Analytical Solution of the Transient Heat Conduction in the Absorber Tube of a Parabolic Trough Solar Collector Under Quasi-Steady Conditions

Temperature fields and their transient behaviors are essential subjects to be considered for modeling and design of absorber tubes in concentrated solar power plants. Both subjects have been addressed by various authors. However, the first subject has been primarily solved in the steady state. While the second has been solved by considering transient variations in the environmental or operating conditions, but with a heat conduction model in steady state. To the best of our knowledge, there are no analytical transient two-dimensional (2D) (r, phi) solutions involving nonuniform heat flux distribution (NUHFD) on the absorber tube of a parabolic trough solar collector (PTC). This study aims to obtain an analytical solution for the transient heat conduction in 2D of the absorber tube. The analytical solution was obtained using the method of separation of variables and the superposition principle. Two NUHFD functions were analyzed: a step function and a local concentration ratio (LCR) function. To the first function, the effect of the inlet fluid temperature and efficiency were also studied. The results agree with experimental and numerical results from the literature. The maximum average root-mean-square was near 6.4% for the step function, while the maximum average error was 1% for LCR function. The theoretical energy balances corroborate the validity of the analytical solution. The analytical solution could be useful to compare other theoretical studies (e.g., to prove new numerical schemes), to simulate other parameters of design, and to calibrate experimental tests. Even this work could be extended for nonlinear boundary conditions.