How to run an alias in a shell script?

Alias are deprecated in favor of shell functions. From bash manual page:

For almost every purpose, aliases are superseded by shell functions.

To create a function, and export it to subshells, put the following in your ~/.bashrc:

petsc() { ~/petsc-3.2-p6/petsc-arch/bin/mpiexec "$@"
}
export -f petsc

Then you can freely call your command from your scripts.