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


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.


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


Characteristic length


Relaxation time


Constant magnetic field strength


Gravitational acceleration


Fluid density


Linear thermal expansion coefficient


Nonlinear thermal expansion coefficient


Linear concentration expansion coefficient


Nonlinear concentration expansion coefficient


Radius of cylinder


Heat transfer coefficient


Kinematic viscosity


Dynamic viscosity


Ratio of effective thermal capacity of nanoparticles to the fluid


Thermal conductivity

\(\rho C_{p}\)

Effective heat capacity


Brownian diffusion coefficient


Stefan–Boltzman constant


Thermophoretic diffusion coefficient


Electrical conductivity


Wall mass transfer coefficient


Chemical reaction rate


Thermal conductivity at surface


Specific heat


Stretching velocity


Reference velocity


Radiative heat flux


Surface temperature

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

Ambient temperature


Fluid temperature


Fluid concentration


Surface concentration

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

Ambient concentration


Surface heat flux


Surface mass flux


Dimensionless space variable


Nonlinear convection parameter due to temperature


Nonlinear convection parameter due to concentration


Mixed convection parameter


Ratio of concentration to thermal buoyancy forces


Magnetic parameter


Deborah number


Grashof number for temperature


Grashof number for concentration


Thermophoresis parameter


Eckert number


Curvature parameter


Brownian motion parameter


Thermal Biot number


Radiation parameter


Concentration Biot number


Prandtl number


Chemical reaction parameter


Schmidt number


Local Reynolds number


Nusselt and Sherwood numbers



Dimensionless velocity


Nonzero auxiliary velocity parameter


Linear operator

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

Initial guess


Residual error


\(\tilde{\varphi }\)

Dimensionless velocity

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

Nonzero auxiliary parameter


Linear operator

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

Initial guess

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

Residual error


\(\tilde{\theta }\)

Dimensionless temperature

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

Nonzero auxiliary parameter


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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