Non-local Heat Flow in a Sheared Slab with a Single-helicity Island

In this work, we review the derivation and implimentation of non-local closures\footnote{E. D. Held, J. D. Callen and C. C. Hegna, Phys. Plasmas 10, 3933 (2003).} for $\vec{q}_\|$ in the electron and ion plasma temperature equations which are valid in all geometries and for plasmas of all collisionalities. We then apply the closures to a plasma embedded in a magnetic field with a single-helicity perturbation. We compare quantities such as effective radial thermal diffusivity ($\chi_r$) and on-axis plasma temperature with those obtained using a flux-limiting and a local diffusive form for the closure. Calculations are made in sheared-slab geometry using new algorithms for rapid approximation of the heat-flow integrals. A description of the algorithms will be presented along with results from validity and convergence tests.