The article presents a one-dimensional mathematical model for simulating the transient processes which occur in liquid flat-plate solar collectors. The proposed method considers a collector model with distributed parameters. In the model, the boundary conditions can be time dependent. The proposed model is based on solving equations which describe the energy conservation for the glass cover, air gap between cover and absorber, absorber, working fluid, and insulation. The differential equations derived were solved using the implicit finite-difference method in an iterative scheme. All thermo-physical properties of the fluid, absorber and air gap are computed in real time. The time-spatial distributions of heat transfer coefficients are also computed in the on-line mode. In order to experimentally verify the proposed method, a test bench was built and measurements were carried out. Comparing the measurement results of the transient fluid temperature at the collector outlet with computational results, satisfactory convergence is found. The proposed method is appropriate for the verification of the effectiveness of various absorbers and their surface coatings, without the need to carry out research on existing collectors. It allows the influence of fluid mass flowrate on the collector performance to be analysed and collector time constant to be determined. The presented model is suitable for collectors working in a parallel or in a serpentine tube arrangement with single or double covers.

The paper presents a one-dimensional mathematical model for simulating the transient processes which occur in the liquid flat-plate solar collector tubes. The proposed method considers the model of collector tube as one with distributed parameters. In the suggested method one tube of the collector is taken into consideration. In this model the boundary conditions can be time-dependent. The proposed model is based on solving the equation describing the energy conservation on the fluid side. The temperature of the collector tube wall is determined from the equation of transient heat conduction. The derived differential equations are solved using the implicit finite difference method of iterative character. All thermo-physical properties of the operating fluid and the material of the tube wall can be computed in real time. The time-spatial heat transfer coefficient at the working fluid side can be also computed on-line. The proposed model is suitable for collectors working in a parallel or serpentine tube arrangement. As an illustration of accuracy and effectiveness of the suggested method the computational verification was carried out. It consists in comparing the results found using the presented method with results of available analytic solutions for transient operating conditions. Two numerical analyses were performed: for the tube with temperature step function of the fluid at the inlet and for the tube with heat flux step function on the outer surface. In both cases the conformity of results was very good. It should be noted, that in real conditions such rapid changes of the fluid temperature and the heat flux of solar radiation, as it was assumed in the presented computational verification, do not occur. The paper presents the first part of the study, which aim is to develop a mathematical model for simulating the transient processes which occur in liquid flat-plate solar collectors. The experimental *