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Local non-similar solutions of convective flow of Carreau fluid in the presence of MHD and radiative heat transfer

  • Humara SardarEmail author
  • Masood Khan
  • Latif Ahmad
Technical Paper
  • 23 Downloads

Abstract

In this research article we studied a realistic methodology to inspect the non-similar solutions for the two-dimensional steady Carreau fluid flow in the presence of applied magnetic field and mixed convection within the sight of infinite shear rate viscosity. With the help of local non-similar method, we presented the nonlinear PDEs for the flow and heat transfer analysis. The leading PDEs are converted into an system of nonlinear ODEs by using the local non-similarity method. The final resulting non-dimensional set of coupled nonlinear PDEs is then solved with the help of bvp4c function in MATLAB. This investigation discover numerous physical aspects of flow and heat transfer. Major outcomes in the form of velocity enhancement and temperature reduction for the higher values of buoyancy parameter \(\left( \xi \right)\) are observed. On the other hand, for increasing values of  \(N_{\mathrm{R}}\) the temperature of the fluid increases, while for larger values of suction/injection parameter the temperature of the fluid reduces. Parallel variation of buoyancy parameter and Weissenberg number shows a slight difference regarding local similar and local non-similar solution while computing the local skin friction number. The enhancement in buoyancy parameter causes enhancement in local skin friction as well as local Nusselt number. Additionally this investigation is validated through a comparison with previous results and found a good correlation with the previous results.

Keywords

Non-similar solutions Carreau fluid Stagnation point Thermal radiation Mixed convection 

List of symbols

(xy)

Cartesian coordinates \(\left( \hbox {ms}^{-1}\right)\)

\(U_{0}\)

Constant velocity

\({\mathbf{V}}\)

Velocity vector \(\left( \hbox {LT}^{-1}\right)\)

(uv)

Velocity components \(\left( \hbox {ms}^{-1}\right)\)

\(\beta ^{*}\)

Ratio of \(\mu _{\infty }\) and \(\mu _{0}\)

\(\mu _{\infty }\)

Infinite shear rate viscosity

\(\beta\)

Volumetric coefficient of thermal expansion

\(q_{\mathrm{w}}\)

Wall heat flux

k

Thermal conductivity

T

Temperature of fluid

\(T_{\mathrm{w}}\)

Temperature at the wall

\(T_{\infty }\)

Ambient temperature \(\left( \hbox {K}\right)\)

C

Nanoparticle volume friction \(\left( \hbox {K}\right)\)

\(C_{\mathrm{w}}\)

Concentration at the wall

\(C_{\infty }\)

Ambient concentration \(\left( \hbox {K}\right)\)

\(N_{\mathrm{R}}\)

Thermal radiation parameter

\(\sigma ^{*}\)

Stefan–Boltzmann constant

\(k^{*}\)

Mean absorption coefficient

g

Acceleration because of gravity

\(\theta\)

Dimensionless temperature

\(\alpha _{1}\)

Thermal diffusivity

\(\xi\)

Buoyancy parameter

k

Thermal conductivity

n

Power law index

\(\alpha _{1}\)

Thermal diffusivity

\(\psi\)

Stream function

\(v_{0}\)

Constant suction velocity

\(\rho\)

Fluid density \(\left( \frac{\hbox {kg}}{\hbox {m}^{3}}\right)\)

\(\mu _{0}\)

Zero shear rate viscosity

\(c_{p}\)

Specific heat \(\left( \frac{\hbox {J}}{\hbox {kg}^{-1}\hbox {K}^{-1}}\right)\)

\(\eta\)

Dimensionless variable

\(\tau _{\mathrm{w}}\)

Surface shear stress

\({\mathbf{I}}\)

Identity tensor

\(\Gamma\)

Relaxation parameter

\(C_{fx}\)

Skin friction coefficient

\(Nu_{x}\)

Nusselt number

\(Gr_{x}\)

Grashof number

\({\mathbf{Re}}_{x}\)

Local Reynolds numbers

\(\Pr\)

Prandtl number

We

Local Weissenberg number

M

Magnetic parameter

\(\Pr\)

Prandtl number

s

Suction parameter

\(q_{\mathrm{r}}\)

Radiative heat flux

\(\nu\)

Kinematic viscosity \(\left( \frac{\hbox {m}^{2}}{\hbox {s}}\right]\)

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan
  2. 2.Department of MathematicsShaheed Benazir Bhutto University SheringalUpper DirPakistan

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