Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

Investigation of Entropy generation in Axisymmetric Stagnation Point Flow of Nano Fluid Impinging on the Cylinder With Constant Wall Temperature

Authors
1 Department of mechanical engineering, shahrood branch, islamic azad university, shahrood, iran
2 Young Researchers and Elite Club, Shahrood Branch, Islamic Azad University, Shahrood, Iran
3 Department of mathematics, shahrood university of technology
Abstract
In this research dimensionless temperature, convection heat transfer and entropy generation for the steady state flow in the stagnation point of nanofluid impinging on an infinite cylinder have been investigated. The impinging free stream is steady with a constant strain rate . Similarity solution of the Navier-Stokes and energy equations is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations introduced in this research. The general self similar solution is obtained when the wall temperature is constant. All the solutions above are presented for Reynolds numbers  ranging from 0.1 to 1000 and selected values of particle fractions where a is radius of the cylinder and is kinematic viscosity of the base fluid. Results show that for all Reynolds numbers, as the particle fraction increases, the depth of diffusion of the fluid velocity field in radial and axial directions and shear-stresses decreases whereas convective heat transfer coefficient and Nusselt number increases also maximum value of entropy generation has been calculated. 
Keywords

Subjects


[1]    Choi, S.U.S., "Enhancing Thermal Conductivity of Fluid with Nanoparticles", Dev. Appl Non-Newtonian Flows, Vol. 66, pp. 99–105, (1995).
 
[2]   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, pp. 453–462, (2004).
 
[3]   Heris, S.Z., Etemad, S.Gh., and Esfahani, M.N., "Experimental Investigation of Oxide Nanofluid Laminar Forced Flow Convective Heat Transfer", International Communications in  Heat and Mass Transfer, Vol. 33, pp. 529–535, (2006).
 
[4]   Duangthongsuk, W., and Wongwises, S., "Heat Transfer Enhancement and Pressure Drop Characteristics of TiO2-water Nanofluid in a Double-tube Counter Flow Heat Exchangers", International Journal of Heat and Mass Transfer, Vol. 52, pp. 2059–2067, (2009).
[5]   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", International Journal of Thermal Sciences, Vol. 48, pp. 391–400, (2009).
 
[6]    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", International Journal of Thermal Sciences , Vol. 48, pp. 401–411, (2009).
 
[7]   Kuznetsov, A. V., and Nield, D, A., "Natural Convection Boundary-layer Flow of a Nanofluid Past a Vertical Plate", International Journal of Thermal Sciences, Vol. 49, pp. 243–247, (2010).
 
[8]   Kuznetsov, A. V., and Nield, D. A., "Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: Brinkman Model", Transport in Porous Media, Vol. 81, pp. 409–422, (2010).
 
[9]   Khan, W. A., and Pop, I., "Boundary-layer Flow of a Nanofluid Past a Stretching Sheet", International Journal of Heat and Mass Transfer, Vol. 53, pp. 2477–2483, (2010).
 
[10]  Hiemenz, K., "Die Grenzchicht an Einem in den Gleichformingen Flussigkeitsstrom Eingetauchten Geraden", Kreiszylinder. Dinglers Polytech. J. Vol. 326, pp. 321-410, (1911).
 
[11]  Homann, F. Z., "Der Einfluss Grosser Zahighkeit bei der Strmung um den Zylinder und um die Kugel", Zeitsch. Angew. Math. Mech, Vol. 16, pp. 153-164, (1936).
 
[12]  Howarth, L., "The Boundary Layer in Three Dimensional Flow", Part II, the Flow near a Stagnation Point", Phil. Mag. Series 7, Vol. 42, pp. 1433-1440, (1951).
 
[13]  Davey, A., "Boundary Layer Flow at a Saddle Point of Attachment", Journal of Fluid Mechanics, Vol. 10, pp. 593-610, (1951).
 
[14]  Wang, C., "Axisymmetric Stagnation Flow on a Cylinder", Quarterly of Applied Mathematics, Vol. 32, pp. 207-213, (1974).
 
[15]  Gorla, R.S.R., "Unsteady Laminar Axisymmetric Stagnation Flow over a Circular Cylinder", Dev. Mech, Vol. 9, pp. 286-288, (1977).
 
[16]  Gorla, R.S.R., "Nonsimilar Axisymmetric Stagnation Flow on a Moving Cylinder", International Journal of Engineering Science, Vol. 16, pp. 397-400, (1978).
 
[17]  Gorla, R.S.R., "Transient Response Behaviour of an Axisymmetric Stagnation Flow on a Circular Cylinder due to Time Dependent Free Stream Velocity", International Journal of Engineering Science, Vol. 16, pp. 493- 502, (1978).
 
[18]  Gorla, R.S.R., "Unsteady Viscous Flow in the Vicinity of an Axisymmetric Stagnation-point on a Cylinder", International Journal of Engineering Science, Vol. 17, pp. 87-93, (1979).
 
[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, 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, 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", ASME Journal of Fluids Engineering, Vol. 126, 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", ASME Journal of Fluids Engineering, Vol. 129, 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", ASME Journal of Heat Transfer, Vol. 130, 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", ASME Journal of Fluids Engineering, Vol. 131, 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", AIAA Journal of Thermophysics and Heat Transfer, Vol. 23, 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", AIAA Journal of Thermophysics and Heat Transfer, Vol. 25, 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", ASME Journal of Heat Transfer, Vol. 134, pp. 064501.1-064501.5, (2012).
 
[28]   Mohammadiun, H., and Rahimi, A. B., "Stagnation-point Flow and Heat Transfer of a Viscous, Compressible Fluid on a Cylinder", AIAA Journal of Thermo Physics and Heat Transfer, Vol. 26, 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, Vol. 20, 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 Journal of Heat Transfer, Vol. 138, pp. 022201.1-022201.9, (2016).
 
