#### Lumped Capacitance Method for Analyzing Transient Conduction Problems: Screencasts

Derives the lumped capacitance method and explores one of its major limitations.

We suggest that after watching this screencast, you list the important points as a way to increase retention.

A second introductory screencast

We suggest that after watching this screencast, you list the important points as a way to increase retention.

##### Important Equations:

The Biot number, \(Bi\) is a dimensionless quantity defined by this equation:

\[Bi = \frac{hL_c}{k}\]

where \(h\) = heat transfer coefficient \((W/m^2-K)\) or \((W/m^2-^{\circ} C)\),

\(L_c\) = characteristic length \((m)\), and

\(k\) = thermal conductivity \((W/m-K)\) or \((W/m-^{\circ}C)\).

The characteristic length is defined by

\[L_c = \frac{V}{A}\]

where \(V\) = volume of the object \((m^3)\), and

\(A\) = area of the object \((m^2)\).

Conservatively, the characteristic length can be the distance between the temperature extremes, such as the radius in the case of a sphere.

You must confirm that \(Bi\) < 0.1 before using the following equation, which is used to predict temperature as a function of time:

\[T = T_{\infty} + (T_i \,-\, T_{\infty})e^{-\frac{hAt}{\rho Vc}}\]

where \(T\) = temperature at time \(t \, (s)\),

\(T_{\infty}\) = temperature of the surrounding fluid,

\(T_i\) = object’s initial temperature,

\(\rho\) = object’s density \((kg/m^3)\), and

\(c\) = object’s heat capacity \((J/kg-K)\) or \((J/kg-^{\circ}C)\).