In this thesis, magnetic and porous media thermoacoustic systems have been investigated by developing rigorous mathematical models and subsequent experiments. The inherent irreversibility of the thermoacoustic stack is analyzed in the presence of a magnetic field applied across the stack perpendicular to the direction of fluid oscillations to improve the stack efficiency. Two different types of stacks are considered for the analytical modelling:​ a porous medium coupled with a thick solid plate and a multi-plate stack with a transverse magnetic field.

For the porous medium coupled with a thick solid plate stack, the analytical expressions of the fluctuating velocity and temperature of the oscillating fluid are derived from the governing Darcy momentum and energy equations. Consequently, the simplified analytical expressions for the Nusselt number, heat flux, work flux, entropy generation rate, and the efficiency are derived and presented graphically. It is observed that the thermoacoustic irreversibility can be minimized by increasing the applied magnetic field resulting in increased efficiency of the system.

For the multi-plate thermoacoustic stack, the effects of magnetic field on the heat transfer are analyzed using complex Nusselt number. The unsteady-compressible-viscous forms of the continuity, momentum, and energy equations are used to derive the analytical solution for the fluctuating velocity and temperature. Then, the simplified analytical solutions for the complex Nusselt number are derived. The first order analytical equations for the energy, heat, and work fluxes for a thermoacoustic refrigerator are also derived and presented graphically. In the absence of a magnetic field, all of these simplified analytical expressions are compared with the data available in the literature and an excellent agreement is observed.

Finally, an experimental setup is designed and constructed which is utilized to measure the performance of porous medium thermoacoustic refrigerator and heat pump systems. The stack length and position of a prototype thermoacoustic refrigerator are optimized using numerical, analytical, and experimental analysis. For an optimal stack length (175mm) and position (42mm from the acoustic driver’s end) at a constant frequency and drive ratio, the maximum temperature of 88.9 °C at the hot end and -8.5 °C at the cold end of the stack are achieved. The maximum cooling capacity achieved is 17.85 watts at 5.42% coefficient of performance relative to the Carnot’s coefficient of performance. The results from the thermoacoustics theories developed in this thesis can be potentially applied to design the next generation thermoacoustic systems.