New analytical solutions of heat transfer flow of clay-water base nanoparticles with the application of novel hybrid fractional derivative

Abstract

Clay nanoparticles are hanging in three different based fluids (water, kerosene, and engine oil). The exact terminologies of Maxwell-Garnett and Brinkman for the current thermophysical properties of clay nanofluids are used, while the flow occurrence is directed by a set linear PDE with physical initial and boundary conditions. The classical governing equations are extended to non-integer order hybrid fractional derivative which is introduced in [33]. Analytical solutions for temperature and ve?locity fields are attained via Laplace transform technique. Some limiting solutions are also obtained from the existing literature and compared for different values of fractional parameter. To vision the impact of several flow parameters on the temperature and velocity some graphs are drawn using Mathcad software and designed in different figures. As a result, we found that hybrid fractional model is better in describing the decay behavior of temperature and velocity in comparison of classical derivatives. In comparison of nanofluid with different base fluids, it is concluded that water-based nanofluid has higher velocity than others.

Analysis of Fractional Bioconvection with Hybrid Nanoparticles in Channel Flow

“…Danish Ikram et al [48] calculated the heat transfer of viscous fluid with clay nanoparticles over an exponentially moving upright plate. Asjad Imran et al [49] analyzed the thermophysical properties of clay nanofluids using a hybrid fractional operator. Ikram et al [50] discussed the fractional model of Brinkman-type fluid (BTF) holding hybrid nanoparticles in a bounded microchannel via a constant proportional Caputo fractional operator.…”

Solution of hybrid time fractional diffusion problem via weighted inner product

“…where α > 0 denotes the order of the integral. This new fractional derivative is drawing the attention of many researchers in various branches of science and, as a result, there is a substantial amount of study in the literature such as on the hybrid fractional derivative [2][3][4][5][6], heat and mass transportation [7][8][9][10] and dynamics of processes [11][12][13][14].…”