The Biot number during a heat transfer process between a...

The Biot number during a heat transfer process between a sphere and its surroundings is determined to be 0.02 . Would you use lumped system analysis or the transient temperature charts when determining the midpoint temperature of the sphere? Why?

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Key Concepts

Biot Number

A dimensionless parameter that compares the internal thermal resistance within a body to the external convective resistance. It helps evaluate whether temperature gradients inside the object can be neglected. A small Biot number (typically less than 0.1) indicates that the object’s temperature distribution is nearly uniform during transient processes.

Lumped System Analysis

An approach in transient heat transfer that assumes the entire body has a uniform temperature at any given time. This simplifies the analysis by reducing it to a time-dependent ordinary differential equation. It is valid when the Biot number is low, meaning the internal conduction resistance is negligible compared to the convection resistance at the surface.

Transient Temperature Charts

Graphical tools used to determine temperature distributions and time responses in heat conduction problems where significant spatial temperature gradients exist within the object. They are more appropriate when the Biot number is high and the assumption of a uniform temperature distribution (as in lumped system analysis) does not hold.

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