Modelling and economic optimisation of under-floor heating system

Abstract

Modelling and optimisation of the under-floor heating system (UFHS) with Pex pipes are studied in this paper. For modelling the system, two regions were considered. The first one was the over-floor region which included room air and walls. This region was considered as one control volume and the system of non-linear energy equations for room air and walls were solved using Newton–Raphson method. The second or under-floor region included heating pipes, concrete and floor finish. This region was modelled using finite volume method. For optimising the UFHS, an objective function (sum of investment and operating costs of UFHS) was proposed and type and thickness of the floor finish, velocity of hot water passing through the pipe, concrete thickness and pipe diameter, were considered as the decision variables (design parameters). The sensitivity analysis showed 19.8%, 10.5%, 2.8% and 0.3% increase in the objective function with the deviation of the four above-mentioned design parameters from their optimum values (floor finish from tile to marble, water velocity from 1.5 to 2.5 m/s, concrete thickness from 6 to 8 cm and pipe diameter from ½ to ¾ in.). Finally, with the decrease in external temperature from −10°C to −20°C, the objective function increased by 21.7% and the required floor heat flux increased by 33.1%. Increasing the insulation thickness from 2.5 to 7 cm also decreased the objective function by 20.5% and decreased the required floor heat flux by 38.5%. Practical application: A new and fast combined numerical and analytical procedure for thermal modelling of UFHS was proposed in this paper. By applying the proposed modelling procedure, the optimum values of UHFS design parameters for reaching the system lowest cost were obtained. The variation of total cost with deviation of design parameters from their optimum values was investigated. The effects of change in atmospheric temperature and wall insulation thickness on building thermal load and the total cost were studied.