PAT312, Section 59, December 2006 S59-1 Copyright 2007 MSC.Software Corporation SECTION 59 RADIATION OVERVIEW

PAT312, Section 59, December 2006 S59-2 Copyright 2007 MSC.Software Corporation

PAT312, Section 59, December 2006 S59-3 Copyright 2007 MSC.Software Corporation RADIATION OVERVIEW Basic equation, q ij = F ij A i (T i 4 – T j 4 ) l q ij is the net rate of radiation between surface i and j l T i and T j is the temperature of surface i and j, respectively l T is in absolute units, Kelvin or Rankine is the Stefan-Boltzmann constant l E-8 Watt/(m2*K4) l E-9 Btu/(hr*ft2*R4) l F ij (script-F) is the gray body configuration factor. It is a function of: l f ij, the geometric view-factor from surface i to surface j i, the emissivity of surface i j, the emissivity of surface j l A i is the area of surface i

PAT312, Section 59, December 2006 S59-4 Copyright 2007 MSC.Software Corporation VIEW FACTOR ILLUSTRATION 12 BG F 1-2 approaches 1 F 1-BG approaches 0

PAT312, Section 59, December 2006 S59-5 Copyright 2007 MSC.Software Corporation VIEW FACTOR ILLUSTRATION 1 2 BG F 1-2 approaches 0 F 1-BG approaches 1

PAT312, Section 59, December 2006 S59-6 Copyright 2007 MSC.Software Corporation RADIOSITY CONCEPT l Radiosity node added for each surface node l FA is separated into two terms l A space resistance which is a function of only F ij Each surface resistance a function of i or j only 1- i i A i 1- j j A j 1 A i F ij l This technique facilitates l Change in surface properties without new view factor run l Independently variable emissivity values = 1.0 will eliminate radiosity nodes l Facilitates debugging of surface-to-surface connections

PAT312, Section 59, December 2006 S59-7 Copyright 2007 MSC.Software Corporation NODE ELEMENTAL SUB-AREA l The portion of an element face associated with a particular node.

PAT312, Section 59, December 2006 S59-8 Copyright 2007 MSC.Software Corporation NODE ELEMENTAL SUB-AREA l The portion of an element face associated with a particular node. l e.g. Area for node 5 is ¼ of 4 adjoining elements

PAT312, Section 59, December 2006 S59-9 Copyright 2007 MSC.Software Corporation SIMPLE RADIOSITY NETWORK

PAT312, Section 59, December 2006 S59-10 Copyright 2007 MSC.Software Corporation PERTINENT DOCUMENTS l MSC.Patran User Manual l MSC.Thermal Users Manual Volumes 1 and 2 l Gebhart, Benjamin, Heat Transfer, 2nd Editions, 1971, McGraw-Hill, N.Y. l Howell, John R., A Catalog of Radiation Configuration Factors, 1982, McGraw-Hill, N.Y. l Siegel, Robert, and Howell, John R., Thermal Radiation Heat Transfer, 2nd Edition, 1981, McGraw-Hill, N.Y. l Holman, J.P., Heat Transfer, 5th Edition, 1981, McGraw- Hill, N.Y.

PAT312, Section 59, December 2006 S59-11 Copyright 2007 MSC.Software Corporation

PAT312, Section 59, December 2006 S59-12 Copyright 2007 MSC.Software Corporation