Stability characteristics of variable-gravity channel flows with partial porous filling: A dual linear–nonlinear study

This study investigates the influence of variable gravity on the onset of convection in a channel partially filled with a porous medium and overlying fluid layer. The gravitational acceleration is assumed to vary vertically according to four distinct functional forms: (i) Gz=−z, (ii) Gz=−z2, (iii) Gz=−z3 and (iv) Gz=−ez−1. Linear stability is analysed using the normal mode technique, while nonlinear stability is examined through the energy method. The resulting eigenvalue problem is solved via the Chebyshev–Tau–QZ spectral approach. The findings reveal that the functional dependence of gravity significantly affects system stability: the linear profile exerts the strongest stabilizing influence, delaying convection, whereas the exponential profile is the least stabilizing, promoting earlier onset. Streamline and isotherm patterns illustrate the profound impact of variable gravity on flow structure linear gravity induces intense, symmetric rolls near the heated base, while higher-order or exponential profiles weaken and localize convection, confining motion to thin boundary layers. The study demonstrates that steeper or rapidly decaying gravity fields suppress large-scale convective motion and limit heat transport to near-wall regions. Beyond theoretical relevance, these findings have practical implications for environmental engineering, geothermal energy extraction, and microgravity research, where understanding convection under non-uniform gravitational fields is essential for accurate modelling of fluid–porous systems.