Radiation Exchange Between Surfaces

1. Radiation Exchange Between Surfaces EGR 4345 Heat Transfer

2. View Factor Fij(Configuration or Shape Factor)

3. View Factor Fij • Defined as the fraction of the radiation leaving surface i that is intercepted by surface j

4. Total Rate Equation qij • Rate at which radiation leaves dAi and is intercepted by dAj Assumes surface i emits and reflects diffusely Assumes radiosity Ji is uniform over surface Ai

5. View Factor Fij • Defined as the fraction of the radiation leaving surface i that is intercepted by surface j Assumes surfaces emit and reflect diffusely Assumes uniform radiosity

6. Use View Factor to Calculate Net Radiative Exchange, qij • qij = Ai Fij(Ti4 – Tj4) • Net rate at which radiation leaves surface i as a result of interaction with j • Equal to the net rate at which j gains radiation due to its interaction with i

7. View Factor Relations 1 • Tables and Figures • Table 13.1 – Two-Dimensional Geometries • Table 13.2 – Three-Dimensional Geometries • Figure 13.4 – Aligned Parallel Rectangles • Figure 13.5 – Coaxial Parallel Plates • Figure 13.6 – Perpendicular Rectangles with a Common Edge

8. View Factor Relations 2 • Reciprocity AiFij = AjFji Determine one view factor from knowledge of the other

9. View Factor Relations 3 • Summation rule for enclosures • Fii – fraction of radiation that leaves surface i and is directly intercepted by i • For a plane or convex surface, Fii = 0

10. View Factor Relations 4 • By inspection

11. 1 3 2 View Factor Relations 5 • Symmetry - Isosceles Triangle F12 = F13

12. View Factor Relations 6 • Multiple component surfaces reciprocity