Two film cross-sections are heated by the same hotspot for the same time, with the same cold sink underneath. The top panel is an ordinary isotropic plate (equal conductivity in every direction): heat digs straight down in a half-circle. The bottom panel is a graphene-like film whose in-plane conductivity k∥ is tens of times its through-plane k⊥ (illustrative — real film ratios span a wide range): heat races sideways along the plane first, painting a wide bright band before it crosses the thickness. The small gauge beside each panel shows the same physics as moving energy pulses: orange pulses race along the plane at the in-plane rate, blue pulses crawl across the thickness — and in the isotropic panel all four move alike. That side-by-side difference is the whole story of why graphene films excel as lateral heat spreaders.
Model: two independent explicit finite-difference solutions of ρcp ∂T/∂t = k∥∂²T/∂x² + k⊥∂²T/∂z² on identical normalized cross-section grids, advanced in lockstep: the same constant hotspot on the top face, the bottom face pinned cold, insulated sides, and one fixed conservative time step shared by both panels and every ratio (below the explicit-scheme stability limit), so the two materials are always compared at the same dimensionless time. The top panel is pinned at k∥/k⊥ = 1; the slider sets the bottom panel’s diffusivity ratio, which equals its conductivity ratio only when volumetric heat capacity is approximately direction-independent, as assumed here. Vertical scale exaggerated for visibility — a schematic of directional spreading, not a simulation of any specific film or device.