<p>This study analyzes Hiemenz flow to understand the fluid’s behavior over a biaxial stretching/shrinking surface after applying boundary layer approximation. Cattaneo–Christov’s model is used which addresses the physical controls of Fourier’s law and expands the classical theory of heat conduction by incorporating the concepts of thermal and solutal relaxation time. This indicates that precise temperature control and thermal response are intensely beneficial in material processing and biomedical engineering applications. Furthermore, the mathematical model is formulated by considering thermal generation/absorption, Ohmic heating, and chemical reactions to investigate thermal and solutal distribution. The resulting nonlinear system equations contain singularity which is effectively managed by applying the perturbation technique. A built-in module in Python is used to obtain numerical solutions by converting highest-order equations to first-order equations. Graphical representations depict numerical solutions against the constraints on temperature, concentration distributions, fluid velocities, and friction drag. The numerical results indicate that the increase in the Prandtl number and relaxation time reduce heat transport due to decreased thermal diffusivity and slower response to temperature changes. Additionally, variations in molecular diffusion rates decrease mass transfer. The results are validated and compared with previously published results in tabular form. The novelty of this study lies in the implementation of Cattaneo–Christov theory, which effects the thermal and solutal transfer mechanisms by propagating thermal waves with finite speed and incorporates non-Fourier thermal behavior. Due to its practical and scientific importance in preservation of solar energy, biomedical science, food industries, oil spill clean-up and textile industries, the study holds significant importance.</p>