This paper presents the geothermal analysis of Uturu-Nigeria using the Rayleigh-Ritz-Chebyshev collocation method. To develop the optimal geothermal design parameters for theUturu-okigwe axis, the developed model was used to analyze the geothermal performance and investigate the effects of geothermal parameters using a longitudinal fin. The results, however, showed that whenever there is an increase in convective, radioactive, and magnetic parameters, the rate of heat transferred from the geothermal longitudinal fin increases. The result also showed that the Rayleigh-Ritz-Chebyshev spectral collocation method providedthe best fit for analyzing the geothermal parameters of Uturu.