Symbolic regression for convective heat transfer correlation development: Applicability and practical guidelines

Convective heat transfer correlations are traditionally developed through empirical curve fitting, which usually requires assumptions about the final functional form. Symbolic regression offers an alternative by simultaneously discovering functional forms and numerical coefficients directly from data. In this study, we systematically investigate the use of modern symbolic regression for convective heat transfer correlation development using laminar free convection over an isothermal vertical flat plate as a benchmark problem. A high-fidelity dataset was generated from Ostrach’s similarity solution across a wide range of Grashof and Prandtl numbers, and correlations were identified with the PySR framework. Beyond predictive performance, we examine the recovery of physically meaningful structures and assess sensitivity to representation choices, operator sets, search-budget parameters, maximum allowed complexity, dataset size, and measurement noise. Results show that symbolic regression can autonomously recover key physical structures of natural convection correlations, including the characteristic Nu∼Gr^1/4 scaling and asymptotic blending forms for Prandtl number dependence, despite the absence of explicit physical constraints. For the present benchmark, the best expressions exceed the accuracy of established engineering correlations while remaining interpretable. These findings demonstrate that symbolic regression can complement traditional correlation development, and practical guidelines are proposed for its reliable application in thermal engineering.