The paper presents a mathematical solution of the one node transient equation for a flat-plate collector by removing approximations like mean fluid temperature and constant initial temperature used in earlier Am solutions of the equation. Analytical expressions have been obtained for many cases of practical interest. Test procedures for flat-plate collectors often involve transient studies. Deconvolution of these results and extraction of the desired parameters of the collector become easier with the analytical expression obtained here as compared to the numerical methods used earlier. The theory also allows us to predict the performance of the collector under various pumping conditions and can be applied to actual field conditions when storage and load are included. (c) 2004 Elsevier Ltd. All rights reserved.