ConvectionCoolant_Part1_web

ConvectionCoolant_Part1_web - ENU 4134 – Convection to...

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Unformatted text preview: ENU 4134 – Convection to Coolant and Full Single-Channel Analysis – Part I D. Schubring December 2, 2009 (Driving Towards) Single-Channel Analysis I Conduction in fuel – 1+ I Gap conductance – 1 I Conduction in cladding – << 1 I Convection to coolant – 2-3 Included in these final notes (in several parts) is the full single-channel analysis problem Convection to Coolant I General equation for T co- T m I Single-phase coolant, constant properties & heat transfer coefficient (analytical solutions) I Single-phase coolant, variable properties & heat transfer coefficient (numerical solution) I Two-phase coolant I Miscellanea I Engineering judgment and single-channel analysis Remarks T&K Chapter 13 covers some of these topics, but in a different way than notes. The goal of these notes is to get you to be able to solve a “full” single-channel analysis problem without relying on code as a crutch (so you actually understand it!) Topics covered in Chapter 13, but not in class (notes or examples) are “enrichment”. This is almost certainly the hardest material in this course. It requires an understanding of two-phase flow (including heat transfer), as well as conduction heat transfer, careful arithmetic, and (often) some programming/scripting. This is almost certainly the most important material in this course. The goal here is to compute the temperatures (on which limits are directly applied) in a reactor geometry. (We’ll get Δ P , too.) So, ask questions as needed in class or office hours. The two days of advanced reactors at the end of the class can easily be deleted if we need to focus on the present material. General Equation for T co- T m Convective heat transfer is typically understood through the heat transfer coefficient: q 00 co = h ( T co- T m ) (1) T co- T m = q 00 co h = q 2 π R co h (2) Computation of h can be non-trivial, but this equation is general for any h . Equations of Single-Channel Analysis Most frequently, T m is the initial known, so analysis proceeds outside-in. T co- T m = q 2 π R co h (3) T ci- T co = q 2 π k c ln R co R ci (4) T fo- T ci = q 2 π R g h g = q π ( R ci + R fo ) h g (5) T max- T fo = q 4 π k f (6) Axial Dependence These are simple enough equations for the unknown temperatures....
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ConvectionCoolant_Part1_web - ENU 4134 – Convection to...

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