TIME-AVERAGE TEMPERATURE DISTRIBUTION IN A THERMOACOUSTIC STACK

The three-dimensional time-average temperature distribution in a pore of a thermally isolated thermoacoustic stack is calculated. A boundary -value problem is formulated in the acoustic and short-stack approxima tions from the equation of conservation of energy using literature res ults for the time-average energy flux. In the central region of the po re, the solution for the time-average temperatures of the wall, T-w, a nd of the gas along its center line, T-g, share a common profile, line ar in the axial coordinate, z. Near the pore ends, where the energy fl ux approaches zero, the axial gradient of T-g approaches the critical temperature gradient over a distance of order the acoustic displacemen t amplitude. The axial gradient of T-w approaches zero over a much sma ller distance, provided the wall has small thermal conductivity. The t ransverse heat-flux density, q, is nonzero only near pore ends. Under certain conditions, q=h(1)(T-g-T-w), where h(1) is proportional to the thermal conductivity of the gas divided by the thermal penetration de pth. The constant of proportionality, of order unity, depends on pore width and Prandtl number. Results agree favorably with recently publis hed numerical calculations. (C) 1998 Acoustical Society of America.