The influence of stellar activity on the fundamental properties of stars around and below 1 Msun is not well understood. We aim to determine absolute dimensions and abundances for the solar-type detached eclipsing binary V636 Cen. The results are based on uvby light curves, uvby-beta standard photometry, radial velocity observations, and high-resolution spectra. Masses and radii that are precise to 0.5% have been established for the components of V636 Cen. The 0.85 Msun secondary component is moderately active with starspots and CaII H and K emission, and the 1.05 Msun primary shows signs of activity as well, but at a much lower level. We derive a [Fe/H] abundance of -0.20+/-0.08 and similar abundances for Si, Ca, Ti, V, Cr, Co, and Ni. Corresponding solar-scaled stellar models are unable to reproduce V636 Cen, especially its secondary component, which is ~10% larger and ~400 K cooler than predicted. Models adopting significantly lower mixing-length parameters l/H_p remove these discrepancies, seen also for other solar-type binary components. For the observed [Fe/H], Claret models for l/H_p = 1.4 (primary) and 1.0 (secondary) reproduce the components of V636 Cen at a common age of 1.35 Gyr. V636 Cen and 10 other well-studied inactive and active solar-type binaries suggest that chromospheric activity, and its effect on envelope convection, is likely to cause radius and temperature discrepancies, which can be removed by adjusting the model mixing length parameters downwards. Noting this, the sample may also lend support to theoretical 2D radiation hydrodynamics studies, which predict a slight decrease of the mixing length parameter with increasing temperature/mass for inactive main sequence stars.
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