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Nonlinear convective flow of Maxwell nanofluid past a stretching cylinder with thermal radiation and chemical reaction

  • Tasawar Hayat
  • Madiha RashidEmail author
  • Ahmed Alsaedi
  • Saleem Asghar
Technical Paper
  • 49 Downloads

Abstract

Present article investigates the nonlinear mixed convective flow of Maxwell nanofluid due to stretching cylinder. Electrically conducting fluid is considered in addition to heat and mass transfer. Silent features of thermal radiation, Joule heating, and first-order chemical reaction are attended. Concentration and energy expression consist of Brownian motion and thermophoresis phenomena. Heat and mass transfer are described by convective conditions associated with cylinder. Strong nonlinear systems solve for convergent homotopy solutions. Physical quantities of interest are examined in detail for the influential variables. Our findings show that the velocity, temperature, and concentration fields enhance for higher curvature number.

Keywords

Maxwell nanofluid MHD Nonlinear mixed convection Convective heat and mass conditions Thermal radiation Joule heating First order chemical reaction 

List of symbols

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{u} ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{v} ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{w}\)

Velocity components

r, z

Space coordinates

L

Characteristic length

\(\varepsilon\)

Relaxation time

B0

Constant magnetic field strength

g

Gravitational acceleration

\(\rho\)

Fluid density

A1

Linear thermal expansion coefficient

A2

Nonlinear thermal expansion coefficient

A3

Linear concentration expansion coefficient

A4

Nonlinear concentration expansion coefficient

a

Radius of cylinder

h

Heat transfer coefficient

\(\nu\)

Kinematic viscosity

\(\mu\)

Dynamic viscosity

\(\tau\)

Ratio of effective thermal capacity of nanoparticles to the fluid

k

Thermal conductivity

\(\rho C_{p}\)

Effective heat capacity

DB

Brownian diffusion coefficient

\(\sigma^{*}\)

Stefan–Boltzman constant

DT

Thermophoretic diffusion coefficient

\(\sigma\)

Electrical conductivity

km

Wall mass transfer coefficient

Kc

Chemical reaction rate

\(\alpha\)

Thermal conductivity at surface

Cp

Specific heat

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{w}_{w}\)

Stretching velocity

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{w}_{0}\)

Reference velocity

q

Radiative heat flux

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{T}_{f}\)

Surface temperature

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{T}_{\infty }\)

Ambient temperature

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{T}_{{}}\)

Fluid temperature

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{C}\)

Fluid concentration

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{C}_{f}\)

Surface concentration

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{C}_{\infty }\)

Ambient concentration

qw

Surface heat flux

jw

Surface mass flux

\(\zeta\)

Dimensionless space variable

\(\zeta_{T}\)

Nonlinear convection parameter due to temperature

\(\zeta_{C}\)

Nonlinear convection parameter due to concentration

\(\lambda_{1}\)

Mixed convection parameter

\(\lambda_{2}\)

Ratio of concentration to thermal buoyancy forces

M

Magnetic parameter

β

Deborah number

Gr

Grashof number for temperature

\(G_{r}^{*}\)

Grashof number for concentration

NT

Thermophoresis parameter

Ec

Eckert number

γ

Curvature parameter

DB

Brownian motion parameter

BT

Thermal Biot number

R

Radiation parameter

BC

Concentration Biot number

Pr

Prandtl number

LC

Chemical reaction parameter

Sc

Schmidt number

Rez

Local Reynolds number

Nu,Sh

Nusselt and Sherwood numbers

Velocity

\(\tilde{f}\)

Dimensionless velocity

\(\hbar_{{\tilde{f}}}\)

Nonzero auxiliary velocity parameter

\({\mathbf{L}}_{1}\)

Linear operator

\(\tilde{f}_{0} (\zeta )\)

Initial guess

\(\Delta_{m}^{{\tilde{f}}}\)

Residual error

Concentration

\(\tilde{\varphi }\)

Dimensionless velocity

\(\hbar_{{\tilde{\varphi }}}\)

Nonzero auxiliary parameter

\({\mathbf{L}}_{3}\)

Linear operator

\(\tilde{\varphi }(\zeta )\)

Initial guess

\(\Delta_{m}^{{\tilde{\varphi }}}\)

Residual error

Temperature

\(\tilde{\theta }\)

Dimensionless temperature

\(\hbar_{{\tilde{\theta }}}\)

Nonzero auxiliary parameter

\({\mathbf{L}}_{2}\)

Linear operator

\(\tilde{\theta }_{0} (\xi )\)

Initial guess

\(\Delta_{m}^{{\tilde{\theta }}}\)

Residual error

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  • Tasawar Hayat
    • 1
    • 2
  • Madiha Rashid
    • 1
    Email author
  • Ahmed Alsaedi
    • 2
  • Saleem Asghar
    • 3
  1. 1.Department of MathematicsQuaid-I-Azam University 45320IslamabadPakistan
  2. 2.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of MathematicsCOMSATS UniversityIslamabadPakistan

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