AbstractA variational analysis is applied in helical co‐ordinates to the problem of a developed, steady‐state flow in a screw extruder. The functional involves only two dimensionless coordinates and is suitable for minimisation, e.g. by the finite element method. It is applicable to non‐isothermal, purely viscous flows and contains terms representing effects of inertia, convective and conductive transport of heat, pressure gradient, and viscous dissipation. The analysis takes account of the true helical geometry and involves assumptions only in taking the fluid density, specific heat and thermal conductivity of the fluid to be constant, in regarding the fluid to be homogeneous and isotropic, and in simplifying the pressure distribution.