Numerical Investigation of Overburden FailureMechanisms and Structural Evolution in Partial Gob-BackfillingMining of Steeply Inclined Coal Seams

Abstract

This study investigates the linear stability of double-diffusive convection in magnetic nanofluids (MNFs) within a horizontal porous medium, accounting for field–dependent viscosity (FDV). A modified Buongiorno– type model incorporates Brownian motion, thermophoresis, magnetophoresis, and Darcy resistance. The resulting eigenvalue problem is solved via a Chebyshev pseudospectral–QZ algorithm under rigid–rigid (RR), rigid–free (RF), and free–free (FF) boundary conditions for both water–based (W b) and ester–based (E b) MNFs. Results show that magnetic and solutal effects lower the critical Rayleigh number (Ra c) from the classical Darcy–Bénard limit of≈39.48 to as low as ≈23.8, indicating enhanced instability. In contrast, increasing the FDV coefficient (δ), Langevin parameter (α

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