Thermomechanical coupling in frictionally heated circular Couette flow

Tile thernaonaeclaanical coupling in circular Couette rheometers is investigated. Asymptotic solutions of second order in tile Brinkman number. Br, are developed Ibr Newtonian fluids whose viscosity and thermal conductivity can bc expressed as quadratic functions of temperature. The derived solutions are validated by comparison to previously published series solutions as the limit of planar Ilow is approached as well as to numerical solutions and are found to be reliable Ibr a practical range of the Nahme number. These solutions are explicit in Br and in the properties of the Iluid and thus provide yah,able insight into the functionality of tile relevant dependences, something that is lost in purely numerical solutions.