compressible-couette-flowlisted

Use when you must compute the exact constant-property solution for compressible Couette flow in a high-Mach plate gap: the linear velocity profile u = Ue y / h, the Crocco energy-integral temperature profile, the insulated moving-plate temperature from the recovery relation r = Pr, the wall shear tau_w = mu Ue / h, the wall heat flux q_w into the stationary plate and the dissipation energy-balance check at a given plate Mach number, Prandtl number and gap Reynolds number. Produces the full gap solution with velocity and temperature profiles. Trigger: compressible-couette-flow, shear-driven-gap-flow, crocco-energy-integral, gap-reynolds-number, plate-gap, linear-velocity-profile, moving-plate, high-mach-plate-gap.
ashfordeOU/aero-agent-skills · ★ 0 · AI & Automation · score 78

Install: claude install-skill ashfordeOU/aero-agent-skills

# Compressible Couette Flow (aerodynamics/high-speed/compressible-couette-flow) Use when you must compute the exact constant-property solution of the shear-driven plate gap in a high-Mach Couette flow: a stationary cold plate at y = 0 held at the static temperature T_e and an insulated (adiabatic) moving plate at y = h dragged at the edge velocity Ue = Me * a(T_e). The velocity profile is exactly linear, the temperature profile follows the Crocco energy integral over that linear profile, and the moving plate is not cooled, so its surface floats to the recovery temperature and every joule of viscous dissipation leaves through the stationary plate. This is the canonical closed-form anchor of the aeroheating vein, useful as a laminar-regime heating estimate for a plate gap and as a CFD verification case. It pairs with aerodynamics/high-speed/flat-plate-skin-friction-heating (the EXTERNAL boundary layer on a plate with regime-dependent recovery factors) and aerodynamics/high-speed/aerodynamic-heating (stagnation-point heating): those are different geometries and different recovery physics, while this leaf owns the INTERNAL shear-driven gap with the identity r = Pr. Fully closed form, pure stdlib. ## Domain quick reference - Edge state: sound speed of the stationary-plate gas a_e = sqrt(gamma R T_e), moving-plate velocity Ue = Me * a_e (edge_velocity). Constants: GAMMA = 1.4, R = 287.0, and the derived CP = GAMMA * R / (GAMMA - 1) = 1004.5 J/(kg K), PR = 0.72, MU = 1.8e