Influence of nanoparticle shapes on natural convection flow with heat and mass transfer rates of nanofluids with fractional derivative

Abstract

Nanofluids are gaining extensive attention due to their thermo-physical properties in technological and industrial fields for controlling the effects of heat transfer. Classical nanofluid studies are generally confined to models described by partial differential equations of an integer order where the memory effect and hereditary properties of materials are neglected. In order to overcome these downsides, the present work focuses on studying nanofluids with fractional derivative formed by differential equations with Caputo time derivatives that provides memory effect on nanofluid characteristics. Also, investigation on natural convective flow, heat, and mass transfer of nanofluids formed by different base fluids with different shapes of copper nanoparticles past an infinite vertical plate with radiation effect is carried out. The governing fractional differential equations are solved by employing Laplace transform technique with suitable boundary conditions. The different base fluids-water (H 2 O), SA:sodium alginate (C 6 H 9 Na O 7 ), and EG:ethylene glycol (C 2 H 6 O 2 ) and different shapes of nanoparticles-blade, brick, platelet, and cylinder are considered for the study.The exact solutions are obtained for the temperature, concentration, and velocity distributions and the respective Nusselt number, Sherwood number, and skin-friction coefficient. The influence of non-dimensional parameters provides physical interpretations of temperature, concentration, and velocity fields, Nusselt number, Sherwood number, and skin friction in detail with the help of graphical representations. From the results, it is found that nanofluid with water-based blade-shaped nanoparticle exhibits more velocity and temperature distributions. Also, strengthen of fluid flow, temperature, and concentration of nanofluids are inversely correlate with fractional order derivatives.

Study of Effect of Different Shapes of Nanoparticles in Three-Layer Model for Blood Flow in Arterioles

“…Platelets and cylinders have almost the same viscosity in nanofluid due to elongated structures, thus they show an overlapping profile for velocity. Similar results were given by Madhura et al [28]. Blade-shaped nanoparticles show maximum viscosity while brick-shaped nanoparticles have the least viscosity.…”

“…The Hamilton-Crosser model describes the total thermal conductivity of two components in a heterogeneous mixture. It is a relation to the thermal conductivity of the pure materials, their respective compositions and the fashion in which they are scattered throughout the mixture [28]. It calculates the total thermal conductivity (k nf ) of the heterogeneous mixture.…”

“…But practically, they have limited applications. Clinical diagnosis and drug delivery have a major usage of non-spherical shaped nanoparticles [28]. Nanoparticles of shapes like cylinder, blade, brick and platelets have enormous utilization in drug delivery.…”

Study of Nanoparticle Diffusion in Capillary-Tissue Exchange System using Jeffrey Nanofluid Model: Effects of Shapes of Nanoparticles

“…where 𝐴 is specific to the shape of nanoparticles [23] in the fluid (Table 1) and 𝜙 is the volume fraction of nanoparticles in blood. 𝜇 𝑓 is the viscosity of blood.…”

“…The diffusion of nanoparticles in blood is particularly necessary to comprehend drug delivery. Mun et al, [22] studied the diffusion of nanoparticles in polymer solutions of different types and revealed that geometry of nanoparticle [23,25], the viscosity of base fluid [26,32] and the interactions of the nanoparticles with the base fluid strongly effect their diffusivity. Therefore, in this research article we have taken two factors that affect nanoparticle diffusivity i.e., nanoparticle shape and the viscosity of the base fluid.…”