Abstract
.Fractional order derivatives are more efficient compared to classical derivatives to formulate a physical phenomenon having diverse and widespread applications in science and technology. Their results are comparatively accurate and can interpret memory effect. On the other hand, nanofluids are considered as the next generation of fluids having superior thermo-physical properties to enhance heat transfer rate. Therefore, it is important to study nanofluids and fractional derivatives together. This article deals with the natural convection flow of Carboxy-Methyl-Cellulose (CMC) based carbon nanotubes (CNTs) nanofluid in a two parallel plates channel. CNTs are taken in single and multiple wall shapes (SWCNTs and MWCNTs). The non-Newtonian CMC base fluid is presented by the governing equation of the Jeffery fluid and energy equation with effective thermophysical properties of nanofluids. The problem is subjected to static velocity and constant temperature boundary conditions on the plates together with initial conditions. The governing equations are generalized using the Caputo-Fabrizio fractional derivative (CFFD) approach without a singular kernel. Exact solutions are obtained via the Laplace transform method. In the limiting sense, the results of fractional second grade and Newtonian viscous nanofluids and fluid are recovered. Moreover, for 1, the solutions for classical Jeffery, classical second grade and classical Newtonian viscous nanofluids regular fluid are obtained. To examine the influences of various pertinent parameters, the parametric study is carried out through graphs. An opposite trend of velocity and temperature is noticed for increasing and phi for both SWCNTs and MWCNTs whereas the Nusselt number increases with an increase in and phi .