In this study, we investigate the enhancement of horizontal geothermal heat exchangers equipped with helical fins on the pipe's exterior and internally ribbed turbulators. Our approach focuses on the interplay between geometry and thermal efficiency through innovative design modifications. Utilizing the finite element method, three-dimensional numerical simulations assessed the effects of varying geometric parameters such as the diameter and thickness of the fins. Our findings indicate significant increases in heat transfer efficiency with the addition of helical fins; specifically, increasing the fin diameter from 5 mm to 10 mm results in a 15 % increase in the heat transfer rate, while doubling the fin thickness from 2 mm to 4 mm enhances the rate by 10 %. These improvements are due to the expanded surface area facilitating greater heat exchange. Optimization using the desirability function approach yielded models with high performance, achieving desirability scores of 0.9879 for outlet temperature and 0.9534 for the heat transfer coefficient. This reflects the effective tuning of geometric parameters to maximize thermal performance. The study also introduces two predictive mathematical models for the outlet temperature and convective heat transfer coefficient of the U-shaped pipe equipped with these enhancements. These models, derived from extensive numerical data, provide practical tools for future design and operational applications of geothermal heat exchangers. This research advances the design and operational efficiency of geothermal heat exchange systems, establishing new benchmarks for thermal efficiency in the field with actionable insights and robust mathematical tools.