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Computational Mechanics

, Volume 53, Issue 2, pp 257–271 | Cite as

Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method in computation of non-Newtonian fluid flow and heat transfer with moving boundaries

  • Fang-Bao Tian
  • Ram P. Bharti
  • Yuan-Qing Xu
Original Paper

Abstract

This work presents an extension of the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method to non-Newtonian fluid flow and heat transfer with moving boundaries. In this method, the variational formulation is written over the space–time domain. Three sets of stabilization parameters are used for the continuity, momentum and thermal energy equations. The more efficient solution for highly non-linear problems is achieved by using the Newton–Raphson iterative method for non-linear terms and the generalized minimal residual method for algebraic equations. This work makes the computations feasible with third-order accuracy in time, which is higher then most versions of the FEM. To validate this method, it is used to solve the well-known benchmark problems such as channel-confined flow, lid-driven cavity, flow around a cylinder, and flow in channel with wavy wall, where the non-Newtonian fluid rheological behaviour is incorporated. In particular, the results in terms of the Nusselt number, wall shear stress (WSS), vorticity fields and streamlines are discussed. It shows that the flow and heat transfer characteristics are quite different if the moving boundaries are taken into account. In summary, this work provides an effective extension of the DSD/SST method to hydrodynamics and heat transfer problems involving complex fluids and moving boundaries.

Keywords

Non-Newtonian fluids DSD/SST method Moving boundaries Channel flow Cylinder flow  Wavy wall 

Notes

Acknowledgments

Prof. R. P. Bharti is supported by the “Faculty Initiation Grant–Scheme A”, Reference No. IITR/SRIC/886/F.I.G. (Scheme-A) out of “Sponsored Research & Industrial Consultancy (SRIC) Fund” of Indian Institute of Technology Roorkee, India. Dr. Y.-Q. Xu is supported by the Fund for Basic Research (No. 3160012211305) of Beijing Institute of Technology.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringVanderbilt UniversityNashvilleUSA
  2. 2.Department of Chemical EngineeringIndian Institute of Technology RoorkeeRoorkeeIndia
  3. 3.School of Life ScienceBeijing Institute of TechnologyBeijingPeople’s Republic of China

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