Lumped Capacitance Method

Lumped Capacitance really means that heat transfer is a function of time only.

- Dr. Paul

Lumped Capacitance Method is a continuation of the ideas laid down in thermal circuits. As the name suggests we now have a thermal capacitance, .

This method is an approximation and it only works is there is no temperature gradient across the object. This can be quantified by checking to make sure the biot number is much smaller than 1. See ME3304 S24 Lecture Note (2) Conduction.

Given a solid of a high temperature that is in an environment that rapidly changes temperature (for example heat treating metal) we imagine that the solid is a capacitor (or battery). As soon as our solid changes environment it will start to discharge its energy as heat.

Equation 5.4 (temperature difference):

Equation 5.5:

Where is density, is volume, is specific heat, is convection heat transfer coefficient, is cross-sectional area, and is time. The component in front of the natural log () is used frequently and is called the thermal time constant.

Equation 5.6:

See also ME3304 S24 Lecture Note (2) Conduction.

Where and are the convection thermal resistance and and are the lumped capacitance coefficient.

Relating to thermocouple somehow.

An example of a problem using this method can be found in ME3304 Conduction Previous Test Solution.

Allows you to write energy-stored as the following?

See 6E - Class 2 - Transient Heat Transfer 2024-02-26 17_38_48.