Shape FactorsSection 4.3CH EN 3453 – Heat Transfer Reminders…• Homework #4 due Friday– Help session Wednesday 4:30 pm• Engineering Career Fair September 23– Internship (and job) opportunities!– ca. 220 days until end of spring term finals week– Most of you have about 600 days until graduationFin EfficienciesFin EfficienciesFin EfficienciesModified Bessel function of the first kind(Appendix B.5)Modified Bessel function of the second kind(Appendix B.5)Fin Efficiencies, continuedOverall Efficiency• Definitions–ηf efficiency of a single fin–ηo overall efficiency of a finned surface– Af surface area of a single fin– Ab area of base where fins are NOT attached– At total area Af + Ab • Overall efficiency of finned surfacewhereThermal Circuits2-D Heat Flow• Heat flow lines ("adiabats") represent how heat "flows." • There is no heat transfer in a direction perpendicular to heat flow lines• Isotherms – constant temperature• Adiabats and isotherms are perpendicular to one anotherGraphical Method - Plotting Heat Flux1. Consider lines of symmetry and choose sub-system if possible.2. Symmetry lines adiabatic and count as heat flow lines.3. Identify constant temperature lines at boundaries. Sketch isotherms between the boundaries.4. Sketch heat flow lines perpendicular to isotherms, attempting to make each cell as square as possible.Graphical Solution…Shape FactorsShape Factors, Cont.Example – Book Problem 4.10A pipeline, used for the transport of crude oil, is buried in the earth such that its centerline is a distance of 1.5 m below the surface. The pipe has an outer diameter of 0.5 m and is insulated with a layer of cellular glass 100 mm thick. What is the heat loss per unit length of pipe under conditions for which heated oil at 120°C flows through the pipe and the surface of the earth is at a temperature of