Investigation of Entropy Generation in Stagnation Point Flow of Nano Fluid Impinging on the Cylinder with Constant Wall Heat Flux
Authors
Abstract
: In this research, dimensionless temperature and entropy generation for the steady state flow in the stagnation point of incompressible nanofluid impinging on an infinite cylinder have been investigated. The impinging free stream is steady with a constant strain rate k. Similarity solution of the Navier-Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained using appropriate transformations introduced in this research. The general self similar solution is obtained when the heat flux on the cylinder wall is constant. All solutions brought above are presented for Reynolds numbers Re=ka^2/2vf that range from 0.1 to 1000 and the selected values of particle fractions, where a is the radius of the cylinder and υf is the kinematic viscosity of the base fluid. Results show that for Reynolds numbers examined, as the particle fraction increases, the depth of diffusion of the fluid velocity field in axial direction decreases, whereas Nusselt number is raised. Also, the maximum value of entropy generation has been calculated.
Keywords
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2. 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, No. 3, pp. 409–422, 2010.
3. 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, No. 11-12, pp. 2477–2483, 2010.
4. Wang, C., “Axisymmetric Stagnation Flow on a Cylinder”, Quarterly of Applied Mathematics, Vol. 32, No. 2, pp. 207-213, 1974.
5. Gorla, R. S. R. , “Nonsimilar Axisymmetric Stagnation Flow on a Moving Cylinder”, International Journal of Engineering Science, Vol. 16, No. 6, pp. 397-400, 1978.
6. 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, No. 7, pp. 493- 502, 1978.
7. Gorla, R. S. R., “Heat Transfer in Axisymmetric Stagnation Flow on a Cylinder”, Applied Scientific Research Journal, Vol. 32, No. 5, pp. 541-553, 1976.
8. 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, No.1, pp. 87-93, 1979.
9. 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.
10. 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.
11. Rahimi, A. B., and Mohammadiun, H., Mohammadiun, M., “Axisymmetric Stagnation Flow and Heat Transfer of a Compressible Fluid Impinging on a Cylinder Moving Axially”, Journal of Heat Transfer, Vol. 138, No. 2, pp. 022201:1-9, 2016.
12. Bejan, A., and Ledezma, G. A., “Thermodynamic Optimization of Cooling Techniques for Electronic Packages”, International Journal of Heat and Mass Transfer, Vol. 39, No. 6, pp. 1213–1221, 1996.
13. Lin, W. W., Lee, D. J., “Second Law Analysis of a Pin Fin Array Under Cross Flow”, International Journal of Heat and Mass Transfer, Vol. 40, No. 8, pp. 1937–1945, 1997.
14. Sasikumar, M., and Balaji, C., “Optimization of Convective Fin Systems: A Holistic Approach”, Heat and Mass Transfer, Vol. 39, No.1, pp. 57–68, 2002.
15. 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, No. 4, pp.481-503, 2015.
16. 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, No.5, pp. 1289–1295, 2012.
17. Freidoonimehr F., 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. 2, pp. 671-685, 2017.
18. Corcione M., “Empirical Correlating Equations for Predicting the Effective Thermal Conductivity and Dynamic Viscosity of Nanofluids”, Energy Conversion and Management, Vol. 52, No. 1, pp. 789-793, 2011.
19. Arun Kummar T., Pradyumna G., and Jahar S., “Investigation of Thermal Conductivity and Viscosity of Nanofluids”, Journal of Environmental Research and Development, Vol. 7, No. 2, pp. 768-777, 2012.
20. Bejan, M., Entropy Generation Through Heat and Fluid Flow, New York: Wiley, 1982.
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