Second law analysis of porous thermoacoustic stack systems

The objective of this paper is to analyze the irreversibility of the porous thermoacoustic stacks in terms of entropy generation. Thermoacoustic stacks are modeled in this paper as porous channels having wall with finite thickness. The flow field in the porous channel is described by the Darcy momentum equation. The thermal field inside the porous stack is modeled by volume averaged energy equation with local thermal equilibrium assumption. While the thermal field inside the solid wall is modeled by the heat conduction equation. The entire problem is treated as a conjugate heat transfer problem. The governing momentum equation inside the porous stack and the energy equations inside both porous stack and solid wall are simplified and linearized using a first order perturbation expansion in the low Mach number limit. The linearized governing differential equations are solved using the complex exponential method. Velocity and temperature results thus obtained are applied for subsequent entropy generation analysis. Entropy generation rate is used as a measure of irreversibilities associated with viscous and heat transfer effects in the porous stack region. For the specific thermoacoustic situation considered in this paper, a time-averaged entropy generation rate followed by local and global entropy generation rates are calculated and graphically presented. The entropy generation distribution in the stack thus enables the designers to find and modify the parameters producing high energy losses characterized by large entropy production rates. A limited experimental work is performed to measure the temperature difference generated across the stack ends. A fair qualitative agreement between the experimental and analytical results is obtained.