An analytical study of the unsteady nonlinear convection flow of nanofluids in an infinitely rectangular channel

An analytical study of the unsteady, nonlinear buoyancy-driven convection flow of nanofluids in a horizontal infinitely long channel under the influence of an external magnetic field is carried out. Analytical solutions for velocity components, temperature, and pressure gradients are determined by considering a particular form of the stream function and the temperature field and an appropriate separation of variables. The analytical solutions are expressed by two functions that satisfy diffusion-type partial differential equations, solved by employing the Laplace and Fourier transforms. The obtained solutions are new in the literature. These solutions are suitable for studying various flows of nanofluids in channels or verifying some numerical schemes applied to solve similar problems. The movement of a water-based nanofluid with aluminum oxide nanoparticles and heat transfer is investigated using the obtained analytical solutions. The influence of the volume fraction of nanoparticles on temperature, velocity, and pressure is analyzed with numerical simulations and graphical illustrations. It is found that the heat transfer process can be improved by changing the volume fraction of nanoparticles. Also, the pressure gradients can be modified by the presence of nanoparticles.