## THERMAL SCIENCE

International Scientific Journal

### ENTROPY ANALYSIS IN MOVING WAVY SURFACE BOUNDARY-LAYER

**ABSTRACT**

It is a well-established fact that significant gain in the heat transfer rate can be obtained by altering that flat surface texture of the working body. The most convenient alteration, in view of mathematical handling, is the wavy one. Existing studies reveal that the convective heat transfer phenomenon is affected significantly due to the presence of a solid wavy surface. How does the phenomena of entropy generation is effected due to a wavy surface is the question investigated in this manuscript. The expressions for irreversibility distribution rate, Bejan number, and volumetric entropy generation number have been evaluated by Keller-Box method. The effect of important parameters of interest, such as wavy amplitude, Prandtl number, and group parameter on irreversibility distribution rate, Bejan number and entropy generation number, have been discussed in detail. The study reveals that entropy generation number decreases and irreversibility rate increases by increasing the amplitude of the wavy surface.

**KEYWORDS**

PAPER SUBMITTED: 2016-10-29

PAPER REVISED: 2017-02-13

PAPER ACCEPTED: 2017-02-25

PUBLISHED ONLINE: 2017-03-03

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Issue 1**, PAGES [233 - 241]

- Bejan, A., Entropy Generation Minimization, CRC Press, Boca Raton, New York, 1996
- Bejan, A., Entropy Generation Through Heat and Fluid Flow, Wiley, New York, 1982
- Paoletti, S. et al., Calculation of exergetic losses in compact heat exchanger passages, ASME AES, 10 (1989), 2, pp. 21-29
- Benedetti, P., Sciubba, E., Numerical calculation of the local rate of entropy generation in the flow around a heated finned-tube, Mechanical and Aerospace Engineering, 30 (1993), pp. 81-91
- Bejan, A., A study of entropy generation in fundamental convective heat transfer, Journal of Heat Transfer-Transactions of the ASME, 101 (1979), 4, pp. 718-725
- Abu-Hijleh, B. A. K., Heilen, W. N., Entropy generation due to laminar natural convection over a heated rotating cylinder, International Journal of Heat and Mass Transfer, 42 (1999), 22, pp. 4225-4233
- Tasnim, S. H. et al., Entropy generation in a porous channel with hydromagnetic effect, Exergy, An International Journal, 2 (2002), 4, pp. 300-308
- Mahmud, S., Fraser, R. A., The second law analysis in fundamental convective heat transfer problems, International Journal of Thermal Sciences, 42 (2003), 2, pp. 177-186
- Carrington, C. G., Sun, Z. F., Second law analysis of combined heat and mass transfer in internal and external flows, International Journal of Heat and Fluid Flow, 13 (1992), 1, pp. 65-70
- Selamet, A., Arpaci, V. S., Entropy production in boundary layers, Journal of Thermophysics and Heat Transfer, 4 (1990), 3, pp. 404-407
- Munawar, S. et al., Thermal analysis of the flow over an oscillatory stretching cylinder, Physica Scripta, 86 (2012), 6, 065401 pp. 065401
- Munawar, S. et al., Second law analysis in the peristaltic flow of variable viscosity fluid, International Journal of Exergy, 20 (2016), 2, pp. 170-185
- Razavi, S. E. et al., Second law analysis of laminar forced convection in a rotating curved duct, Thermal Science, 19 (2015), 1, pp. 95-107-
- Eegunjobi, A. S. et al., Irreversibility analysis of unsteady couette flow with variable viscosity, Journal of Hydrodynamics, Ser. B, 27 (2015), 2, pp. 304-310
- Adesanya, S. O., Makinde, O. D., Irreversibility analysis in a couple stress film flow along an inclined heated plate with adiabatic free surface, Physica A: Statistical Mechanics and its Applications, 432 (2015), 0, pp. 222-229
