A two-dimensional (2D) laminar flow of nanofluids confined within a square cavity having localized heat source at the bottom wall has been investigated. The governing Navier–Stokes and energy equations have been non dimensionalized using the appropriate non dimensional variables and then numerically solved using finite volume method. The flow was controlled by a range of parameters such as Rayleigh number, length of heat source and nanoparticle volume fraction. The numerical results are represented in terms of isotherms, streamlines, velocity and temperature distribution as well as the local and average rate of heat transfer. A comparative study has been conducted for two different base fluids, ethylene glycol and water as well as for two different solids and . It is found that the ethylene glycol-based nanofluid is superior to the water-based nanofluid for heat transfer enhancement.

Hybrid nanofluids possess exceptional thermal conductivity, but one of the major concerns with nanoparticles is agglomeration. While the usage of surfactants or dispersants can be used to mitigate this issue, numerical investigation and sensitivity analyses can be more affordable when attempting to optimize and design a thermal device. The consideration of thermal radiation with conductive and convective heat transfer and appropriate nanoparticles may provide a greater solution without compromising the efficacy of hybrid nanofluids. In the present work, the concept of magnetohydrodynamics (MHD) is used to examine the impact of thermal radiation on a stable, two-dimensional, incompressible hybrid fluid consisting of nanoparticles (MWNCT)${\mathrm{-Fe}}_3{\mathrm{O}}_4$ and water flowing over a vertical surface. The flow is governed by established equations of fluid dynamics, which use the Rosseland diffusion model to incorporate radiation effects. The implicit finite difference (IFD) was used to solve the mathematical equations. Sensitivity analyses were conducted as functions of volume fraction, radiation and magnetic variables. This study also examines the streamlines and isotherm lines with respect to the volume fraction, radiation parameter and magnetic parameter of the heat source. The results indicate that for a fixed radiation parameter, increasing the nanoparticle volume fraction by up to $20\%$ leads to a reduction of approximately $37\%$ in the skin friction coefficient, while the corresponding Nusselt number increases by nearly $50\%$. Furthermore, the introduction of a magnetic field parameter significantly suppresses wall shear stress and modifies the thermal boundary layer thickness, demonstrating the competing interaction between Lorentz-force-induced momentum damping and radiation-enhanced thermal diffusion. These quantified trends highlight the sensitivity of coupled momentum and heat transport to combined magnetic and radiative effects in hybrid nanofluid systems.