HEAT TRANSFER IN ENCLOSURES FILLED WITH NANOFLUIDS IN CASE OF THE FRACTIONAL DERIVATIVES

Abstract

In this article, influences of the fractional derivatives on the heat transfer enhancement by free convective flow of nanofluids in a square enclosure that includes a heat source at the bottom are examined. All the cavity walls are considered to be cold except the bottom wall that is considered thermally insulated and contains a heat source. The nanofluids consist of water as a base fluid and copper as nanoparticles. The fractional partial differential equations are transformed to non-dimensional form and then solved numerically using the finite differences method. The obtained numerical data are presented in terms of streamlines and isotherms contours as well as local and average Nusselt numbers. The results revealed that both of the local and average Nusselt numbers are supported as the order of the fractional derivatives decreases.