Linear stability analysis on the onset of the viscous fingering of a miscible slice in a porous medium

► A new approach has been applied to study the onset of miscible viscous fingering in finite slice. ► The effect of finite slice on the instability has been considered in the analysis. ► Initial growth rate has been conducted without the quasi-steady state approximation (QSSA). ► The analytical eigenanalysis without QSSA and the numerical shooting method under QSSA has been compared.