Similarity Solution of Axisymmetric Stagnation Point Flow of Nanofluid on Rotating Cylinder

علوم کاربردی و محاسباتی در مکانیک

Article 6, Volume 29, Issue 2 - Serial Number 18, December 2017, Pages 57-70   

Document Type: Original Article

DOI: 10.22067/fum-mech.v29i2.62224

Author

Hamid Mohammadiun^*

Islamic Azad University of Shahrood

Abstract

In this paper the steady state radial stagnation point flow impinging on an infinite cylinder has been investigated. The impinging free stream is steady with a constant strain rate and axis is rotating with constant angular velocity. Similarity solution of the Navier-Stokes and energy equations is presented in this research. A reduced from of these equations are obtained by using appropriate transformations introduced in this study. For all Reynolds numbers, as the particle fraction increases, fluid velocity component in radial and axial directions and axial component of shear-stresses decrease and in the contrary the angular component of shear stress and velocity field and Nusselt number increase.

Keywords

Nanofluid; Stagnation point flow; Heat transfer; Similarity Solution; Particle fraction; Constant angular velocity

Supplementary Files

EA-4-Mohamadion.pdf

References

Choi, S.U.S, "Enhancing thermal conductivity of fluid with nanoparticles", Dev. Appl Non-Newtonian Flows, Vol. 66, pp. 99–105, (1995). 1.

Maiga, S.E.B., Nguyen, C.T., Galanis, N. and Roy, G., "Heat transfer behaviors of nanofluid in a uniformly heated tube", Superlattices Microstruct., Vol. 35, No. 3-6, pp. 453–462, (2004). 2.

Heris, S.Z., Etemad, S.Gh. and Esfahani, M.N., "Experimental investigation of oxide nanofluid laminar forced flow convective heat transfer", Int. Comm. Heat Mass Transf., Vol. 33, No. 4, pp. 529–535, (2006). 3.

Duangthongsuk, W. and Wongwises, S., "Heat transfer enhancement and pressure drop characteristics of TiO2-water nanofluid in a double-tube counter flow heat exchangers", Int. J. Heat Mass Transf., Vol. 52, No. 7-8, pp. 2059–2067, (2009). 4.

Santra, A.K., Sen, S. and Chkroborty, M., "Study of heat transfer due to laminar flow of copper–water nanofluid through two isothermally heated parallel plates", Int. J. Therm. Sci., Vol. 48, No. 1, pp. 391–400, (2009). 5.

Nguyen, C.T., Galanis, N., Polidori, G., Fohanno, S., Pota, C.V. and Beche, A.L., "An experimental study of confined and submerged impinging jet heat transfer using Al2O3-water nanofluid", Int. J. Therm. Sci., Vol. 48, No. 2, pp. 401–411, (2009). 6.

Kuznetsov, A.V. and Nield, D,A., "Natural convection boundary-layer flow of a nanofluid past a vertical plate", Int. J. Therm. Sci., Vol. 49, No. 2, pp. 243–247 (2010). 7.

Kuznetsov, A.V. and Nield, D.A., "Thermal instability in a porous medium layer saturated by a nanofluid: Brinkman model", Transp. Porous Med., Vol. 81, No. 3, pp. 409–422, (2010). 8.

Khan, W.A. and Pop, I., "Boundary-layer flow of a nanofluid past a stretching sheet", Int. J. Heat Mass Transfer, Vol. 53, No. 11-12, pp. 2477–2483, (2010). 9.

Hiemenz, K., "Die Grenzchicht an einem in den gleichformingen Flussigkeitsstrom eingetauchten geraden", Kreiszylinder. Dinglers Polytech. J., Vol. 326, pp. 321-410, (1911). 10.

Homann, F.Z., "Der Einfluss grosser Zahighkeit bei der Strmung um den Zylinder und um die Kugel", Zeitsch. Angew. Math. Mech., 16153-164, (1936) 11.

Howarth, L., "The boundary layer in three dimensional flow. Part II. The flow near a stagnation point", Phil. Mag., Vol. 42, No. 7, pp. 1433-1440, (1951). 12.

Davey, A., "Boundary layer flow at a saddle point of attachment", Journal of Fluid Mechanics, Vol. 10, No. 4, pp. 593-610, (1951). 13.

Wang, C., "Axisymmetric stagnation flow on a cylinder", Quarterly of Applied Mathematics, Vol. 32, No. 2, pp. 207-213, (1974). 14.

Gorla, R.S.R., "Unsteady laminar axisymmetric stagnation flow over a circular cylinder", Dev. Mec, Vol. 9, pp.286-288, (1977). 15.

Gorla, R.S.R., "Nonsimilar axisymmetric stagnation flow on a moving cylinder", Int. J. Engineering Science, Vol. 16, No. 6, pp. 397-400, (1978). 16.

