A ¬High Order Accurate Numerical Solution of Incompressible Slip Flow in Microchannels with Heat Transfer by Using Artificial Compressibility Method

Mohafez, Mir Hamed | 2009

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 39605 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In the present study, a high-order accurate numerical solution of steady incompressible slip flow and heat transfer in 2D microchannels is presented. The numerical method used is an alternating direction implicit operator scheme which is efficiently implemented to solve the incompressible Navier-Stokes equations in the primitive variables formulation using the artificial compressibility method. To stabilize the numerical solution, numerical filters are used. The present methodology considers the solution of the Navier-Stokes equations with¬ employing different slip boundary condition¬¬ (Maxwell,¬ ¬¬Hyperbolic tangent function of Knudsen number¬ and Beskok slip models)¬ ¬¬on the wall to model the slip flow ¬ ¬¬¬in microchannels. The capability of the present methodology for computing microchannel flows in the transition flow regime using different slip boundary conditions is also examined. The computations are also performed for the entrance region of a 2D microchannel and the effect of Knudsen and Reynolds numbers on the flow field and the hydrodynamic development length are studied. The effect of gas rarefaction on flow field of microcavity is also investigated. Moreover, the solution of the Navier-Stokes equations with employing the Maxwell and Smoluchowski boundary conditions to model the slip flow and temperature jump on the walls in microchannels are studied.¬ Since the slip and temperature jump boundary conditions contain the derivatives of the velocity and temperature, using the compact method the slip boundary conditions can be easily and accurately implemented. ¬The present numerical results show good agreement with the available analytical and numerical solutions. The study demonstrates that the present flow solver is accurate and efficient for computing the incompressible slip flow and heat transfer in microchannels and can be extended for solving the flow fields of the other problems like 2D microcavity in the slip flow regime.

  9. Keywords:
  10. Microchannel ; Slip Flow ; Compact Method ; Transition Regime ; Incompressible Fluid Flow ; Artificial Compressibity Method

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