Natural bio-convective flow of Maxwell nanofluid over an exponentially stretching surface with slip effect and convective boundary condition

Fuzhang Wang,Muhammad Naveed Khan,Maha Alammari,Shafiq Ahmad,Aysha Rehman,Qasem Al Mdallal

doi:10.1038/s41598-022-04948-y

Abstract

The under-consideration article mainly focuses an unsteady three-dimensional Maxwell bio-convective nanomaterial liquid flow towards an exponentially expanding surface with the influence of chemical reaction slip condition. The feature of heat transport is achieving in the existenceof convective boundary condition and variable thermal conductivity. With the help of similarity variables, the flow form of equations is turned into a nonlinear form of coupled ODEs. The numerical solutions are calculated by adopting bvp4c function of MATLAB. Impact of distinct characteristics on the temperature, velocity microorganism and concentration field is graphically evaluated. Moreover, physical quantities are observed via graphs and tabulated data in details. It has been seen by the observation that the involvement of unsteadiness parameter restricts the change of laminar to turbulent flow. Further, for increasing velocity slip parameter velocity component in both directions shows lessening behavior. The Nusselt number exhibits diminishing behavior for larger values of Deborah number, and it shows the opposite behavior for larger values of convective parameter.

Highlights

The under-consideration article mainly focuses an unsteady three-dimensional Maxwell bioconvective nanomaterial liquid flow towards an exponentially expanding surface with the influence of chemical reaction slip condition
Incompressible, and three-dimensional flow of chemically reactive Maxwell bioconvective nanomaterials liquid towards an exponentially extending surface with z = 0
To transform the flow model PDEs into non-dimensionalized form, we introduced the following non dimensional variable[43], η=

Summary

Introduction

The under-consideration article mainly focuses an unsteady three-dimensional Maxwell bioconvective nanomaterial liquid flow towards an exponentially expanding surface with the influence of chemical reaction slip condition. List of symbols (a, b) Stretching constants (1/s) DT Thermal diffusion coefficient DB Mass diffusivity k0 Chemical reaction constant θ(η) Dimensionless factor for temperature S Extra stress tensor f (η), g(η) Dimensionless variables x- and y-direction (T0, C0, n0) Positive constant T∞, C∞, n∞ Ambient temperature, concentration, and microorganism k(T) Variable Thermal conductivity Ecx, Ecy Eckert number in x- and y-direction Shx Sherwood number Nux Nusselt number Nt Thermophoresis parameter (uw, vw) Stretching velocities ms−1. X, y, z Space coordinates (m) B0 Magnetic field T, C, n Temperature, concentration, and microorganism density cp Specific heat capacity hw Heat transport coefficient A Unsteadiness parameter φ(η) Dimensionless factor for concentration Wc Cell swimming speed χ(η) Dimensionless variables for microorganism density Nb Brownian motion parameter f (η), g(η) Dimensionless variables x- and y-direction k Thermal conductivity Wm−1 K−1 Dm Microorganism diffusion coefficient qm, jw Heat flux and mass flux Qnx Microorganism number zw Microorganism flux. Stretching ratio parameter τ Ratio of capacities σ Electrical conductivity ν Kinematic viscosity (m2/s) μ Dynamic viscosity (kg/ms)

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Conclusion