3a-r - One-Dimensional, Steady-State One-Dimensional,...

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Unformatted text preview: One-Dimensional, Steady-State One-Dimensional, Steady-State 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 Fouriers law to determine the heat flux . Simplest Case: One-Dimensional , Steady-State 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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3a-r - One-Dimensional, Steady-State One-Dimensional,...

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