Purpose <p>This study investigates steady mixed convection boundary-layer flow over a vertical plate under velocity and thermal slip conditions, incorporating stochastic effects to account for uncertainty in the flow and heat transfer processes.</p> Methods <p>The governing equations are transformed into a system of ordinary differential equations using similarity variables and solved numerically via the shooting method with a fourth-order Runge–Kutta scheme. Stochasticity is introduced by modeling the system with additive and multiplicative Wiener processes, and the resulting stochastic system is solved using the Euler–Maruyama method. Ensemble simulations and heat-map visualizations are employed to analyze uncertainty effects.</p> Results <p>The results show that stochastic perturbations significantly influence velocity and temperature profiles, especially near the wall region. Heat-map visualizations reveal broader uncertainty ranges, while parametric studies demonstrate the effects of the mixed convection parameter, Prandtl number, and slip coefficients on the flow and thermal behavior.</p> Conclusion <p>The proposed stochastic framework provides deeper insight into uncertainty-aware modeling of mixed convection boundary-layer flows and highlights the importance of random effects in convective transport, with potential applications in microfluidics, electronic cooling, and thermal sensing systems.</p> Graphical Abstract <p></p>