Convective instabilities in the mushy layer during time-dependent solidification in aqueous ammonium chloride solution cooled from below are analyzed under linear stability theory by using propagation theory. The stability equations for liquid and mushy layers are transformed self-similarly by using the developing mushy-layer thickness as a length scaling factor. The critical conditions to mark convective motion in the mushy layer are obtained numerically when the Lewis number is zero. The present predictions compare reasonably well with existing experimental data.