The instability of magnetohydrodynamic (MHD) duct flow is crucial in related industrial applications. The laminar flow in rectangular ducts at different Hartmann numbers (Ha = 100 to 1200) and wall conductance ratios (C = 0.001 to 5), as well as for two types of nonuniform conducting walls, has been numerically simulated and the instability trend analyzed using the energy gradient theory. The results show that the stability of Hunt’s case II at the core zone increases, the most unstable region appears near the parallel layer, and the stability near the parallel layer gradually weakens as the Ha increases at a constant Reynolds number and wall conductance ratio.

Similarly, the most unstable belt gradually transfers from the Hartmann layer to near the parallel layers as the wall conductance ratio increases at constant Reynolds number and Ha. The trend of the K value demonstrates an initial decrease followed by an increase, indicating that an increase in the wall conductance ratio initially enhances stability before leading to instability.

In the simulation of two types of nonuniform conducting ducts, it was found that the most unstable region in the duct occurred near the Hartmann layer attached to the insulating wall surface, with the Kmax value significantly higher than those of the insulating and uniform conducting ducts. This indicates that the flow in the nonuniform conducting ducts is the most unstable at the same Reynolds number and Ha. This study provides a reference for understanding the internal flow characteristics and stability of MHD flow in conducting ducts.