CHME 333 Workbook - Chapter 5 HANDOUT

# CHME 333 Workbook - Chapter 5 HANDOUT - CHME 333 Workbook...

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1 CHME 333 Workbook Chapter 5 – Transient Conduction Objectives o Understand how temperature varies with time during unsteady state conditions o Understand how and when to use the “____________________ ” assumption o Perform 1-dimensional transient conduction analysis o Transient conduction in ____________________ Introduction So far everything has been steady state – conditions in the system were not changing with time. Now we get rid of that assumption. Typically transient conduction occurs when the boundary conditions change. A typical example of transient conduction is the quenching or tempering of metallic objects. A hot metal object is quickly immersed in a cold fluid. The boundary condition at the surface quickly changes, and thermal energy is transferred to the fluid. The ratio of conductive heat transfer in the object to convective heat transfer to the fluid is very important to the process, and will dictate how we do the calculations. If conduction is very fast compared to convection, we will use the “lumped capacitance” simplification (borrowing yet again from electrical engineering analysis of circuits). If the conduction and convection are roughly equal, then we must take into account the spatial temperature distribution within the object.

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2 The Lumped Capacitance Method o Consider a hot metal object being quenched in a cold water bath. o Assumptions ± ____________________ ± ____________________ ± ____________________ ± ____________________ o Apply energy balance ± Accumulation = Input – Output + Generation ± where ± Separate variables and integrate to obtain Or = = t Vc hA T T T T p s i i ρ θ exp Where s p hA Vc is a thermal time constant t t t C R = τ R t = convection resistance C t = lumped capacitance
3 o Calculate the total heat transferred from the object = = t s t dt hA dt q Q 0 0 θ = t i p t Vc Q τ ρ exp 1 When is this approach valid???

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CHME 333 Workbook - Chapter 5 HANDOUT - CHME 333 Workbook...

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