[31]  Rahimi, A. B., Mohammadiun, H., and Mohammadiun, M., "Self-similar Solution of Radial Stagnation Point Flow and Heat Transfer of a Viscous, Compressible Fluid Impinging on a Rotating Cylinder", Iranian Journal of Science and Technology, Transactions of Mechanical Engineering,  pp. 1-13, (2018).
 
[32]  Bejan, A., "Second-law Analysis in Heat Transfer and Thermal Design", Advances in     Heat Transfer, Vol. 15, pp. 1–58, (1982).
 
[33]  Bejan, A., "Entropy Generation Minimization", 1st Edition, CRC Press, Boca Raton, Florida, (1996).
 
[34]  Bejan, A., "A Study of Entropy Generation in Fundamental Convective Heat Transfer", ASME Journal of Heat Transfer, Vol. 101, pp. 718–725, (1979).
 
[35]  Bejan, A., "The Thermodynamic Design of Heat and Mass Transfer Processes and Devices", International Journal of Heat and Fluid Flow, Vol. 8, pp. 259-276, (1987).
 
[36]  Mahmud, S., Tasnim, S. H., and Mamun, H. A. A., "Thermodynamic Analysis of Mixed Convection in a Channel with Transverse Hydromagnetic Effect", International Journal of Thermal Sciences, Vol. 42, pp. 731–740, (2003).
 
[37]  Aziz, A., "Entropy Generation in Pressure Gradient Assisted Couette Flow with Different Thermal Boundary Conditions", Entropy, Vol. 8, pp. 50-62, (2006).
 
[38]  Aïboud-Saouli, S., Saouli, S., Settou, N., and Meza, N., "Thermodynamic Analysis of Gravity-driven Liquid Film along an Inclined Heated Plate with Hydromagnetic and Viscous Dissipation Effects", Entropy, Vol. 8, pp. 188–199, (2006).
 
[39]  Aiboud-Saouli, S., Settou, N., Saouli, S., and Meza, N., "Second-law Analysis of Laminar Fluid Flow in a Heated Channel with Hydro-magnetic and Viscous Dissipation Effects", Applied Energy, Vol. 84, pp. 279–289, (2007).
 
[40]  Aїboud-Saouli, S., and Saouli, S., "Entropy Analysis for Viscoelastic Magneto Hydrodynamic Flow over a Stretching Surface, International Journal of Nonlinear Mechanics", Vol. 45, pp. 482–489, (2010).
 
[41]  Rezaiguia, I., Mahfoud, K., Kamel, T., Belghar, N., and Saouli, S., "Numerical Simulation of the Entropy Generation in a Fluid in Forced Convection on a Plane Surface while using the Method of Runge-Kutta", European Journal of Scientific Research, Vol. 42, pp. 637-643, (2010).
 
[42]  Hirschfelder, J. O., Curtiss, C. F., and Bird, R.B., "Molecular Theory of Gases and Liquids", John Wiley, New York, (1954).
 
[43]  San, J. Y., Worek, W.M., and Lavan, Z., "Entropy Generation in Combined Heat and Mass Transfer", International Journal of Heat and Mass Transfer, Vol. 30, pp. 1359-1369, (1987).
 
[44]  Bianco, V., Nadini, S., and Manca, O., "Enhancement of Heat Transfer and Entropy Generation Analysis of Nanofluids Turbulent Convection Flow in Square Section Tubes", Nanoscale Research Letters, 6:252, pp. 1-12, (2011).
 
[45]  Rashidi, M. M., Mohammadi, F., Abbasbandy, S., and Alhuthali, M. S., "Entropy Generation Analysis for Stagnation Point Flow in a Porous Medium over a Permeable Stretching Surface", Journal of Applied Fluid Mechanics, Vol. 8, pp. 753-765, (2015).
 
[46]  Bejan, A., and Ledezma, G. A., "Thermodynamic Optimization of Cooling Techniques for Electronic Packages", International Journal of Heat and Mass Transfer, Vol. 39, pp. 1213–1221, (1996).
 
[47]  Lin, W. W., and Lee, D. J., "Second Law Analysis of a Pin Fin Array under Cross Flow", International Journal of Heat and Mass Transfer, Vol. 40, pp. 1937–1945, (1997).
 
[48]  Sasikumar, M., and Balaji, C., "Optimization of Convective Fin Systems: a Holistic Approach", Heat and Mass Transfer, Vol. 39, pp. 57–68, (2002).
 
[49]  Rashidi, M. M., Mahmud, S., Freidoonimehr, N., and Rostami, B., "Analysis of Entropy Generation in an MHD Flow over a Rotating Porous Disk with Variable Physical Properties", International Journal of Exergy, Vol. 16, pp. 481-503, (2014).
 
[50]  Malvandi, A., Ganji, D. D., Hedayati, F., Kaffash, M. H., and Jamshidi, M., "Series Solution of Entropy Generation toward an Isothermal Flat Plate", Thermal Science, Vol. 16, pp. 1289–1295, (2012).
 
[51]  Freidoonimehr, F., 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, pp. 671-685, (2016).
 
[52]  Corcione M., "Empirical Correlating Equations for Predicting the Effective Thermal Conductivity and Dynamic Viscosity of Nanofluids", Energy Conversion and Management, Vol. 52, pp. 789-793, (2011).
 
[53]  Bejan, A., "Entropy Generation through Heat and Fluid Flow", 1st Edition, Wiley, New York, (1982).
Volume 21, Issue 4 - Serial Number 57
Fluid Mechanics and Heat Transfer
Winter 2020
Pages 58-34

  • Receive Date 12 October 2018
  • Revise Date 15 May 2020
  • Accept Date 16 June 2020