Heat exchange within the partially heated C-shape cavity filled with the water based SWCNTs

•Heat transfer analysis of Water-SWCNT enclosed in a C-shape cavity is presented.•Thermal conductivity depending upon the radius of nanoparticles and fluid molecules.•FEM approach is acquire to attained the useful results of this model.•Effects of Rayleigh number, Hartmann number and nanoparticle are determined.•Obtained results described the behavior of Nusselt number and isotherms. In this article, heat transfer analysis is performed for Magnetohydrodynamic (MHD) water based Single Wall Carbon Nanotubes (SWCNTs) inside a C-shape cavity that is partially heated along the left vertical wall in the presence of magnetic field. The convection inside the cavity due to the temperature difference along the sides of the walls give rise in the temperature and the complete structure is based upon the system of nonlinear coupled partial differential equations. Governing equation are further modified in term of effective thermal conductivity expression that depends upon the radius of nanoparticle and fluid molecule. These equations are solved via Finite Element Method (FEM) utilizing Galerkin approach. The results are presented and analyzed in the form of streamlines, isotherms and Nusselt number for emerging physical parameter, that are, Rayleigh number (104⩽Ra⩽106), Hartmann number (0⩽Ha⩽200) and nanoparticle volume fraction (0⩽ϕ⩽0.2). The study reveals that increase in Rayleigh number enhances the heat transfer rate and increase in magnetic field strength decreases it. For the considered range of nanoparticle volume fraction (0⩽ϕ⩽0.2) have significant impact on the temperature distribution. It is finally concluded that increase in the Rayleigh number enhances the stream flow and isotherms behavior. However, increase in Hartman number decreases the heat transfer rate inside the cavity.