A house with a $200$ m$2$ living area will be heated by geothermal water flowing through pipes laid in the ground under the slab. The house has a wall height of $4$ m and $10$ single$-$glazed windows with a width of $1\mathrm{.}2$ m and a height of $1\mathrm{.}8$ m$.$ The house has R$-3\mathrm{.}3$ insulation $($m$2.\backslash$deg C$/$W$)$ on the walls and R$-5\mathrm{.}3$ insulation on the ceiling. The floor temperature will not exceed $40\backslash$deg C$.$ The hot geothermal water is $90\backslash$deg C and the inner and outer diameters of the pipes to be used are $2\mathrm{.}4$ cm and $3\mathrm{.}0$ cm$.$ Design a heating system for this house.