Lecture 6 Lumped Systems and Radiation

Lecture 6 Lumped Systems and Radiation - Thermal and Fluids...

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Thermal and Fluids Engineering I Prof. Deborah A. Kaminski Lecture 6 – Lumped Systems and Radiation Lumped System Approximation Consider a solid body that is cooled or heated by convection. In general, temperature varies with time and location in the solid. But suppose temperature does not vary much with location, but only with time, that is, the body is relatively isothermal. The body will be relatively isothermal if cond conv R R << Define Biot number as Lecture 6 Page 1
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Thermal and Fluids Engineering I Prof. Deborah A. Kaminski 1 char cond char conv L Rh kA Bi Rk hA === L If Bi < 0.1, then we are reasonably justified in assuming that the temperature does not vary with location. But what is L char ? A good choice is char V L A = where V is the volume and A is the surface area of the body. For example, consider three cylinders of different sizes: For each cylinder 2 2 2 2 2 char D H V L A D DH π ππ ⎛⎞ ⎜⎟ ⎝⎠ == + 0.244cm 0.167cm 0.455cm A B C L L L = = = The formula gives reasonable lengths for arbitrary-shaped bodies as well. Lecture 6 Page 2
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Thermal and Fluids Engineering I Prof. Deborah A. Kaminski In the lumped-system approximation, we assume conduction resistance is low and the body is fairly isothermal. Suppose we have an isothermal body at an initial temperature of T i that is exposed at time zero to a fluid with constant temperature T f . To find the temperature of the body as a
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Lecture 6 Lumped Systems and Radiation - Thermal and Fluids...

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