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Chapter 5 -Transient Conduction 2012 - Web

# Chapter 5 -Transient Conduction 2012 - Web - CHAPTER 5...

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C HAPTER 5: T RANSIENT C ONDUCTION In practical terms, very few processes operate at a true steady-state. Variations in operation may arise from “noise” caused by controller accuracy and/or mechanical variation inherent to the different pieces of equipment that make up the process Processes such as this may be considered to be at steady state For other processes, disturbances consistently arise, causing the controller to continuously adjust to search for the specified set-point Processes such as these virtually always operate in transient mode. dT/dt 0

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D EALING W ITH N ON -S TEADY S TATE C ONDUCTION Transient conduction may be simple or extremely difficult to consider, depending on the assumptions applied. Consider the case of suddenly changing the temperature of one surface of an object. If temperature gradients within the solid may be neglected (small, high k ) lumped capacitance method If the only significant temperature gradient is 1D approximations of heat diffusion equation solutions If significant temperature gradients exist in 2-3 dimensions finite element/finite difference method
L UMPED C APACITANCE M ETHOD The lumped capacitance method can be used to find dT/dt if it is assumed that the temperature T ( x,y,z ) is identical throughout the entire object at any instantaneous time point . With no spatial variation in T , d 2 T/dx 2 , d 2 T/dy 2 , and d 2 T/dz 2 are all zero . This assumption is reasonable when R (conduction through body) ( x / kA ) << R (heat loss at surface) (1/ hA ) if the body is very small if the thermal conductivity (k) is very large ( k ) if h, h r are small q z T y T x T k 2 2 2 2 2 2 t T c p

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