Parametric and sensitivity analysis of a nonlinear flat-plate solar air collector model: An analytical study

This study presents a semi-analytical solution for the nonlinear heat transfer equation governing a flat-plate solar air collector using the Temimi–Ansari Method (TAM) . The model accounts for temperature-dependent specific heat capacity, which introduces a significant nonlinearity into the system. A closed-form solution is constructed up to the 14th-order approximation, and its accuracy is validated against the numerical Runge–Kutta method. Furthermore, sensitivity analysis is conducted for key parameters such as collector width (W), effective transmittance–absorptance product ( τ α), mass flow rate ( m • ) , and heat loss coefficient (U L ). The analysis demonstrates that increasing the product of transmittance and absorptance ( τ α) significantly enhances the outlet temperature rise (ΔT), while higher heat loss coefficients (U L ) cause substantial performance degradation, especially in longer collectors. Mass flow rate exhibits an inverse effect on ΔT due to increased thermal capacity, whereas greater collector width improves heat gain by increasing the absorption area. These findings highlight that optimizing optical and insulation properties can yield the most substantial gains in efficiency, making the proposed approach a practical and accurate tool for solar thermal system design.