4 - 4.1TransientState ,. heatingtimeofovens,.However,evenin...

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4.1 Transient State Transient state is a state of non-equilibrium, when the temperatures are still changing with time. Some simple examples are the pre- heating time of ovens, when you are waiting for the temperature inside the oven to reach a specified temperature. However, even in  a heated oven, cooking occurs by transient conduction because the heat is conducted through the food as it cooks. The internal  temperature of the food, therefore, is usually increasing during cooking. 4.2 Lumped Body Model The simplest case of transient conduction is the  lumped body model . This model considers the heat transfer between a solid and a  surrounding fluid. The main assumption in the model is that the solid can be approximated to have a uniform temperature; that is,  there are no temperature gradients within the solid. Furthermore, the surrounding fluid must be large enough so that its temperature  remains a constant throughout the process. This approximation can be made when the following condition is satisfied:   (Eq. 4.1) where  h  is the convection coefficient,  k  is the conductivity of the solid, and  L c  is the characteristic length of the solid, defined as the  volume/area ratio. For a wall of thickness 2 L L c  =  L ; for a cylinder,  L c  =  r /2; for a sphere, it is  r /3. The number  Bi  is a dimensionless  parameter called the  Biot  number. For a lumped body, the temperature of the solid which is introduced into the fluid at time  t  = 0 is given by:   (Eq. 4.2) where  A  is the surface area of the solid,  m  is the mass of the solid,  c p  is the specific heat of the solid,  T i  is the initial temperature of  the solid, and  T  is the temperature of the fluid. This equation assumes that  T  remains constant through the process. The newly  introduced variable  θ /   θ i  is the "normalized temperature," which measures the temperature in relative terms. That is, the normalized 
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This note was uploaded on 10/23/2011 for the course ENGINEERIN 251 taught by Professor Staff during the Spring '11 term at Bangladesh University of Eng and Tech.

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4 - 4.1TransientState ,. heatingtimeofovens,.However,evenin...

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