Application of the Bernoulli wavelet method on the convective-radiative Fin with heat generation

This study explores the application of the Bernoulli wavelet method (BWM) to analyze the thermal performance of convective-radiative fins with heat generation. These fins play a critical role in enhancing heat transfer efficiency in engineering systems, making accurate thermal analysis essential. The governing nonlinear differential equation, derived from the energy balance, accounts for conduction, convection, radiation, and internal heat generation. The BWM is employed to discretize the highly nonlinear governing equation into a system of algebraic equations, which are solved numerically. The wavelet approach ensures high computational accuracy and efficient convergence, even for highly nonlinear scenarios. Key parameters, including thermal conductivity variation, convective and radiative heat transfer coefficients, and the heat generation rate, are systematically analyzed to assess their impact on temperature distribution. The results are validated against existing numerical and analytical solutions, demonstrating the reliability and accuracy of the proposed method. This research highlights the BWM as an effective tool for solving complex nonlinear heat transfer problems in thermal systems.