Modify the model from problem 12-16 to include the thermal capacitance of the cylinder as well as convection from the cylinder surface to the atmosphere. The heat transfer coefficient for the cylinder inside wall is h1, and for the outside wall it is h2. The thermal capacitance of the wall is CW.
Problem 12-16
Consider the system from Problem 12-5. Neglect thermal capacitance of the piston walls but include leakage past the piston to the atmosphere. Using one thermodynamic accumulator and one 4-port isentropic nozzle, construct a bond graph model of the system. The crank radius is R, crank length is L, piston area is Ap, leakage area is AL, and piston mass is m.
Problem 12-5
Consider the compression of a gas by means of a crank-piston arrangement. Let the cylinder have a single average temperature, and define thermal resistances between the gas temperature T and the cylinder temperature and between the cylinder temperature and the atmospheric temperature T0. Make a bond graph that would allow you to predict the crank torque τ for low speeds of rotation, ω. (Note that you do not have enough information to evaluate all the system parameters.)
