Combination of Karhunen-Loève and intrusive polynomial chaos for uncertainty quantification of thermomagnetic convection problem with stochastic boundary condition

•Uncertainty propagation analysis of thermomagnetic convection problem with stochastic boundary condition was investigated.•A novel and comprehensive computational framework based on intrusive polynomial chaos was proposed.•The expression for the chaos expansion of a six-dimensional second-order Hermite polynomial was derived.•The intrusive polynomial chaos expansion approach offers a precise and efficient prediction of the evolution characteristics of random boundary during the process of thermomagnetic convection.•The statistical characteristics from the intrusive polynomial chaos approach, exhibit a remarkable consistency with those from the direct Monte Carlo approach.