\textit{Thermal and viscous energy conversion in a thermoacoustic device occurs inside a particular porous material, named stack/regenerator. Viscous losses and thermal exchanges arise thanks to the interaction of an acoustic field and the solid skeleton of a porous material. Its microstructure strongly influences the amount of energy which can be converted or dissipated due to viscous and thermal boundary layers. Thermal and viscous losses are strictly interconnected, meaning that by altering the pore size (i.e. the hydraulic radius) of the microstructure, both thermal and viscous effects are generally affected. However, there are cases where independent control of thermal or viscous effects could be crucial such as in the thermoacoustics devices. Enhancing heat exchanges while minimizing viscous losses becomes necessary to enhance power conversion. This work paves the way to the design of a microstructure suitable for controlling viscous and thermal effects in a relatively independent way.