Purpose This paper aims to study the magneto-radiative gas (water vapor) on an unsmooth boundary. Design/methodology/approach This paper provided a numerical treatment via the implicit Chebyshev pseudo-spectral method to investigate unsteady compressible magneto-radiative gas (water vapor Pr = 1) flow near a heated vertical wavy wall through porous medium in the presence of inclined magnetic field. The impacts of viscous dissipation, temperature-dependent fluid properties, thermal conductivity and viscosity in the presence of nonlinear thermal radiation are studied. The sinusoidal surface is transformed into a flat one using a suitable transformation. The comparison figures of published data with the present outcomes illustrate a good match. The present steady-state outcomes are presented for the temperature, velocity, Nusselt number and the shearing stress through figures for several interested physical parameters, namely, compressibility, magnetic, radiation, viscosity–temperature variation, thermal conductivity–temperature variation, surface sinusoidal waveform and porous parameters. Findings The present numerical outcomes confirm the importance of applying nonlinear thermal radiation cases in all studies that investigate heat transfer under the influence of thermal radiation. Originality/value A mathematical model is established for a wavy boundary, and Chebyshev pseudo-spectral method is adopted for the numerical study.
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