Thermal analysis for convective transport of nanoparticles with effective phenomenon of damped shear-thermal flux: A fractional model

Abstract

The researchers are interested to enhance the temperature characteristics of convection heat transportation investigation. The studies based on nanofluids are accomplished because these phenomena exhibit an abnormal elevation in thermal transportation. This analysis captures historical impacts on heat and momentum transfer that traditional models ignore by using the Caputo fractional derivative in to model damped shear-thermal flux in nanofluid convection. In this manuscript, the natural convection flow, as well as heat transference of nanofluids, is studied. The classical expressions are fractionalized with the help of constitutive shearing stress expression along with Fourier relation. The Caputo kernel (power-law and non-local) engenders the damping on gradients of momentum and temperature; consequently, transportation approaches are affected by the histories entirely of the previous and current time. The fractional differential equations of velocity as well as temperature are solved analytically by invoking Laplace and the finite Sine-Fourier transform method. In a particular case, the solution to the classical model is also found. Moreover, these solutions are described in respect of the Lorenzo-Hartley G-function together with the Mittag-Leffler function. This investigation exposes that rising nanoparticle volume fraction improves the heat transfer rate, however the skin friction coefficient is affected by time and fractional parameters. The influences of diverse parameters are debated graphically. This study has numerous operations in thermal engineering.

Keywords

• Heat transfer
• Free convection
• Laplace transform
• Caputo time-fractional derivative
• Nanofluid
• Fourier law