Transient simulation of a storage floor with a heating/cooling parallel pipe system

The exact 2-D transient solution of a slab with an embedded array of parallel circular pipes for heating/cooling is developed. The boundary and initial conditions are: constant temperature at the pipe surface, upper slab surface subjected to convection heat transfer, thermal insulation at the slab bottom, and constant initial temperature. The analytical solution of the transient bi-dimensional problem is obtained together with the fluid temperature. A calculation example is analysed at the end of the paper to enlighten practical issues appearing in the computation of the analytical solution.