Context : The influence of stellar activity on the fundamental properties of stars around and below 1 M _ { \sun } is not well understood .
Accurate mass , radius , and abundance determinations from solar-type binaries exhibiting various levels of activity are needed for a better insight into the structure and evolution of these stars .

Aims : We aim to determine absolute dimensions and abundances for the solar-type detached eclipsing binary V636 Cen , and to perform a detailed comparison with results from recent stellar evolutionary models .

Methods : uvby light curves and uvby \beta standard photometry were obtained with the Strömgren Automatic Telescope , radial velocity observations with the CORAVEL spectrometer , and high-resolution spectra with the FEROS spectrograph , all at ESO , La Silla .
State-of-the-art methods were applied for the photometric and spectroscopic analyses .

Results : Masses and radii that are precise to 0.5 % have been established for the components of V636 Cen .
The 0.85 M _ { \sun } secondary component is moderately active with starspots and Ca ii H and K emission , and the 1.05 M _ { \sun } primary shows signs of activity as well , but at a much lower level .
We derive a [ \mathrm { Fe / H } ] abundance of -0.20 \pm 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 \sim 10 \% larger and \sim 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 [ \mathrm { 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 .
The orbit is eccentric ( e = 0.135 \pm 0.001 ) , and apsidal motion with a 40 % relativistic contribution has been detected .
The period is U = 5 270 \pm 335 yr , and the inferred mean central density concentration coefficient , log ( k _ { 2 } ) = -1.61 \pm 0.05 , agrees marginally with model predictions .
The measured rotational velocities , 13.0 \pm 0.2 ( primary ) and 11.2 \pm 0.5 ( secondary ) km s ^ { -1 } , are in remarkable agreement with the theoretically predicted pseudo-synchronous velocities , but are about 15 % lower than the periastron values .

Conclusions : 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 \it inactive main sequence stars .
More binaries are , however , needed for a description/calibration in terms of physical parameters and level of activity .