Viscous decay in dwarf-nova outbursts is studied using self-similar solutions. We find that the brightness temperature distribution of the dwarf nova Z Cha in outburst, obtained by the eclipse mapping methods, is well-reproduced by a self-similar solution. The temperature distribution of this solution is close to that of the steady disc (T(e) proportional r-3/4, where T(e) is the effective temperature) at inner radii, but the mass-flow rate through the disc gradually decreases with increase in radius and becomes negative (mass outflow) beyond a certain radius. The original self-similar solution with constant angular momentum, however, produces longer decay times (longer than a month) than the observed values (a few days). To avoid this difficulty, we need to assign large values for the viscosity parameter, alpha(> 1), or to efficiently remove angular momentum from hot portions of the disc by some mechanism, such as the thermal instability predicted by the disc instability model.