Homotopy Analysis Method for Solving System of Non-Linear Partial Differential Equations

Authors

  • Naveed Imran Department of Mathematics, HITEC College, Taxila Cantt. Pakistan https://orcid.org/0000-0003-2887-1097
  • Raja Mehmood Khan Department of Mathematics, HITEC College, Taxila Cantt. Pakistan

DOI:

https://doi.org/10.54938/ijemdm.2022.01.2.30

Keywords:

System of non-linear partial differential equations, Homotopy Analysis Method

Abstract

This paper applies Homotopy Analysis Method (HAM) to obtain analytical solutions of system of non-linear partial differential equations. Numerical results clearly reflect complete compatibility of the proposed algorithm and discussed problems. Moreover, the validity of the present solution and suggested scheme is presented and the limiting case of presented findings is in excellent agreement with the available literature. The computed solution of the physical variables against the influential parameters is presented through graphs. Several examples are presented to show the efficiency and simplicity of the method.

Downloads

Download data is not yet available.

References

M.J. St efan, Versuch Uber die scheinbare adhesio n, Akademie der Wissenschaf ten in Wien. Mat hemat isc h-Naturwisse nsc ha ft liche, 69, 713 (1874).

D.C. Kuzma, Flu id inert ia effect s in squeeze films, App. Sci. Res. 18, 15-20 (1968).

https://doi.org/10.1007/BF00382330

E.A. Hamza, The magneto hydro dyna mic squeeze film, J. Tribology, 110, 375-377 (1988).

https://doi.org/10.1115/1.3261636

G. Do ma irry, A. Aziz, Appro ximat e analysis o f MHD Squeeze flo w between t wo paralle l disks wit h suct io n or inject io n by ho motopy pert urbat io n met ho d, Math. Prob. Eng. (2009).DOI: 10.1155/2009/603916.

https://doi.org/10.1155/2009/603916

T. Hayat , A. Yousaf, M. Must af, S. Obaidat, MHD squeezing flo w o f seco nd-grade fluid bet ween two paralle l d isks, Int. J. Numer. Meth. Fluid, (2011).

https://doi.org/10.1002/fld.2565

T. Hayat , M. Nawaz, A. A. Hendi, S. Asghar, MHD Squeezing Flo w o f a Micropo lar Flu id Bet ween Paralle l D isks, J. Fluids Eng. 133,111206(2011).

https://doi.org/10.1115/1.4005197

A. Qayyu m, M. Awa is, A. Alsaed i, T. Ha yat, Unst eady squeezing flo w o f Jeffer y flu id bet ween two paralle l d isks, Chin. Phys. Lett. 29,034701(2012).

https://doi.org/10.1088/0256-307X/29/3/034701

A.-R.A. Kha led, K. Vafai, Hydro magnet ic squeezed flo w and heat transfer o ver a sensor surface, Int. J. Eng. Sci. 42,509-519(2004).

https://doi.org/10.1016/j.ijengsci.2003.08.005

M. Mahmoo d, S. Asghar, M.A. Hossain, Squeezed flo w and heat transfer o ver a porous surfacefo r visco us flu id, Heat Mass Transf. 44,165-173(2007).

https://doi.org/10.1007/s00231-006-0218-3

H.M. Duwair i, B. Tashto ush, R.A. Damseh, On heat transfer effect s in a visco us flu id squeezed and ext ruded bet ween two paralle l p lat es, Heat Mass Transf. 41,112-117(2004).

https://doi.org/10.1007/s00231-004-0525-5

M. Must afa, T. Hayat, S. Obaidat , On heat and mass transfer in t he unst eady squeezing flo w between paralle l p lat es, Meccanica(2012).

https://doi.org/10.1007/s11012-012-9536-3

B. Tashtoush, M. Tahat, S.D. Pro bert, Heat transfer and radia l flo ws via a visco usflu id squeezed bet ween t wo paralle l d isks, Appl. Energy, 68,275-288(2001).

https://doi.org/10.1016/S0306-2619(00)00058-1

A.R. Bahadir, T. Abba so v, A numer ica l approach to hydro magnet ic squeezed flo w and heat transfer between t wo paralle l d isks, Industrial Lubrication and Tribology63,63-71(2011).

https://doi.org/10.1108/00368791111112171

C. Neto, D.R. Evans, E. Bo naccurso, H.J. Butt, V.S.J. Craig, Bo undary slip in Newto nia n liqu ids: a review o f experime nt al studie s, Rep. Prog. Phys. 68,2859-2897(2005).

https://doi.org/10.1088/0034-4885/68/12/R05

C.L.M.H Navier, Mem. Acad. Sci. Inst . France,1,414-416(1823).

https://doi.org/10.1002/asna.18230011508

J. H. He, The ho motopy perturbat io n met ho d for no nlinear o scillat ors wit h disco nt inuit ie s, Appl. Math. Comput. 151,287-292(2004).

J. H. He, A co upling met hod o f ho motopyt echnique and perturbat io n t echnique fo r no nlinear pro ble ms, Int. J. Nonlin. Mech. 35(1),115-123(2000).

J. H. He, Variat io nal it erat io n met ho d-So me recent result s and new int erpret at io ns, J. Co mput. Appl. Math. 207,3-17(2007).

Downloads

Published

2022-05-14

How to Cite

Imran, N., & Mehmood Khan , R. (2022). Homotopy Analysis Method for Solving System of Non-Linear Partial Differential Equations. International Journal of Emerging Multidisciplinaries: Mathematics, 1(2), 35–48. https://doi.org/10.54938/ijemdm.2022.01.2.30

Issue

Section

Research Article

Categories