Applied Physics A

, 125:161 | Cite as

Transient thin-film spin-coating flow of chemically reactive and radiative Maxwell nanofluid over a rotating disk

  • Jawad AhmedEmail author
  • Masood Khan
  • Latif Ahmad


In recent years, the investigation on nanofluids has developed a hot topic among researchers, because in the presence of the nanoparticles in the fluids enhances appreciably the thermal conductivity of the fluid and thus improves the heat transfer characteristics. The current work aims to study the unsteady finite thin-film flow of upper convected Maxwell fluid due to horizontal rotating disk in the presence of nanoparticles. The development of a thin conducting liquid film on the surface of a rotating disk is investigated under the impacts of nonlinear thermal radiations, variable magnetic field, and Joule heating. A significant perspective of this attempt is to incorporate the features of exothermic chemical reaction with activation energy for Buongiorno’s model of nanofluid owing to their improved heat transfer. The leading equations of the governing problem are modeled by utilizing the notion of Boussinesq approximation. The non-dimensional analysis is performed to acquire the ordinary differential equations. A finite-difference-based numerical scheme, namely, bv4c is implemented for the numerical simulation of the nonlinear problem. The physical consequence of the active parameters, that influenced the model, are argued through graphs on nanofluid velocity, temperature, solute concentration, local Nusselt number, and Sherwood number. The obtained results intimate that nanofluid film thickness decay with the growing values of unsteadiness parameter, magnetic parameter, and Deborah number. It is noted that the nanoparticles’ volume fraction increases with incremented values of activation energy parameter. Moreover, the nanofluid temperature shows a remarkable increase with the thermophoresis parameter.

List of symbols


Velocity components

\(r,\varphi ,z\)

Cylindrical coordinate system


Stretching rate


Positive constant


Kinematic viscosity


Dynamic viscosity


Rotation rate


Magnetic field

\(\lambda _{1}\)

Relaxation time

\(c_{\text {p}}\)

Specific heat at constant pressure


Fluid pressure and temperature

\(T_{\text {s}}\)

Surface temperature


Temperature at the origin



\(T_{\text {ref}}\)

Reference temperature

\(C_{\text {s}}\)

Surface concentration


Concentration at the origin

\(C_{\text {ref}}\)

Reference concentration


Fluid concentration


Fluid density


Dimensionless variable


Magnetic field strength


Fluid thermal conductivity


Thermal diffusivity

\(\sigma ^{*}\)

Stephan–Boltzmann constant


Mean absorption coefficient


Heat capacities ratio

\(D_{\text {T}}\)

Thermophoresis diffusion coefficient

\(D_{\text {B}}\)

Brownian diffusion coefficient


Thin-film thickness

\(q_{\text {rad}}\)

Radiative heat flux

\(F^{\prime }\)

Dimensionless radial velocity


Dimensionless azimuthal velocity


Dimensionless axial velocity


Dimensionless temperature


Dimensionless concentration


Prandtl number


Local Reynolds number


Unsteadiness parameter


Rotation parameter


Magnetic parameter

\(\beta _{1}\)

Deborah number


Dimensionless film thickness


Radiation parameter

\(\theta _{\text {w}}\)

Temperature ratio parameter


Eckert number

\(N_{\text {t}}\)

Thermophoresis parameter

\(N_{\text {b}}\)

Brownian motion parameter


Schmidt number

\(\sigma ^{**}\)

Reaction rate parameter


Fitted rate constant


Activation energy parameter


Temperature difference parameter

\(Nu_{\text {r}}\)

Local Nusselt number

\(Sh_{\text {r}}\)

Local Sherwood number


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan
  2. 2.Department of Basic SciencesUniversity of Engineering and TechnologyTaxilaPakistan
  3. 3.Department of MathematicsShaheed Benazir Bhutto UniversitySheringal Upper DirPakistan

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