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Unformatted text preview: OneDimensional, SteadyState OneDimensional, SteadyState Conduction without Conduction without Thermal Energy Generation Thermal Energy Generation Chapter Three Chapter Three Sections 3.1 through 3.4 Sections 3.1 through 3.4 Methodology • Specify appropriate form of the heat equation . • Solve for the temperature distribution . • Apply Fourier’s law to determine the heat flux . Simplest Case: OneDimensional , SteadyState Conduction with No Thermal Energy Generation . • Common Geometries: – The Plane Wall : Described in rectangular ( x ) coordinate. Area perpendicular to direction of heat transfer is constant (independent of x ). – The Tube Wall : Radial conduction through tube wall. – The Spherical Shell : Radial conduction through shell wall. Methodology of a Conduction Analysis Plane Wall • Consider a plane wall between two fluids of different temperature: The Plane Wall • Implications: d dT k dx dx = (3.1) • Heat Equation: ( 29 Heat flux is independent of . x q x ′′ ( 29 Heat rate is independent of . x q x • Boundary Conditions: ( 29 ( 29 ,1 ,2 , s s T T T L T = = • Temperature Distribution for Constant : ( 29 ( 29 ,1 ,2 ,1 s s s x T x T T T L = + (3.3) k Plane Wall (cont.) • Heat Flux and Heat Rate : ( 29 ,1 ,2 x s s dT k q k T T dx L ′′ =  = (3.5) ( 29 ,1 ,2 x s s dT kA q kA T T dx L =  = (3.4) • Thermal Resistances and Thermal Circuits: t T R q ∆ = Conduction in a plane wall: , t cond L R kA = (3.6) Convection: , 1 t conv R hA = (3.9) Thermal circuit for plane wall with adjoining fluids: 1 2 1 1 tot L R h A kA h A = + + (3.12) ,1 ,2 x tot T T q R ∞ ∞ = (3.11) Plane Wall (cont.) • Thermal Resistance for Unit Surface Area : , t cond L R k ′′ = , 1 t conv R h ′′ = Units: K/W t R ↔ 2 m K/W t R ′′ ↔ ⋅ • Radiation Resistance...
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This note was uploaded on 02/21/2009 for the course MAE 310 taught by Professor Kuznetsov during the Spring '08 term at N.C. State.
 Spring '08
 Kuznetsov
 Heat Transfer

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