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In order for superconducting coil applications to operate safely at high current densities, thermal stability of the wire must be addressed in terms of quench development and protection. In this study, we investigate quench propagation in stacks of commercially available MgB2 superconducting wire taking into account both longitudinal heat transfer along the wire and transverse heat transfer across the insulation to adjacent wire segments. We present a two-dimensional Finite Element Method model, to simulate quench propagation. Wires and insulation layers are explicitly modeled as separate subdomains, where the wire domain takes into account the composite nature of these tapes. We report results for Minimum Quench Energy and Quench Propagation Velocity as a function of operating temperature and applied magnetic field. We also present a comparison of the behavior of the present model to alternative formulations where layers of tape and insulation are treated as a homogeneous single domain with lumped properties.