Numerical Analysis of MHD Flow and Heat Transfer of a Nanofluid over a Stretching Surface with Thermal Radiation

Abstract

This study investigates steady, two-dimensional magnetohydrodynamic (MHD) boundary-layer flow and heat transfer of an Al₂O₃–water nanofluid over a linearly stretching sheet in the presence of additive Rosseland thermal radiation. The similarity-reduced momentum and energy equations were solved with an adaptive collocation boundary-value method. Solver accuracy was verified against the exact Newtonian MHD stretching-sheet relation, with a maximum wall-shear error below 0.001%. Rather than relying on a few one-factor profile plots, the study evaluates the complete 5 × 5 × 5 parameter grid: magnetic parameter M = 0–2, radiation parameter Rd = 0–2, and nanoparticle volume fraction φ = 0–0.04, yielding 125 deterministic computational runs. These runs are design points, not random experimental observations; therefore, correlations, regression coefficients, ANOVA quantities, and nominal p values are interpreted as design-space screening diagnostics rather than population-level inferential statistics. Across marginal means, increasing M from 0 to 2 increased reduced wall drag by 73.2% and decreased the reduced total Nusselt response by 13.7%. Increasing Rd from 0 to 2 increased the reduced total Nusselt response by 48.2%. Increasing φ from 0 to 0.04 increased marginal mean wall drag by 11.3% and the total Nusselt response by 1.5%. The radiation result is not contradictory: higher Rd thickens the thermal field and reduces the local dimensionless wall-temperature gradient, but the reported total Nusselt response multiplies the wall gradient by the combined conductive-plus-radiative conductivity contribution, which more than offsets that gradient reduction over the present design space. The first-order heat-transfer model gave R² = 0.9705, whereas the quadratic response-surface model achieved adjusted R² = 0.9995 and identified important M × Rd, M × φ, and Rd × φ interactions. The principal novelty is the integration of a benchmark-validated similarity solver, a complete factorial computational dataset, explicit heat-flux definition, and reproducible response-surface screening in a single framework for radiative MHD nanofluid analysis.