Fourth-Order Compact Formulation for the Resolution of Heat Transfer in Natural Convection of Water-Cu Nanofluid in a Square Cavity with a Sinusoidal Boundary Thermal Condition

In the present work, we numerically study the laminar natural convection of a nanofluid confined in a square cavity. The vertical walls are assumed to be insulated, non-conducting, and impermeable to mass transfer. The horizontal walls are differentially heated, and the low is maintained at hot condition (sinusoidal) when the high one is cold. The objective of this work is to develop a new height accurate method for solving heat transfer equations. The new method is a Fourth Order Compact (F.O.C). This work aims to show the interest of the method and understand the effect of the presence of nanofluids in closed square systems on the natural convection mechanism. The numerical simulations are performed for Prandtl number ( ), the Rayleigh numbers varying between  and for different volume fractions varies between 0% and 10% for the nanofluid (water + Cu).