Here is a possible solution:
\documentclass[10pt,a4paper]{article}
\usepackage{amsmath}
\usepackage{array}
\begin{document}
\begin{table*}[tb]
\centering
\caption{Device Modelling Specifications.}
\label{tab:deviceModelling}
\begin{tabular}{|m{2.4cm}|m{1.4cm}|m{1.4cm}|m{1.4cm}|}
\hline
\textbf{Fist model} &
{\begin{align*}
a &= b\\
a2 &= b2
\end{align*}} &
another cell & last cell\\
\hline
dummy & text & I & entered\\
\hline
\end{tabular}
\end{table*}
\end{document}
As David Carlisle put it in his comment, you will need a paragraph type of cell, so l, r or c columns won't do. I assumed you would like to have things centered vertically, so I chose type m (note that this option requires the array package). If you have other preferences, instead of m you can use p (top) or b (bottom).
The amsmath package will give you the possibility to use the align environment, as I did in the example. You can also choose from a wide variety of environments described in the amsmath documentation.
One last thing: The entire align environment is put between curly braces, because otherwise LaTeX will try to expand it at the wrong moment and the document will not compile. This comes from the fact that align uses & to set the alignment points and the same character is used as a cell separator in tabular. Of course in an environment without ampersand (e.g. multline) there is no need for these braces.
pcolumns or other par-mode contexts as in your commented out line. They may not be inccolumns which have to be one line. – David Carlisle Jun 30 '12 at 11:39