Abstract: In this study, the similarity solutions of unsteady mixed convective boundary layer flow, heat transfer, and mass transfer of viscous incompressible fluid above an isothermal horizontal plate are investigated through incorporating the effect of suction. The governing nonlinear partial differential equations of the specified problem are simplified by the usual Boussinesq approximation and are made dimensionless through similarity transformations by introducing non-dimensional coordinates and variables. Using the similarity technique, the system of equations is transformed into a set of coupled nonlinear ordinary differential equations. The transformed set of similarity ordinary differential equations is then solved numerically adopting the shooting method through ODE45 MATLAB software. The solutions are obtained for the non-dimensional velocity, temperature, and concentration fields for different selected values of the established dimensionless parameters and numbers, namely, suction parameter (Fw), modified buoyancy parameter (Ja), porosity parameter (K), modified thermal Grashof number (Gr), modified solute Grashof number (Gc), Prandtl number (Pr), Schmidt number (Sc), and other similarity parameters (A1, A2, and A3). The influences of different values of these established dimensionless parameters and numbers on the non-dimensional field variables are extensively investigated and exhibited graphically. The effects of suction on the parameters of physical interest like the coefficient of skin friction, local Nusselt number and local Sherwood are computed and presented numerically in the table. It is observed that the velocity, temperature, and concentration fields within the boundary layer decreased significantly with the increase of the suction parameter (Fw). Consequently, the increase of the suction parameter causes to increase the skin friction coefficient, the rate of heat transfer and the rate of mass transfer. The other dimensionless parameters/numbers have reasonable impact on the field variables as observed from the numerical results.
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Keywords and phrases: mixed convection, suction, Boussinesq approximation, similarity transformations, shooting method, MATLAB.
Received: November 15, 2021; Accepted: January 25, 2022; Published: March 15, 2022
How to cite this article: Most. Sharifa Pervin, M. M. Touhid Hossain and Md. Hasanuzzaman, Similarity solutions of unsteady mixed convective boundary layer flow above a horizontal porous surface with the effect of suction, JP Journal of Heat and Mass Transfer 26 (2022), 111-142. http://dx.doi.org/10.17654/0973576322016
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] C. A. Hieber, Mixed convection above a heated horizontal surface, International Journal of Heat and Mass Transfer 16(4) (1973), 769-785. https://doi.org/10.1016/0017-9310(73)90090-2. [2] N. Ramachandran, B. F. Armaly and T. S. Chen, Mixed convection over a horizontal plate, ASME J. Heat Transfer 105(2) (1983), 420-423. [3] N. Afzal and T. Hussain, Mixed convection over a horizontal plate, ASME J. Heat Transfer 106(1) (1984), 240-241. https://www.researchgate.net/journal/Journal-of-Heat-Transfer-0022-1481. [4] T. S. Chen, B. F. Armaly and N. Ramachandran, Correlation for laminar mixed convection flows on vertical, inclined and horizontal flat plates, ASME J. Heat Transfer 108 (1986), 835-840. [5] M. A. Hossain and M. S. Munir, Mixed convection flow from a vertical flat plate with temperature dependent viscosity, International Journal of Thermal Sciences 39(2) (2000), 173-183. http://dx.doi.org/10.1016/S1290-0729(00)00237-4. [6] M. A. Seddeek and A. M. Salem, Laminar mixed convection adjacent to vertical continuously stretching sheets with variable viscosity and variable thermal diffusivity, Heat and Mass Transfer 41 (2005), 1048-1055. http://dx.doi.org/10.1007/s00231-005-0629-6. [7] H. Lin and W. Yu, Free convection on a horizontal plate with blowing and suction, ASME J. Heat Transfer 110(3) (1988), 793-796. https://doi.org/10.1115/1.3250564. [8] L. E. Erikson, L. T. Fan and V. G. Fox, Heat and mass transfer on a moving continuous flat plate with suction or injection on the flat plate, Industrial Engineering Chemical Fundamentals 5 (1996), 