Question

3. (40pts) | In the thermal system shown in Figure 7-28(a), it is assumed that the tank is insulated to eliminate heat loss to the surrounding air, that there is no heat storage in the insula tion, and that the liquid in the tank is perfectly mixed so that it is at a uniform temper ature. (Thus, a single temperature can be used to denote both the temperature of the liquid in the tank and that of the outflowing liquid.) It is further assumed that the flow rate of liquid into and out of the tank is constant and that the inflow temperature is constant at 6,C Fort < 0, the system is at steady state and the heater supplies heat at the rate H J/s. At t0, the heat input rate is changed from H to H + hJ/s. This change causes the outflow liquid temperature to change from 50 to o + θ°C. Sup- pose that the change in temperature, θ°C, is the output and that the change in the heat input, h J/s, is the input to the system. Determine the transfer function (s)/H(s),where 6(s) se[θ(t)) and H(s) se[h(t). Show that the thermal system is analogous to the electrical system of Figure 7-28(b), where voltage eo is the output and current i is the input. Solution Define G - liquid flow rate, kg/s c-specific heat of liquid, J/kg-K M - mass of liquid in the tank, kg R-thermal resistance, K-s/J C-thermal capacitance, J/K ho- change in heat added to outflowing liquid, J/s en Hot uid Heater Mixer Cold liquid

Answer 1

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