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Review:ConductionCH EN 3453 – Heat Transfer Reminders…• No homework assignment this week• Midterm Wednesday– Covers chapters 1, 2, 3, 4, 5– Closed book– One 8.5x11 sheet of notes (both sides) allowed– Kevin will provide tables (see “misc” of website)– Bring calculator and paper. Do not write answers on test– No cell phones allowed• Review session today at 4:00 pm in WEB 1230– Come with questions• Lecture overheads posted onlineChapter 1:Introduction to Heat Transfer• Heat vs. heat flux vs. heat per length• Conduction– Fourier’s Law– Ranges of k (Table 2.4 + appendices)• Convection– Newton’s Law of cooling– Ranges of h (Table 1.1)• Radiation– Stefan-Boltzmann Law– Emissivity, absorptivityChapter 2:Introduction to Conduction• Thermal properties of matter• Heat diffusion equation: ∂∂xk∂T∂x⎛⎝⎜⎞⎠⎟+∂∂yk∂T∂y⎛⎝⎜⎞⎠⎟+∂∂zk∂T∂z⎛⎝⎜⎞⎠⎟+q =ρcp∂T∂tRange of Thermal ConductivitiesFigure 2.4 Range of thermal conductivity for various states of matter at normal temperatures and pressure.Thermal Conductivity of GasesFigure 2.8 The temperature dependence of the thermal conductivity of selected gases at normal pressures. The molecular weight of the gases is also shown.Chapter 3:Steady-State Conduction (1-D)• The plane wall• Radial systems• Energy generation• Extended surfacesHeat Transfer through a Wall R1R2R3Complex Heat TransferThis type assumes lateral heat transfer (in the y direction) at interfaces, which is often not a good assumption.This is a “safer” way to structure the thermal circuit. Assumes parallel heat transfer through all layers.Contact ResistanceA CylinderReview of Conduction…Page 126Extended Surfaces (fins)Figure 3.12 Use of fins to enhance heat transfer from a plane wall.(a) Bare surface. (b) Finned surface.Types of FinsFour Scenarios for Treating Pin TipsFin Effectiveness vs Efficiency• Fin Effectiveness (ε)– A measure of how much more heat one can transfer to a given base (attachment) area by adding a fin.– Greater than 1.0– qwith fin = ε·qwithout fin • Fin Efficiency (η)– Ranges from 0 to 1.0– Relative heat transfer from fin compared to case where all of fin surface is at base temperatureFin EfficienciesFin EfficienciesFin EfficienciesModified Bessel function of the first kind(Appendix B.5)Modified Bessel function of the second kind(Appendix B.5)Fin Efficiencies, continuedChapter 4:2-D Steady-State Conduction• Graphical methods • Shape factors• Finite-difference equations2-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 anotherShape Factors q = Sk(T1-T2)Shape Factors, Cont.2-D SolidConduction between NodesFigure 1.5Chapter 5:Unsteady-State Conduction• Lumped analysis and the Biot number• Spatial effects• Semi-infinite solids• Constant surface temp. and const. heat fluxReview: The Biot Number• If Bi < 0.1 then the lumped capacitance approach can be used– Eq. 5.5 to find time to reach a given T– Eq. 5.6 to find T after a given time– Eq. 5.8a to find total heat gain (loss) for given time• L depends on geometry– General approach is L = V/As• L/2 for wall with both sides exposed• ro/2 for long cylinder• ro/3 for sphere• Use L = V/As when geometry is neither plate, cylinder nor sphere– Conservative approach (preferred) is to use the maximum length• L for wall (note that L is measured from midpoint when heated from both sides)• ro for cylinder or sphere Bi =hLkLumped Capacitance Equations• Time as a function of temperature• Temperature as a function of timeSpatial Effects(When lumped analysis cannot be used)Dimensionless VariablesTemperature:θ*!≡!θθi!= !T − T∞Ti− T∞Position:x*≡xLTime:t*≡αtLc2=ktρcLc2Table 5.1 – ζ1 and C1 vs.


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U of U CHEN 3453 - Review - Conduction

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