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Self-Similar Solution of Radial Stagnation Point Flow and Heat Transfer of a Viscous, Compressible Fluid Impinging on a Rotating Cylinder

  • Asghar B. Rahimi
  • Hamid MohammadiunEmail author
  • Mohammad Mohammadiun
Research Paper
  • 27 Downloads

Abstract

In this study, the radial stagnation point flow of strain rate \(\bar{k}\) impinging on a cylinder rotating at constant angular velocity ω and its heat transfer are investigated. Reduction in the Navier–Stokes equations and energy equation to primary nonlinear ordinary differential equation systems is obtained by use of appropriate transformations when the angular velocity and wall temperature or wall heat flux all are constant. The impinging free stream is steady and normal to the surface from all sides, and the range of Reynolds number variation (\(Re = \bar{k}a^{2} /2\upsilon\)) is 0.1–1000 in which a and υ are cylinder radius and kinematic viscosity, respectively. Flow results are presented for selected values of compressibility factor and different values of Prandtl numbers along with shear stress and Nusselt number. For all values of Reynolds numbers and surface temperature or surface heat flux, as compressibility factor increases the radial velocity field, the heat transfer coefficient and the wall shear stress increase, whereas the angular velocity field decreases. The rotating movement of the cylinder does not have any effect on the radial component of the velocity, but its increase increases the angular component of the fluid velocity field and the surface shear stress.

Keywords

Stagnation point flow Constant angular velocity Heat transfer Compressibility factor Constant wall temperature and heat flux 

List of symbols

a

Cylinder radius

\(c(\eta )\)

Density ratio

\(f(\eta )\)

Function of \(\eta\)

\(G(\eta )\)

Function of \(\eta\)

\(k\)

Thermal conductivity

\(\bar{k}\)

Free stream strain rate

\(p\)

Fluid pressure

\(P\)

Non-dimensional pressure

\(Pr\)

Prandtl number

\(q_{\text{w}}\)

Heat flux at the wall

\(r,\phi ,z\)

Cylindrical coordinates

\(Re = \frac{{\bar{k}a^{2} }}{2\upsilon }\)

Reynolds number

\(T\)

Temperature

\(T_{\text{w}}\)

Wall temperature

\(T_{\infty }\)

Free stream temperature

\(u\)

Radial component of the velocity

\(v\)

Angular component of the velocity

\(w\)

Axial component of the velocity

\(Nu\)

Nusselt number

Greek symbols

\(\beta\)

Compressibility factor

\(\varGamma (\eta )\)

Function related to density

\(\eta\)

Similarity variable

\(\theta (\eta )\)

Non-dimensional temperature

\(\mu\)

Viscosity

\(\upsilon\)

Kinematic viscosity

\(\omega\)

Angular velocity of the cylinder

\(\rho (\eta )\)

Fluid density

\(\rho_{\infty }\)

Free stream density

\(\sigma\)

Shear stress

\(\psi\)

Stream function

\(\hat{\psi } = \frac{\psi }{{0.5\bar{k}a^{3} }}\)

Normalized stream function

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Copyright information

© Shiraz University 2018

Authors and Affiliations

  • Asghar B. Rahimi
    • 1
  • Hamid Mohammadiun
    • 2
    Email author
  • Mohammad Mohammadiun
    • 2
  1. 1.Faculty of EngineeringFerdowsi University of MashhadMashhadIran
  2. 2.Department of Mechanical EngineeringShahrood Branch, Islamic Azad UniversityShahroodIran

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