- Mkwizu, M. H., Makinde, O. D., Entropy generation in a variable viscosity channel flow of nanofluids with convective cooling, Comptes Rendus Mécanique, 343 (2015), 1, pp. 38-56
- Butt, A. S. et al., Entropy generation in hydrodynamic slip flow over a vertical plate with convective boundary, Journal of Mechanical Science and Technology, 26 (2012), 9, pp. 2977-2984
- Tamayol, A. et al., Thermal analysis of flow in a porous medium over a permeable stretching wall, Transport in Porous Media, 85 (2010), 3, pp. 661-676
- Butt, A. S. et al., Entropy generation in the Blasius flow under thermal radiation, Physica Scripta, 85 (2012), 3, 035008 pp. 6
- Munawar, S. et al., Entropy production in the flow over a swirling stretchable cylinder, Thermophysics and Aeromechanics, 23 (2016), 3, pp. 435-444
- Yao, L. S., Natural convection along a vertical wavy surface, Journal of Heat Transfer, 105 (1983), 3, pp. 465-468
- Rees, D. A. S., Pop, I., Free convection induced by a horizontal wavy surface in a porous medium, Fluid Dynamics Research, 14 (1994), 4, pp. 151-166
- Hossain, M. A., Rees, D. A. S., Combined heat and mass transfer in natural convection flow from a vertical wavy surface, Acta Mechanica, 136 (1999), 3, pp. 133-141
- Rees, D. A. S., Pop, I., Boundary layer flow and heat transfer on a continuous moving wavy surface, Acta Mechanica, 112 (1995), 1, pp. 149-158
- Hossain, M., Pop, I., Magnetohydrodynamic boundary layer flow and heat transfer on a continuous moving wavy surface, Archives of Mechanics, 48 (1996), 5, pp. 813-823
- Narayana, M. et al., On double-diffusive convection and cross diffusion effects on a horizontal wavy surface in a porous medium, Boundary Value Problems, 2012 (2012), 1, pp. 1-22
- Chen, C. o. K. et al., The effect of thermal radiation on entropy generation due to micro-polar fluid flow along a wavy surface, Entropy, 13 (2011), 9, pp. 1595
- Chen, C. o. K. et al., Entropy generation of radiation effect on laminar-mixed convection along a wavy surface, Heat and Mass Transfer, 47 (2011), 4, pp. 385-395
- Siddiqa, S. et al., Numerical Solutions of Natural Convection Flow of a Dusty Nanofluid About a Vertical Wavy Truncated Cone, Journal of Heat Transfer, 139 (2016), 2, pp. 022503-022503-022511
- Siddiqa, S. et al., Gyrotactic bioconvection flow of a nanofluid past a vertical wavy surface, International Journal of Thermal Sciences, 108 (2016), pp. 244-250
- Siddiqa, S. et al., in International Journal of Nonlinear Sciences and Numerical Simulation. (2016), vol. 17, pp. 185.
- Mehmood, A. et al., Cooling of moving wavy surface through MHD nanofluid, Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences, 71 (2016), 7, pp. 583
- Mehmood, A., Iqbal, M. S., Impact of surface texture on natural convection boundary layer of nanofluid, Thermal Science, 21 (2017), 00, pp. 122-136
- Mehmood, A., Iqbal, M. S., Heat transfer analysis in natural convection flow of nanofluid past a wavy cone, Journal of Molecular Liquids, 223 (2016), pp. 1178-1184
- Mehmood, A., Iqbal, M. S., Effect of heat absorption in natural convection nanofluid flow along a vertical wavy surface, Journal of Molecular Liquids, 224, Part B (2016), pp. 1326-1331
- Bejan, A., Second law analysis in heat transfer, Energy, 5 (1980), 8-9, pp. 720-732
- Na, T. Y., Computational Methods in Engineering Boundary Value Problems, Academic Press, 1979
- Cebeci, T., Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer, Springer, New York, 1988
- Cebeci, T., Bradshaw, P., Momentum transfer in boundary layers, Hemisphere Pub. Corp., 1977
- Cebeci, T. et al., Solution of a hyperbolic system of turbulence-model equations by the "box" scheme, Computer Methods in Applied Mechanics and Engineering, 22 (1980), 2, pp. 213-227