Numerical investigation of laminar forced convection for a non-Newtonian nanofluids flowing inside an elliptical duct under convective boundary condition

Abstract

Purpose The purpose of this study is to investigate the thermal response of the laminar non-Newtonian fluid flow in elliptical duct subjected to a third-kind boundary condition with a particular interest to a non-Newtonian nanofluid case. The effects of Biot number, aspect ratio and fluid flow behavior index on the heat transfer have been examined carefully. Design/methodology/approach First, the mathematical problem has been formulated in dimensionless form, and then the curvilinear elliptical coordinates transform is applied to transform the original elliptical shape of the duct to an equivalent rectangular numerical domain. This transformation has been adopted to overcome the inherent mathematical deficiency due to the dependence of the ellipsis contour on the variables x and y. The yielded problem has been successfully solved using the dynamic alternating direction implicit method. With the available temperature field, several parameters have been computed for the analysis purpose such as bulk temperature, Nusselt number and heat transfer coefficient. Findings The results showed that the use of elliptical duct enhances significantly the heat transfer coefficient and reduces the duct’s length needed to achieve the thermal equilibrium. For some cases, the reduction in the duct’s length can reach almost 50 per cent compared to the circular pipe. In addition, the analysis of the non-Newtonian nanofluid case showed that the addition of nanoparticles to the base fluid improves the heat transfer coefficient up to 25 per cent. The combination of using an elliptical duct and the addition of nanoparticles has a spectacular effect on the overall heat transfer coefficient with an enhancement of 50-70 per cent. From the engineering applications view, the results demonstrate the potential of elliptical duct in building light-weighted compact shell-and-tube heat exchangers. Originality/value A complete investigation of the heat transfer of a fully developed laminar flow of power law fluids in elliptical ducts subject to the convective boundary condition with application to non-Newtonian nanofluids is addressed.

Analytical Solution of Non-Newtonian Nanofluid Flows Within Circular Duct under Convective Boundary Condition

“…This study adopts a single-phase approach supposing that the nanoparticles are uniformly dispersed into the base fluid. According to the mixing theory, the effective physical properties of nanofluids can be calculated using some formulations of density, nanofluid viscosity and specific heat capacity [21,23]:…”

“…It's demonstrated that the non-Newtonian nanofluids show a better efficiency in term of heat transfer compared to the Newtonian nanofluids. Recently, Ragueb and Mansouri [23] have investigated numerically the laminar non-Newtonian nanofluid flows within elliptical ducts under convective boundary conditions at the wall (third kind), without effect of viscous dissipation. The obtained results showed an improvement in the heat transfer coefficient when rising the volume fractions and decreasing the form factor.…”

Theoretical analysis of entropy generation in second grade nanofluid considering heat source/sink over a rotating disk

“…In biological and chemical industries involving manufacturing of ceramics, dehydrating, food processing, vaporization, polymer production and energy transfer in a cooling tower, chemical reaction have numerous applications. Important studies regarding chemical reaction are mentioned in Rout et al (2013), Shehzad et al (2013), Reddya et al (2016), Hayat et al (2015Hayat et al ( , 2016aHayat et al ( , 2016bHayat et al ( , 2016cHayat et al ( , 2016d, Khan et al (2016Khan et al ( , 2017Khan et al ( , 2018aKhan et al ( , 2018bKhan et al ( , 2018cKhan et al ( , 2018d, Umavathi et al (2017), Hayat et al (2017aHayat et al ( , 2017bHayat et al ( , 2017cHayat et al ( , 2017d, Yigit and Chakraborty (2019), Mahdy and Chamkha (2018), Waqas et al (2017aWaqas et al ( , 2017b and Ragueb and Mansouri (2019).…”

Numerical simulation for Darcy-Forchheimer flow of carbon nanotubes due to convectively heated nonlinear curved stretching surface

“…Variation in velocity, Nusselt number, temperature and skin friction coefficient have been studied graphically. Some recent developments through various flow assumptions have been presented in previous works (Hayat et al , 2019; Saif et al , 2019; Hayat et al , 2016d; Yigit and Chakraborty, 2019; Rashid et al , 2019; Ragueb and Mansouri, 2019; Hayat et al , 2016e; Mahdy and Chamkha, 2018; Khan et al , 2017b; Kamal et al , 2018; Hayat et al , 2019; Rahimi et al , 2018; Khan et al , 2018; Nazeer et al , 2018; Khan et al , 2019; Mahanthesh et al , 2018; Hayat et al , 2017e; Khan et al , 2017c; Teleszewski and Sorko, 2018; Khan et al , 2017d; Hdhiri and Beya, 2018; Hayat et al , 2018d; Hammami et al , 2018; Waqas et al , 2017).…”