AbstractThe velocity and temperature profiles for an impulsively started Couette flow have been derived for a fluid with a high and strongly temperature‐dependent viscosity when the flow takes place through a porous medium. The steady as well as the transient state flows are discussed and the influence of the medium permeability is assessed. In the steady state the presence of the porous medium causes higher maximum temperatures only for sufficiently low permeabilities and in all cases significantly lower velocity profiles. The flow development times tend to be higher for the low permeabilities only for high Nahme numbers. For the transient state it is noticeable that, in all cases, the velocity develops much more rapidly than the temperature and that the presence of the porous medium accelerates this tendency. Finally the medium permeability produces skew temperature profiles and higher temperature time gradients at all time