<p>This paper describes a numerical study of thermosolutal magnetohydrodynamic (MHD) mixed convection in a vertical porous pipe using the Chebyshev spectral collocation method. The flow is assumed to be fully developed, electrically conducting, and subjected to internal heat generation or absorption in the presence of a transverse magnetic field. Fluid motion is driven by combined effects of thermal and solutal buoyancy forces together with an imposed axial pressure gradient. The porous medium is modeled using the non-Darcy Brinkman–Forchheimer extended formulation to incorporate both viscous diffusion and inertial resistance effects. A systematic parametric analysis is performed to examine the influence of the Hartmann number (<i>Ha</i>), heat generation/absorption parameter (<i>q</i>), buoyancy ratio (<i>N</i>), and Forchheimer number (<i>F</i>) on the velocity and temperature fields. The results show that increasing the Hartmann number from 0 to 40 suppresses the peak velocity by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(42\%\)</EquationSource> </InlineEquation> due to Lorentz damping. For moderate magnetic field strength (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(Ha &lt; 30\)</EquationSource> </InlineEquation>), the velocity profile exhibits inflection points near the wall, indicating potential instability, whereas for larger <i>Ha</i> the profile becomes smoother and nearly uniform across the core region. Heat generation beyond a critical threshold (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(q &gt; 9.8\)</EquationSource> </InlineEquation>) induces backflow, with reverse velocity reaching <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(16\%\)</EquationSource> </InlineEquation> of the forward peak at <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(q = 15\)</EquationSource> </InlineEquation>. Increasing <i>q</i> from 0 to 50 elevates the centerline temperature by <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(47\%\)</EquationSource> </InlineEquation>, while the near-wall temperature increases by only <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(15\%\)</EquationSource> </InlineEquation>, creating a non-uniform thermal field that promotes profile distortion and potential breakdown of the base flow. In contrast, heat absorption (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(q &lt; 0\)</EquationSource> </InlineEquation>) stabilizes the system and prevents such deviations. A decrease in the Forchheimer number reduces inertial drag and enhances the maximum temperature within the pipe. Comparison with benchmark solutions under limiting conditions demonstrates excellent agreement, confirming the reliability and accuracy of the present spectral approach.</p>