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Chapter 3 Mathematical Modelling of Thermodynamic Section
3.1 Introduction
The main purpose of this chapter is to analyse the thermal performance of the CPAP
machine. The physical laws of thermodynamics and heat transfer will be used to
develop governing equations simulating the dynamic system. This will give the
dynamic fluctuating outputs of evaporation in the chamber, temperature changes and
condensations in HADT and the mask. The model can also provide steady state outputs.
Thus it can be used to compare between steady state outputs and breathing-introduced
fluctuating outputs. When using a CPAP machine, all the components and water will be
at the ambient temperature prior to switching it on. When the machine is switched on,
the temperatures will move through a transient phase, until steady-state is achieved.
This thermodynamic model developed in this thesis does not account for this warm-up
period. The breathing-introduced fluctuating situation is a steady-state-based situation.
The system inputs include ambient air conditions, mask size, pressure, heating element
setting, HADT heating setting and patient’s breathe load.
Several generic assumptions and simplifications for the thermodynamic model are listed
below.
The ambient air is simplified as quiescent.
Air is incompressible [39], however, the density can be considered different due
to different temperature and different pressure at different locations.
The water in the chamber is considered quiescent [19].
3.2 Airflow in ADU
As mentioned in the fluid dynamic analysis, the ADU is a centrifugal blower and is
simplified as a zero order device. Due to inefficiency, some of the electric energy will
be wasted in the form of heat losses. The heat raises the temperature at the blower and
its vicinity and also raises the temperature of airflow passing through it. Compression of
air in the blower may also increase the temperature. Factors influencing the airflow
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