Consider heat transfer between two identical hot solid...

Consider heat transfer between two identical hot solid bodies and the air surrounding them. The first solid is being cooled by a fan while the second one is allowed to cool naturally. For which solid is the lumped system analysis more likely to be applicable? Why?

Key Concepts

Lumped System Analysis

Lumped system analysis is an approach in transient heat transfer problems that assumes the temperature within the object is spatially uniform, meaning that it can be treated as a single temperature node. This assumption simplifies the analysis by reducing the complex conduction problem to an ordinary differential equation, but it is valid only when internal thermal resistance is negligible compared to the resistance to heat transfer at the surface.

Biot Number

The Biot number is a dimensionless parameter defined as the ratio of internal thermal resistance to external convective resistance. A small Biot number (typically less than 0.1) indicates that the temperature gradients within the solid are minimal, thereby validating the lumped system approach. It plays a critical role in determining whether the lumped capacitance model is applicable.

Convection Heat Transfer

Convection heat transfer involves the transfer of heat between a solid surface and a fluid moving over it. The effectiveness of this process depends on the convective heat transfer coefficient, which varies with the fluid flow conditions, and has a direct influence on the thermal resistance at the surface of the solid.

Forced vs. Natural Convection

Forced convection occurs when fluid motion is induced by external means such as a fan or pump, typically resulting in a higher convective heat transfer coefficient compared to natural convection, where fluid motion is caused by buoyancy effects. The difference in the convective heat transfer coefficients directly affects the Biot number, altering the conditions under which lumped system analysis is valid.

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