Diffusion Equations Laplace’s Equation • Analytical Solution (4.2, needs 4 b.c.’s) • Graphical Method (4.3) • Numerical Solution

4. Review of Calculus Definition of derivatives:

5. Review of Calculus Definition of derivatives:

6. Review of Calculus Definition of derivatives:

7. Finite-Difference Equations Definition of Nodal Network

8. Finite-Difference Approximation

9. Finite-Difference Approximation

10. Finite-Difference Approximation

11. The Energy Balance Method Conduction to an interior node from its adjoining nodes

12. The Energy Balance Method

13. The Energy Balance Method Fourier’s Law Similar equations can be derived

14. The Energy Balance Method For Equations for different b.c.’s can be derived (Table 4.2)

15. The Energy Balance Method

16. The Energy Balance Method Equations for different b.c.s can be derived (Table 4.2)

17. The Energy Balance Method Equations for different b.c.s can be derived (Table 4.2) Lecture 7