Fibre reinforced thermoplastic are key materials for lightweight structures in the transport industry, but their industrialisation requires the reliable joining of large integrated structures from subcomponents. Induction welding is a promising joining technique, yet it relies on predictive models since direct measurements at the interface are infeasible. Accurate predictive modelling is challenging due to variations in material properties within and between manufactured samples, in addition to the second-order symmetric positive definite (SPD) nature of fundamental properties such as electrical and thermal conductivity [1]. These variations, arising from limited control over the manufacturing process and inherent material variability, necessitate the use of stochastic models that inherently respect the SPD nature of the tensors throughout each realisation. In this work we present the manifold-based random field used to model an uncertain anisotropic and spatially heterogeneous positive definite material property such as electrical or thermal conductivity [2]. The model distinguishes between the uncertainty related to material symmetry and the one describing the magnitude of material constants. The random field is obtained by corresponding nonlinear transformations of the underlying standard Gaussian random field with an anisotropic Matern kernel. Furthermore, the continuous fields are discretized by spectral representations using Galerkin kind of approach. The model is further used to propagate uncertainty in electrical conductivity and quantify its effect on the induction heating process. In particular, the sensitivity analysis is performed to understand effects of both spatial variation as well as material symmetry variation on the resulting temperature field.