TiO2-water nanofluid in a porous channel under the effects of an inclined magnetic field and variable thermal conductivity

The TiO₂-water based nanofluid flow in a channel bounded by two porous plates under an oblique magnetic field and variable thermal conductivity is formulated as a boundary-value problem (BVP). The BVP is analytically solved with the homotopy analysis method (HAM). The result shows that the concentration of the nanoparticles is independent of the volume fraction of TiO₂ nanoparticles, the magnetic field intensity, and the angle. It is inversely proportional to the mass diffusivity. The fluid speed decreases whereas the temperature increases when the volume fraction of the TiO₂ nanoparticles increases. This confirms the fact that the occurrence of the TiO₂ nanoparticles results in the increase in the thermal transfer rate. The fluid speed decreases and the temperature increases for both the pure water and the nanofluid when the magnetic field intensity and angle increase. The maximum velocity does not exist at the middle of the symmetric channel, which is in contrast to the plane-Poiseuille flow, but it deviates a little bit towards the lower plate, which absorbs the fluid with a very low suction velocity. If this suction velocity is increased, the temperature in the vicinity of the lower plate will be increased. An explicit expression for the friction factor-Reynolds number is then developed. It is shown that the Hartmann number of the nanofluid is smaller than that of pure water, while the Nusselt number of the nanofluid is larger than that of pure water. However, both the parameters increase if the magnetic field intensity increases.