Hi Yi, in this case I would suggest to use the HDF5 package https://github.com/timholy/HDF5.jl. It supports reading and writing julia data file (.jld) if you want to write whole variables. If you want something more portable that you can read from other applications you can use plain HDF5 files. It is possible to read and write slices of arrays to h5 files, so for your heat equation example you would have a 1D array in your julia memory that you iteratively update and write consecutive slices to the h5 file.
Fabian
