Collective Working Regimes for Coupled Heat Engines

Arrays of coupled heat engines are proposed as a paradigmatic model to study the trade-off between individual and collective behavior in linear irreversible thermodynamics. The analysis reveals the existence of a control parameter which selects different operation regimes of the whole array. In particular, the regimes of maximum efficiency and maximum power are considered, giving for the latter a general derivation of the Curzon-Ahlborn efficiency which surprisingly does not depend on whether or not the individual engines in the array work at maximum power.

Figure 1

Array of coupled heat engines.

Figure 2

(a) Plot of $\dot{W}$ (solid line), $J_1=J(T_1)$ (dotted line), and $J_2=J(T_2)$ (dashed line) vs. $\lambda$ [Eqs. (15, 16, 17)] in a model with constant Onsager coefficients. The parameters are (in arbitrary units) $L_{ij}=1$, $T_1=0.5$, and $T_2=1$. (b) Force profiles at maximum efficiency $f_{\mathrm{eq}}(T)$ [Eq. (13), solid line], maximum $\Omega =2\dot{W}-(1-T_1/T_2)J_2$ (dashed line), and maximum power [Eqs. (14, 19), dot-dashed line] for the previous model. The dotted lined represents the force profile $f(T)=f_{\mathrm{eq}}(T)/2$ [7] which follows from the power maximization of each elemental engine individually.