Author(s): Professor William G. GRAY IAHR Membe; Professor Mohamed Salah Ghidaoui IAHR Member
Keywords: Channel flow; Dissipative processes; Minimum entropy generation; Stream flow; Stream thermodynamics; Thermodynamically constrained averaging theory
Abstract: The equation for entropy generation is derived directly from the conservation equations for one-dimensional (1D) channel flow. Mass, momentum, and energy equations are averaged from their microscale forms to the 1D forms used in channel modeling while allowing for channel curvature. The equations of classical irreversible thermodynamics are also averaged so that macroscale energy and entropy are consistently and uniquely related. These averaged equations serve as constraints on an averaged entropy inequality so that the dissipative processes are quantified and can be analyzed for cases where the rate of entropy production is minimized. Specifically, the case of uniform flow in a prismatic channel is presented; and the entropy production rate is obtained. Also, the case of gradually varied flow in a wide rectangular channel is presented and analyzed for conditions of a minimum rate of entropy production. For both these cases, the impact of a nonuniform velocity profile over the flow cross section is accounted for.