## THERMAL SCIENCE

International Scientific Journal

### NUMERICAL INVESTIGATION OF ENTROPY GENERATION IN LAMINAR FORCED CONVECTION FLOW OVER INCLINED BACKWARD AND FORWARD FACING STEPS IN A DUCT UNDER BLEEDING CONDITION

**ABSTRACT**

A numerical investigation of entropy generation in laminar forced convection of gas flow over a recess including two inclined backward and forward facing steps in a horizontal duct under bleeding condition is presented. For calculation of entropy generation from the second law of thermodynamics in a forced convection flow, the velocity and temperature distributions are primary needed. For this purpose, the two-dimensional Cartesian coordinate system is used to solve the governing equations which are conservations of mass, momentum and energy. These equations are solved numerically using the computational fluid dynamic techniques to obtain the temperature and velocity fields, while the blocked region method is employed to simulate the inclined surface. Discretized forms of these equations are obtained by the finite volume method and solved using the SIMPLE algorithm. The numerical results are presented graphically and the effects of bleeding coefficient and recess length as the main parameters on the distributions of entropy generation number and Bejan number are investigated. Also, the effect of Reynolds number and bleeding coefficient on total entropy generation which shows the amount of flow irreversibilities is presented for two recess length. The use of present results in the design process of such thermal system would help the system attain the high performance during exploitation. Comparison of numerical results with the available data published in open literature shows a good consistency.

**KEYWORDS**

PAPER SUBMITTED: 2011-05-31

PAPER REVISED: 2012-01-20

PAPER ACCEPTED: 2012-02-08

**THERMAL SCIENCE** YEAR

**2014**, VOLUME

**18**, ISSUE

**2**, PAGES [479 - 492]

- Armaly, B. F., Durst, F., Pereira, JCF. and chonung, B., Experimental and theoretical investigation of backward-facing step flow, Journal of Fluid Mechanics, 127 (1983), pp. 473-496.
- Vradis G. and Van Nostrand, L., Laminar coupled flow downstream an asymmetric sudden expansion, Journal of Thermophysics Heat Transfer, 6(2) (1992), pp. 288-295.
- Tylli, N., Kaiktsis, L. and Ineichen, B., Side wall effects in flow over backward-facing step: experiments and numerical solutions, Physics Fluids, 14(11) (2002), pp. 3835-3845.
- Brakely, D., Gabriela, M., Gomes, M. and Henderson, R. D., Three - dimensional instability in flow over a backward - facing step, Journal of Fluid Mechanics, 473 (2002), pp. 167- 190.
- Kondoh, T., Nagano, Y. and Tsuji, T., Computational study of laminar heat transfer downstream of a backward-facing step, International Journal of Heat and Mass Transfer, 36(3) (1993), pp. 577-591.
- Uruba, V., Jona´s, P. and Mazur, O., Control of a channel-flow behind a backward-facing step by suction/blowing, International Journal of Heat and Fluid Flow, 28 (2007), pp.665- 672.
- Abu- Mulaweh, H. I., A review of research on laminar mixed convection flow over backward- and forward-facing steps, International Journal of Thermal Sciences, 42, (2003), pp. 897-909.
- Atashafrooz, M., Gandjalikhan Nassab, S. A. and Ansari, A. B., Numerical analysis of laminar forced convection flow over backward and forward facing steps in a duct under bleeding condition, International Review of Mechanical Engineering, 5(3) (2011), pp. 513- 518.
- Bejan, A., A study of entropy generation in fundamental convective heat transfer, Journal of Heat Transfer, 101(1979), pp. 718-725.
- Bejan, A., The thermodynamic design of heat and mass transfer processes and devices, Journal of Heat and Fluid Flow, 8 (1987), pp. 258-275.
- Drost, M. K. and White, M. D., Numerical prediction of local entropy generation in an impinging get, Journal of Heat Transfer, 113 (1991), pp.823-829.
- Abu-Nada, E., Numerical prediction of entropy generation in separated flows, Entropy, 7(2005), pp. 234-252.
- Abu-Nada, E., Entropy generation due to heat and fluid flow in backward facing step flow with various expansion ratios, International Journal of Exergy, 3 (2006), pp. 419-435.
- Abu-Nada, E., Investigation of entropy generation over a backward facing step under bleeding conditions, Energy Conversion and Management, 49 (2008), pp. 3237-3242.
- Bahrami, A. and Gandjalikhan Nassab, S. A., Study of Entropy Generation in Laminar Forced Convection Flow over a Forward-Facing Step in a Duct, International Review of Mechanical Engineering, 4(4) (2010), pp. 399-404.
- Kolsi. L., Abidi. A., Borjini. M. N. and Aissia. H. B., The Effect of an External Magnetic Field on The Entropy Generation in Three-Dimensional Natural Convection, Thermal Science, 14(2) (2010), pp. 341-352.
- Gandjalikhan Nassab, S. A., Moosavi, R. and Hosseini Sarvari, S. M., Turbulent forced convection flow adjacent to inclined forward step in a duct, International Journal of Thermal Sciences, 48 (2009), pp. 1319-1326.
- Ansari, A. B. and Gandjalikhan Nassab, S. A., Numerical analysis of laminar forced convection flow of a radiating gas over an inclined forward facing step, International Review of Mechanical Engineering, 5(1) (2011), pp. 120-127.
- Ansari, A. B. and Gandjalikhan Nassab, S. A., Study of Laminar Forced Convection of Radiating Gas Over an Inclined Backward Facing Step Under Bleeding Condition Using The Blocked-off Method, ASME, Journal of heat transfer, 133 (2011), Issue 7, 072702.
- Patankar, S. V., Spalding, D. B., A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, International Journal of Heat and Mass Transfer, 15(10) (1972), pp. 1787-1806.
- Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Taylor & Francis, Philadelphia, 1981, PA, Chap.7.
- Lari, K. and Gandjalikhan Nassabm S. A. , Modeling of the conjugate radiation and conduction problem in a 3D complex multi-burner furnace, Thermal Science, Online-First Issue (2011).
- Ansari, A. B. and Gandjalikhan Nassab, S. A., Forced Convection of Radiating Gas Over an Inclined Backward Facing Step Using The Blocked-off Method, Thermal Science, Online.