Abstract
This paper aims to provide stability and thermomechanical analysis of hydromagnetic Falkner–Skan Casson conjugate fluid flow over an angular–geometric wedge-shaped surface. Based on the Buongiorno’s model, the governing boundary-layer equations are derived and solved iteratively using the homotopy analysis method (HAM). Furthermore, the HAM-series solution is optimised by minimising its squared residual errors. It is shown that the proposed approach can serve as an efficient criterion for accurately solving nonlinear problems.
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References
V M Falkner and S W Skan, Philos. Mag. 12, 865 (1931)
H Schlichting, Boundary-layer theory, 7th edn (McGraw-Hill, New York, 1978)
J Buongiorno, ASME J. Heat Transfer 128, 240 (2006)
T Hussain, S A Shehzad, A Alsaedi, T Hayat and M Ramzan, J. Cent. South Univ. 22, 1132 (2015)
C S K Raju, M M Hoque and T Sivasankar, Adv. Powder Technol. 28, 575 (2017)
G Kumaran and N Sandeep, J. Mol. Liq. 233, 262 (2017)
N S Akbar, J. Magn. Magn. Mater. 378, 463 (2015)
K U Rehman, A Qaiser, M Y Malik and U Ali, Chin. J. Phys. 55, 1605 (2017)
G S Seth, R Tripathi and M K Mishra, Appl. Math. Mech. 38, 1613 (2017)
M S Abel, J Tawade and M M Nandeppanavar, Int. J. Nonlinear Mech. 44, 990 (2009)
N Casson, Rheology of dispersed systems (C.C. Mills, New York, 1959)
M Nakamura and T Sawada, J. Non-Newton. Fluid 22, 191 (1987)
M Nakamura and T Sawada, J. Biomech. Eng. Trans. ASME 110, 137 (1988)
E C Bingham, Fluidity and plasticity (McGraw-Hill, New York, 1922)
F M White, Viscous fluid flow, 2nd edn (McGraw-Hill, New York, 1991)
K Ahmad, Z Hanouf and A Ishak, Eur. Phys. J. Plus 132, 87 (2017)
S J Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. thesis (Shanghai Jiao Tong University, Shanghai, 1992)
S J Liao, Beyond perturbation: Introduction to the homotopy analysis method (Chapman & Hall\(/\)CRC Press, Boca Raton, 2003)
S J Liao, Commun. Nonlinear Sci. Numer. Simul. 14, 983 (2009)
S J Liao, Appl. Math. Mech. 19, 957 (1998)
S J Liao, Appl. Math. Comput. 147, 499 (2004)
B Yao and J Chen, Appl. Math. Comput. 208, 156 (2009)
E Khoshrouye Ghiasi and R Saleh, Results Phys. 11, 65 (2018)
J Cheng, S J Liao, R N Mohapatra and K Vajravelu, J. Math. Anal. Appl. 343, 233 (2008)
M N Tufail, A S Butt and A Ali, J. Appl. Mech. Tech. Phys. 57, 900 (2016)
M S Hashmi, N Khan, T Mahmood and S A Shehzad, Int. J. Therm. Sci. 111, 463 (2017)
S J Liao, Commun. Nonlinear Sci. Numer. Simul. 15, 2003 (2010)
K Yabushita, M Yamashita and K Tsuboi, J. Phys. A 40, 8403 (2007)
V Marinca and N Herişanu, Int. Commun. Heat Mass 35, 710 (2008)
V Marinca, N Herişanu, C Bota and B Marinca, Appl. Math. Lett. 22, 245 (2009)
D Pal and H Mondal, Appl. Math. Comput. 212, 194 (2009)
S Mukhopadhyay, I C Mondal and A J Chamkha, Heat Trans. Asian Res. 42, 665 (2013)
B L Kuo, Acta Mech. 164, 161 (2003)
A H Craven and L A Peletier, Mathematika 19, 135 (1972)
B Oskam and A E P Veldman, J. Eng. Math. 16, 295 (1982)
M Z Salleh, R Nazar and I Pop, Chem. Eng. Commun. 196, 987 (2009)
M Z Salleh, R Nazar and I Pop, Acta Appl. Math. 112, 263 (2010)
L Fusi, A Farina and F Rosso, Int. J. Nonlinear Mech. 64, 33 (2014)
E Moreno, A Larese and M Cervera, J. Non-Newton. Fluid 228, 1 (2016)
P K Swamee and N Aggarwal, J. Petrol. Sci. Eng. 76, 178 (2011)
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Appendix A
Appendix A
The constitutive equation of the Bingham plastic model can be expressed as [14]
It can be seen from eq. (A1), that the viscosity coefficient \(\mu _{\mathrm{B}} \) diverges while the velocity gradient becomes zero (see [12]). It is noteworthy to mention that more details on the Bingham plastic model have also been reported in some previous studies (see [38,39,40]).
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Ghiasi, E.K., Saleh, R. Nonlinear stability and thermomechanical analysis of hydromagnetic Falkner–Skan Casson conjugate fluid flow over an angular–geometric surface based on Buongiorno’s model using homotopy analysis method and its extension. Pramana - J Phys 92, 12 (2019). https://doi.org/10.1007/s12043-018-1667-1
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DOI: https://doi.org/10.1007/s12043-018-1667-1