Abstract
System thermal modeling allows heat and temperature simulations for many applications, such as refrigeration design, heat dissipation in power electronics, melting processes and bio-heat transfers. Sufficiently accurate models are especially needed in open-heart surgery where lung thermal modeling will prevent pulmonary cell dying. For simplicity purposes, simple RC circuits are often used, but such models are too simple and lack of precision in dynamical terms. A more complete description of conductive heat transfer can be obtained from the heat equation by means of a two-port network. The analytical expressions obtained from such circuit models are complex and nonlinear in the frequency $$\omega $$ . This complexity in Laplace domain is difficult to handle when it comes to control applications and more specifically during surgery, as heat transfer and temperature control of a tissue may help in reducing necrosis and preserving a greater amount of a given organ. Therefore, a frequency-domain analysis of the series and shunt impedances will be presented and different techniques of approximations will be explored in order to obtain simple but sufficiently precise linear fractional transfer function models. Several approximations are proposed to model heat transfers of a human middle bronchus and will be quantified by the absolute errors.
Highlights
Thermal modeling of systems is of particular interest in applications where temperature might be critical
The complexity of heat transfer usually implies the use of finite element methods to solve the heat equation in a chosen region of space
It is usually used in the domain of power electronics [16], building simulation [26, 8] and even to model human heat losses [14, 13]
Summary
Thermal modeling of systems is of particular interest in applications where temperature might be critical. RC circuit models are present in other similar applications, such as the measurement of bio-impedances [5] or lithium-ion battery models [32]. The thermal two-port network models heat conduction in a single direction as a T circuit (see figure 2) with two series impedances Z1(s) and Z2(s) and a shunt impedance Z3(s) These impedance expressions are complex and nonlinear in ω which do not allow obtaining rational transfer functions, the latter being more suited models for control design. It can be shown in high frequency that the thermal impedance of a plane wall is given by a half-order integrator [2, 21]: section 4.
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