Thermal convective transport of nanofluids through a microchannel with rough surfaces under electromagnetohydrodynamics and time-periodic pressure gradient

This study investigates the flow and heat transfer characteristics of nanofluids (water-Al${}_2$O${}_3$) in a microchannel with rough surfaces, considering the combined effects of electromagnetohydrodynamics (EMHD) and time-periodic pressure gradient. The analytical solutions of the velocity and temperature fields are derived using the separation of variables, Fourier cosine series expansion, combined with the superposition principle and Duhamel’s principle. Based on this, the Nusselt number and entropy generation are further obtained. Through numerical simulations and theoretical analyses, the convective characteristics and irreversibility within the microchannel are explored in relation to various dimensionless parameters. Key findings demonstrate that increasing the nanoparticle volume fraction ($\varphi$) to 0.08 enhances convective heat transfer, elevating the Nusselt number ($Nu$) by 13.37% while reducing total entropy generation by 17.53%. Conversely, a larger roughness parameter (${\alpha }_1$) degrades thermal performance, at ${\alpha }_1$=0.12, total entropy generation increases by 17.04% and $Nu$ decreases by 10.76% relative to ${\alpha }_1$=0.06, attributed to nanoparticle aggregation and vortex-induced irreversibility. Electromagnetic regulation via the Hartmann number ($Ha$=7$\sim$9) suppresses the centreline temperature by 60% but reduces $Nu$ by 35.4%. Meanwhile, the pressure gradient at high dimensionless frequency ($\Omega$=60) reduces the oscillation period of entropy generation while decreasing total entropy generation through thermal homogenization. These results offer critical insights for optimizing thermal management in microfluidic systems governed by EMHD.