Lecture_03_-_Steady_State_Conduction.ppt - ME 451 Heat Transfer Steady State Conduction Ref Çengel Yunus A Heat Transfer A Practical Approach John

Lecture_03_-_Steady_State_Conduction.ppt - ME 451 Heat...

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ME 451 - Heat Transfer Steady State Conduction Ref: Çengel, Yunus A., Heat Transfer, A Practical Approach, John Wiley & Sons,
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Lesson Outline Thermal Resistance Thermal Contact Resistance Fins
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Conduction Conduction is heat transfer through a stationary medium The rate of heat transfer is proportional to the temperature difference across the layer and the heat transfer area, but inversely proportional to the layer thickness Thermal conductivity (k – W/mK) is a measure of the ability of a material to conduct heat Fourier’s Law of heat conduction dx dT kA Q cond
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Steady state vs. Transient In general, heat transfer is dynamic (or changing) in nature. There are relatively few cases in which we are truly in equilibrium, or steady state (unchanging) A transient system is one undergoing changing temperature profiles Transient analysis is much more difficult than steady state Real systems are typically analyzed as steady state, using the worst-case transient conditions. Lumped system analysis is a special case of transient system The temperature of the system will change with time; however the system is small enough that the entire system can be modeled to change at the same time (i.e. dropping a small metal object into a liquid bath to quench can be modeled as a lumped system )
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General Solutions to 1D Heat Equation (Cartesian coordinates, constant thermal conductivity) Steady state, no heat generation: Steady state, with heat generation: Transient, no heat generation: Transient, with heat generation: t T k g x T 1 2 2 0 2 2 dx T d 2 1 C x C x T 2 1 2 2 C x C x k g x T 0 2 2 k g dx T d t T x T 1 2 2 t T k g x T 1 2 2 Use empirical (experimental) solution 1 5 4 2 2 cos sin ,   t t e x C e x C t x T
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General Solutions to 1D Heat Equation (cylindrical coordinates, constant thermal conductivity) Steady state, no heat generation: Steady state, with heat generation: Transient, no heat generation: Transient, with heat generation: 2 1 ln C r C r T Use empirical (experimental) solution t T k g r T r r r 1 1 0 r T r r 0 1 k g r T r r r 2 1 2 ln 4 C r C r k g r T t T k g r T r r r 1 1 t T r T r r r 1 1 Use empirical (experimental) solution
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Big Picture Solution path to conduction problems: Formulate appropriate differential equation from Heat equation Find the general solution Apply boundary conditions
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