Gorla, R.S.R., "Transient response behaviour of an axisymmetric stagnation flow on a circular cylinder due to time dependent free stream velocity", Int. J. Engineering science, Vol. 16, No. 7, pp. 493- 502, (1978). 17.

Gorla, R.S.R., "Unsteady viscous flow in the vicinity of an axisymmetric stagnation-point on a cylinder", Int. J. Engineering Science, Vol. 17, No. 1, pp. 87-93, (1979). 18.

Gorla, R.S.R., "Heat transfer in axisymmetric stagnation flow on a cylinder", Applied Scientific Research J., Vol. 32, No. 5, pp. 541-553, (1976). 19.

Cunning, G.M., Davis, A.M.J. and Weidman, P.D., "Radial stagnation flow on a rotating cylinder with uniform transpiration", Journal of Engineering mathematics, Vol. 33, No. 2, pp. 113-128, (1998). 20.

Takhar, H.S., Chamkha, A.J. and Nath, G., "Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder", Int. Journal of Engineering Science, Vol. 37, No. 15, pp. 1943-1957, (1999). 21.

Saleh, R. and Rahimi, A.B., "Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Moving Cylinder with Time- Dependent Axial Velocity and Uniform Transpiration", Journal of Fluids Engineering, Vol. 126, No. 6, pp. 997–1005, (2004). 22.

Rahimi, A.B. and Saleh, R., "Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Rotating Cylinder With Time- Dependent Angular Velocity and Uniform Transpiration", Journal of Fluids Engineering, Vol. 129, No. 1, pp. 107–115 (2007). 23.

Rahimi, A.B. and Saleh, R., "Similarity Solution of Unaxisymmetric Heat Transfer in Stagnation-Point Flow on a Cylinder with Simultaneous Axial and Rotational Movements", Journal of Heat Transfer, Vol. 130, No. 5, pp. 054502-1–054502-5, (2008). 24.

Abbasi, A.S. and Rahimi, A.B., "Non-Axisymmetric Three- Dimensional Stagnation-Point Flow and Heat Transfer on a Flat Plate", Journal of Fluids Engineering, Vol. 131, No. 7, pp. 074501.1– 074501.5, (2009). 25.

Abbasi, A.S. and Rahimi, A.B., "Three-Dimensional Stagnation- Point Flow and Heat Transfer on a Flat Plate with Transpiration", Journal of Thermophysics and Heat Transfer, Vol. 23, No. 3, pp. 513–521, (2009). 26.

Abbasi, A.S., Rahimi, A.B. and Niazmand, H., "Exact Solution of Three-Dimensional Unsteady Stagnation Flow on a Heated Plate", Journal of Thermophysics and Heat Transfer, Vol. 25, No. 1, pp. 55–58, (2011). 27.

Abbasi, A.S. and Rahimi, A.B., "Investigation of Two-Dimensional Stagnation-Point Flow and Heat Transfer Impinging on a Flat Plate", Journal of Heat Transfer, Vol. 134, No. 6, pp. 064501-06450, (2012). 28.

Mohammadiun, H. and Rahimi, A.B., "Stagnation-Point Flow and Heat Transfer of a Viscous, Compressible Fluid on a Cylinder", Journal of Thermo physics and Heat Transfer, Vol. 26, No. 3, pp. 494-502, (2012). 29.

Mohammadiun, H., Rahimi, A.B. and Kianifar, A., "Axisymmetric stagnation-point flow and heat transfer of a viscous, compressible fluid on a cylinder with constant heat flux", Scientia Iranica B, Vol. 20, No. 1, pp. 185–194, (2013). 30.

Rahimi, A.B., Mohammadiun, H. and Mohammadiun, M., "Axisymmetric stagnation flow and heat transfer of a compressible fluid impinging on a cylinder moving axially", ASME J. Heat Transfer, Vol. 138, No. 2, pp. 022201-1-022201-9, (2016). 31.

Mohammadiun, H., Mohammadiun, M., Hazbehian.M. and Maddah, H., "Experimental study of ethylene glycol‑based Al2O3 nanofluid turbulent heat transfer enhancement in the corrugated tube with twisted tapes", Heat Mass Transfer, Vol. 52, No. 1, pp. 141–151, (2016). 32.

Freidoonimehr, N. and Rahimi, A.B, "Exact-solution of entropy generation for MHD nanofluid flow induced by a stretching/shrinking sheet with transpiration: Dual solution", Advanced Powder Technology, Vol. 28, No. 22, pp. 671-685, (2017). 33.

Mansour, M.A., Mahdy, A.S., Ahmed, S.E. and Mohamed, S.S., "Entropy Analysis for Unsteady MHD Boundary Layer Flow and Heat Transfer of Casson Fluid over a Stretching Sheet", Walailak J Sci & Tech, Vol. 14, No. 2, pp. 169‐187, ( 2017). 34.

Corcione, M., "Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids", Ene. Convers. Manage, Vol. 52, No. 1, pp. 789-793, (2011). 35.