Entropy optimized dissipative flow of hybrid nanofluid in the presence of non-linear thermal radiation and Joule heating

Wei-Feng Xia,M U Hafeez,Jae Dong Chung,M Ijaz Khan,Nehad Ali Shah

doi:10.1038/s41598-021-95604-4

Abstract

Present article reads three dimensional flow analysis of incompressible viscous hybrid nanofluid in a rotating frame. Ethylene glycol is used as a base liquid while nanoparticles are of copper and silver. Fluid is bounded between two parallel surfaces in which the lower surface stretches linearly. Fluid is conducting hence uniform magnetic field is applied. Effects of non-linear thermal radiation, Joule heating and viscous dissipation are entertained. Interesting quantities namely surface drag force and Nusselt number are discussed. Rate of entropy generation is examined. Bvp4c numerical scheme is used for the solution of transformed O.D.Es. Results regarding various flow parameters are obtained via bvp4c technique in MATLAB Software version 2019, and displayed through different plots. Our obtained results presents that velocity field decreases with respect to higher values of magnetic parameter, Reynolds number and rotation parameter. It is also observed that the temperature field boots subject to radiation parameter. Results are compared with Ishak et al. (Nonlinear Anal R World Appl 10:2909–2913, 2009) and found very good agreement with them. This agreement shows that the results are 99.99% match with each other.

Highlights

Present article reads three dimensional flow analysis of incompressible viscous hybrid nanofluid in a rotating frame
When surface stretches with certain velocity, it develops an in viscid flow immediately, but the viscous flow near the sheet improves slowly, and it takes a certain instant of time to become a fully developed steady flow
Presence of shear forces reasons the work done by the fluid on its adjacent layers and in irreversible processes this work done transfers into heat

Summary

Transformation procedure

We are considering the following variables u = cxf ′(η), v = −cDf (η), w = cxg(η), θ. Conservation law of mass (Eq 1) is trivially satisfied and the other flow equations yield f iv + Re N2 (ff ′′′ − f ′f ′′) − 2Ro N2 g′ − Mn N5 f ′′ = 0, N1. [N4 + R(1 + (θw − 1)θ )3]θ ′′ + N3 Pr Ref θ ′ + 3R(θw − 1)(1 + (θw − 1)θ )2θ ′2 +N1 Pr[EcD(4f ′2 + g2) + Ecx(f ′′2 + g′2)] + N5MnEcxPrRe(f ′2 + g2) = 0,. N1, N2, N3, N4 and N5 are mathematically given as μhnf μf.

Discussion

Concluding remarks