## THERMAL SCIENCE

International Scientific Journal

### MODELING AND SIMULATION OF NATURAL CONVECTION FLOW ALONG A ROUGH SURFACE OF SINUSOIDAL NATURE WITH VARIABLE HEAT FLUX: USING KELLER BOX SCHEME

**ABSTRACT**

In this study, natural convection flow along a vertical wavy surface has been investigated with variable heat flux. The governing equations are transformed into dimensionless PDE by using the non-dimensional variables and then solved numerically by using an implicit finite difference scheme known as Keller Box method. The effects of the parameters amplitude of the wavy surface, α, exponent of the variable heat flux, m, and Prandtl number on the local skin friction coefficient and local Nusselt number are shown graphically. It is found that for the negative value of exponent of the variable heat flux, m, the local skin friction coefficient increases and Nusselt number decreases but the opposite behavior is observed for the positive values of m. The comparison of limiting case with the previous study is shown through table and it is found that the solution obtained is in excellent agreement with the previous studies.

**KEYWORDS**

PAPER SUBMITTED: 2017-09-29

PAPER REVISED: 2018-01-08

PAPER ACCEPTED: 2018-03-06

PUBLISHED ONLINE: 2018-04-28

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**Issue 6**, PAGES [3391 - 3400]

- Yao L.S., Natural convection along a vertical wavy surface, ASME Journal of Heat Transfer, 105 (1983), pp. 465 - 468.
- Moulic S.G., Yao L.S., Mixed convection along wavy surface, ASME Journal of Heat Transfer, 111 (1989), pp. 974 - 979.
- Bhavnani S.H., Bergles A.E., Natural convection heat transfer from sinusoidal wavy surfaces, Heat and Mass Transfer, 26 (1991), pp. 341 - 349.
- Rees D.A.S., Pop I., Free convection induced by a horizontal wavy surface in a porous medium, Fluid Dynamics Research, 14 (1994), pp. 151 - 166.
- Kim E., Natural convection along a wavy vertical plate to non-Newtonian fluids, International Journal of Heat Mass Transfer, 40 (1997) 3069 - 3078.
- Chiu C.P., Chou H.M., Transient analysis of natural convection along a vertical wavy surface in micropolar fluids, International Journal of Engineering Science, 32 (1994), pp. 19 - 33.
- Wang C.C., Chen C.K., Mixed convection boundary layer flow of non-Newtonian fluids along vertical wavy plates, International journal of Heat and Fluid Flow, 23 (2002), pp. 831 - 839.
- Wang C.C., Chen C.K., Transient force and free convection along a vertical wavy surface in micropolar fluids, International Journal of Heat and Mass Transfer, 44 (2001), pp. 3241 - 3251.
- Kumari M., Pop I., Takhar H.S., Free convection boundary layer flow of a non-Newtonian fluid along a vertical wavy surface, International journal of Heat and Fluid Flow, 18 (1997) 625 - 631.
- Rathish Kumar B.V., Shalini, Non-Darcy free convection induced by a vertical wavy surface in a thermally stratified porous medium, International Journal of Heat and Mass Transfer, 47 (2004) pp. 2353 - 2363.
- Jang J.H., Yan W.M., Mixed convection heat and mass transfer along a vertical wavy surface, International Journal of Heat and Mass Transfer, 47 (2004), pp. 419 - 428.
- Jang J.H., Yan W.M., Liu H.C., Natural convection heat and mass transfer along a vertical wavy surface, International Journal of Heat and Mass Transfer, 46 (2003), pp. 1075 - 1083.
- Jang J.H., Yan W.M., Transient analysis of heat and mass transfer by natural convection over a vertical wavy surface, International Journal of Heat and Mass Transfer, 47 (2004) 3695 - 3705.
- Molla M.M., Hossain M.A., Yao L.S., Natural convection flow along a vertical wavy surface with uniform surface temperature in presence of heat generation/absorption, International Journal of thermal science, 43 (2004), pp. 157 - 163.
- R. S. Gorla, M. Kumari, Free convection along a vertical wavy surface in a nanofluid, Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanoengineering and Nanosystems, 225 (3) (2011) 133-142.
- I. Mustafa, T. Javed, A. Ghaffari, Hydromagnetic natural convection flow of water-based nanofluid along a vertical wavy surface with heat generation, Journal of Molecular Liquids, 229 (2017) 246-254.
- D. Srinivasacharya, P.V. Kumar, Mixed convection over an inclined wavy surface in a nanofluid saturated non-Darcy porous medium with Radiation Effect, International Journal of Chemical Engineering, 2015 (2015) Article ID 927508.
- A. Mahdy, S.E. Ahmed, Laminar free convection over a vertical wavy surface embedded in a porous medium saturated with a nanofluid, Transport in Porous Media, 91 (2012) 423-435.
- F. Habiba, M.M. Molla, M.A.H. Khan, Natural convection flow of Cu-H2O nanofluid along a vertical wavy surface with uniform heat flux, International Conference on Mechanical Engineering, 1754 (2016) 18-20.
- I. Mustafa, T. Javed, Heat Transfer In Natural Convection Flow Of Nanofluid Along A Vertical Wavy Plate With Variable Heat Flux, Thermal Science (2107), doi:10.2298/TSCI161012014M .
- Merkin J.H. and Mahmood T., On the free convection boundary layer on a vertical plate with prescribed surface heat flux, Journal of Engineering Mathematics, 24 (1990), pp. 95 - 107.
- Moulic S.G., Yao L.S., Natural convection along a wavy surface with uniform heat flux, ASME Journal of Heat Transfer, 111 (1989), pp. 1106 - 1108.
- Rees D.A. Pop I., Free convection induced by a vertical wavy surface with uniform heat flux in a porous medium, ASME Journal of Heat Transfer, 117 (1995), pp. 547 - 550.
- Pop I., Takhar H.S., Kumari M., Free convection about a vertical wavy surface with prescribed surface heat flux in a micropolar fluid, Technische Mechanik, 18 (1998), pp. 229 - 237.
- Tashtoush B. Abu-Irshaid E., Heat and fluid flow from a wavy surface subjected to a variable heat flux, Acta Mechanica 152 (2001), pp. 1 - 8.
- Javed T., Ahmad H., Ghaffari A., Influence of radiation on vertical wavy surface with constant heat flux: Using keller box scheme, Alexandria Engineering Journal, 55 (2016) 2221-2228.
- Siddiqa S., Hossain M.A., Saha S.C., Natural convection flow with surface radiation along a vertical wavy surface, Numerical Heat Transfer, Part A, Application, 64 (2013) 400 - 415.
- Cebeci T.,Bradshaw P., Physical and Computational Aspects of Convective Heat Transfer, Springer New York, 1984.