19-25. http://dx.doi.org/10.1021/i160017a004. [9] W. T. Cheng and C. N. Huang, Unsteady flow and heat transfer on an accelerating surface with blowing or suction in the absence and presence of a heat source or sink, Chemical Engineering Science 59 (2004), 771-780. [10] Md. Zakerullah, Laminar natural and combined convection flow, Ph.D. Dissertation, The Victoria University of Manchester, England, March 1976. [11] Md. Zakerullah and J. A. D. Ackroyd, Laminar natural convection boundary layers on horizontal circular disks, J. Appl. Math. Phys. 30(3) (1979), 427-435. [12] J. H. Merkin, A note on the similarity solutions for free convection on a vertical plate, Journal of Engineering Mathematics 19 (1985), 189-201. [13] O. Aydin and A. Kaya, Laminar boundary layer flow over a horizontal permeable flat plate, Applied Mathematical Modeling 161(1) (2005), 229-240. http://dx.doi.org/10.1016/j.apm.2005.12.015. [14] L. Deswita, R. Nazar, R. Ahmed, A. Ishak and I. Pop, Similarity solution of free convection boundary layer flow on a horizontal plate with variable wall temperature, European Journal of Scientific Research 27(2) (2009), 188-198. [15] A. Aziz, A similarity solution for laminar thermal boundary layer over a flat plate with a convection surface boundary condition, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), 1064-1068. [16] M. J. Uddin, W. A. Khan, A. I. Ismail and M. A. A. Hamad, New similarity solutions of boundary layer flow along a continuously moving convectively heated horizontal plate by deductive group method, Thermal Science 19(3) (2015), 1017-1024. https://www.researchgate.net/journal/Thermal-Science-0354-9836. [17] M. M. T. Hossain, R. Mojumder and M. A. Hossain, Solution of natural convection boundary layer flow above a semi-infinite porous horizontal plate under similarity transformations with suction and blowing, Daffodil International University Journal of Science and Technology 6(1) (2011), 43-51. [18] K. Vajravelu, K. V. Prasad and Chiu-On Ng, Unsteady convective boundary layer flow of a viscous fluid at a vertical surface with variable fluid properties, Nonlinear Anal. Real World Appl. 14(1) (2013), 455-464. doi:10.1016/j.nonrwa.2012.07.008. [19] A. Ishak, R. Nazar and I. Pop, Dual solutions in mixed convection boundary-layer flow with suction or injection, IMA Journal of Applied Mathematics 72(4) (2007), 451-463. doi:10.1093/imamat/hxm020. [20] A. Ishak, J. H. Merkin, R. Nazar and I. Pop, Mixed convection boundary-layer flow over a permeable vertical surface with prescribed wall heat flux, Zeitschrift für Angewandte Mathematik und Physik ZAMP 59 (2008b), 100-123. [21] M. M. T. Hossain, B. Mandal and M. A. Hossain, Similarity solution of unsteady combined free and force convective laminar boundary layer flow about a vertical porous surface with suction and blowing, Procedia Engineering 56 (2013), 134-140. [22] Md. Hasanuzzaman, B. Mandal and M. M. T. Hossain, A study of similarity solution of unsteady combined free and force convective laminar boundary layer flow about a vertical porous surface with suction and blowing, Annals of Pure and Applied Mathematics 6(1) (2014), 85-97. [23] Md. Y. Ali, M. N. Uddin, M. J. Uddin and N. M. R. Zahed, Similarity solutions of unsteady convective boundary layer flow along isothermal vertical plate with porous medium, Open Journal of Fluid Dynamics 5 (2015), 391-406. [24] W. Schneider, A similarity solution for combined forced and free convection flow over a horizontal plate, International Journal of Heat and Mass Transfer 22(10) (1979), 1401-1406. https://doi.org/10.1016/0017-9310(79)90202-3. [25] G. Ramanaiah and G. Malarvizhi, Unified treatment of similarity solutions of free, mixed and forced convection problems in saturated porous media, Proceedings of 6th International Conference on Numerical Method in Thermal Problems, Swansea, UK, 1989, pp. 431-439. [26] R. C. Chaudhary, G. N. Purohit and P. Garg, Similarity solutions for laminar boundary layer flow of Darcian fluid over horizontal plate with a convective boundary condition, Appl. Math. 7 (2016), 313-319. [27] M. N. Uddin, Md. Y. Ali, N. M. R. Zahed and Md. J. Uddin, Similarity solutions of unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate, Open Journal of Fluid Dynamics 6 (2016), 279-302
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