Application of HAM to the von Kármán Swirling Flow with Heat Transfer Over a Rough Rotating Disk

  • Abhijit DasEmail author
  • Subrat Kumar Bhuyan
Original Paper


In this study, analytical solution to the classical von Kármán swirling viscous flow with heat transfer is obtained. Using similarity transformations the governing partial differential equations are reduced to a set of coupled, nonlinear ordinary differential equations and the conventional no-slip boundary conditions are replaced by partial slip boundary conditions due to the roughness of the disk. An effective analytical method for fully coupled and highly nonlinear differential equations, called Homotopy Analysis Method (HAM) is adopted and the solutions are obtained in the form of an convergent Taylor series. The effect of azimuthally anisotropic roughness, radially anisotropic roughness and isotropic roughness on the velocity and temperature profiles are studied in detail. Result shows that HAM is very efficient and easy to implement.


Partial slip HAM Kármán flow 



The authors would like to thank the chief editor and the anonymous reviewers for their detailed review and suggestions on our work.


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© Springer Nature India Private Limited 2018

Authors and Affiliations

  1. 1.Department of MathematicsNIT RourkelaRourkelaIndia
  2. 2.Department of Metallurgical and Materials EngineeringNIT RourkelaRourkelaIndia

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