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THE END * 电气信息工程学院自动化教研室 Thermal Systems Modeling of thermal systems by linear differential equations is generally not as common as the other systems since thermal systems tend to be generally nonlinear. However, in order to obtain a first approximation we shall linearize the systems about an appropriate operating point. Often this results in the assumption that the physical system under consideration be characterized by one uniform temperature. The fundamental concept used for deriving the thermal system equation is that the difference of heat coming into and leaving a body is equal to the increase of the thermal energy of the system. The physical properties used are mass, specific heat, thermal capacitance, conductance, and resistance. Temperature is the driving potential and heat is the quantity which flows. Generally, thermal resistance is defined as * 电气信息工程学院自动化教研室 Where is the temperature difference and q the heat flow. Depending upon the system, R may include the contributions of thermal conduction, convection, and radiation. The thermal capacitance C is the product of mass and specific heat and Consider a mass m dropped into an oil bath at temperature .we shall assume that the temperature is uniform inside the mass at any given time and also that the oil bath temperature is constant. The heat entering the mass from the oil at any time is Thermal Systems * 电气信息工程学院自动化教研室 Where is the temperature of the mass. Here R=1/ hA where A is the surface area of mass in contact with the oil and h is the heat transfer coefficient due to convection. This heat entering the mass goes to increase the heat content (or internal energy) of the system, i.e. Equating Eq. (2-16) to Eq. (2-17) we have Defining we obtain Which is a first-order differential equation. For obtaining the transfer function we assume that the initial temperature of the mass is . Letting , Laplace
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