Heat transfer analysis of water based SWCNTs through parallel fins enclosed by square cavity

Abstract

Analysis of natural convection due to various positions of bottom heated fin is performed in a square cavity that is filled by water-based Single Wall Carbon Nanotubes (SWCNTs) via finite element method (FEM). Three vertical parallel fins and one top horizontal fin is also placed inside the cavity. The upper surface of the cavity is adiabatic, however the rest of three parts of the square cavity are cold. Convection is driven through lower horizontal and vertically central heated fins. For convection, horizontal and middle vertical fins are heated with uniform temperature Th and remaining vertical parallel fins are fixed as cold (Tc). Mathematical structure is constructed in the form of system of nonlinear partial differential equations (PDEs) with constraint at the surface. Expressions of nanofluid relations are incorporated into the model. Effective thermal conductivity model includes the radius of nanoparticle and fluid molecules at nanoscale. Dimensionless form of PDEs are tackled through Galerkin technique-based Finite Element Method. Results are obtained for temperature profile and stream function that includes emerging parameters such as: Rayleigh number (Ra), nanoparticle fraction (ϕ), position of heated horizontal fin, variation in length forbottom heated fin (HT), Hartmann number (Ha) and effect of middle vertical fin (adiabatic, cold, hot). The analysis describes the significant effect of heat transfer in the presence of nanoparticle, heated length of bottom fin. Heat transfer rate increases by enlarging the heated length of the lower horizontal fin, and decreases by improving the value of Ra and solid volume fraction of nanoparticles.