Effect of magnetic field on the Nusselt number of a multi-plate thermoacoustic system

Abstract

This paper presents the results of heat transfer of a multi-plate thermoacoustic system using complex Nusselt number in the presence of magnetic field. Assuming the applied magnetic field is perpendicular to the direction of the oscillating fluid flow, we derive the expressions for the fluctuating velocity and temperature from the governing unsteady-compressible-viscous forms of the continuity, momentum, and energy equations. These equations are simplified assuming small amplitude oscillations, a long wave, and a short stack. The hydrodynamic and thermal boundary layers are considered to be very small compared to the acoustic wavelength, and the longitudinal conduction heat transfer inside the boundary layers is assumed to be negligible. Both bulk mean and space averaged temperatures are considered as reference temperatures in the analytical solution. The complex Nusselt number equations are simplified and expressed as a function of the Hartmann number (Haδ), the Swift number (Sw), the modified Swift number (S¯w) and Rott’s functions (fν and fk). The effect of Haδ, Sw, and S¯w on the Nusselt number is analyzed and presented graphically for both viscous and inviscid fluids. The value of Nusselt number in the boundary layer limit for the inviscid fluid is also analyzed. In the absence of a magnetic field, the simplified complex Nusselt number expression that is obtained by using the space averaged temperature as a reference temperature is compared with the data available in the literature and an excellent agreement is observed. This study will offer insight into ways to increase convection heat transfer rate, consequently help the thermoacoustic system designer to design a more power dense thermoacoustic system.