Heat Transfer Analysis in Reiner–Philippoff Fluid via Finite Element Approach

Main Article Content

N. Jabbar
W. Sumelka
U. Nazir


In this article, we discuss the increase in Reiner–Philippoff liquid thermal energy and mass transfer through a perpendicular plane in the presence of the magnetizing field. Characterizations regarding mass dissipation and heat energy are improved using non-Fourier's analysis with the existence of a thermal source. Three kinds of nanoparticles, i.e., titanium dioxide, silicon dioxide, and aluminum oxide, are introduced in engine lubricants to create thermal energy. Darcy–Forchheimer analysis is adopted to examine the effects of flow and thermal energy. Furthermore, the Dufour and Soret effects are also discussed. A developing model is converted into a system of ordinary differential equations using similarity variables and solved using the finite element method. It is observed that the heat energy of the fluid increased as opposed to a higher rate of time relaxation number. Moreover, the fluid concentration declined as opposed to changes in the Schmidt number and chemical reaction parameters.

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How to Cite
N. Jabbar, W. Sumelka, and U. Nazir, “Heat Transfer Analysis in Reiner–Philippoff Fluid via Finite Element Approach”, Acta Phys. Pol. A, vol. 145, no. 5, p. 256, May 2024, doi: 10.12693/APhysPolA.145.256.


A. Ali, S. Saleem, S. Mumraiz, A. Saleem, M. Awais, D.N. Khan Marwat, J. Therm. Anal. Calorim. 143, 1985 (2021)

A. Ali, A. Noreen, S. Saleem, A.F. Aljohani, M. Awais, J. Therm. Anal. Calorim. 143, 2367 (2021)

Z. Ahmed, S. Saleem, S. Nadeem, A.U. Khan, Arab. J. Sci. Eng. 46, 2047 (2021)

D. Gopal, S. Saleem, S. Jagadha, F. Ahmad, A.O. Almatroud, N. Kishan, Alex. Eng. J. 60, 1861 (2021)

A.S. Oke, I.L. Animasaun, W.N. Mutuku, M. Kimathi, N.A. Shah, S. Saleem, Chinese J. Phys. 71, 716 (2021)

S. Saleem, B. Heidarshenas, J. Therm. Anal. Calorim. 45, 1599 (2021)

T. Elnaqeeb, I.L. Animasaun, N.A. Shah, Z. Naturforsch. A 76, 231 (2021)

E. Hou, F. Wang, U. Nazir, M. Sohail, N. Jabbar, P. Thounthong, Micromachines 13, 201 (2022)

F. Wang, U. Nazir, M. Sohail, E.R. El-Zahar, C. Park, P. Thounthong, Nanotechnol. Rev. 11, 834 (2022)

U. Nazir, M. Sohail, H. Alrabaiah, M.M. Selim, P. Thounthong, C. Park, PLOS ONE 16, e0256302 (2021)

S. Manjunatha, V. Puneeth, B.J. Gireesha, A. Chamkha, J. Appl. Comput. Mech. 8, 1279 (2022)

H. Adun, D. Kavaz, M. Dagbasi, J. Clean Prod. 328, 129525 (2021)

U. Nazir, S. Saleem, M. Nawaz, M.A. Sadiq, A.A. Alderremy, Phys. A Statis. Mech. App. 554, 123921 (2020)

U. Nazir, M.A. Sadiq, M. Nawaz, Int. Commun. Heat Mass Transf. 127, 105536 (2021)

I. Zehra, N. Abbas, M. Amjad, S. Nadeem, S. Saleem, A. Issakhov, Case Studies Therm. Eng. 27, 101146 (2021)

M. Saleem, M.N. Tufail, Indian J. Phys. (2023)

M.I. Asjad, N. Sarwar, M.B. Hafeez, W. Sumelka, T. Muhammad, Fractal Fract. 5, 99 (2021)

H. Darcy, Les Fontaines Publiques De La Ville De Dijon, Victor Dalmont, Paris 1856

P. Forchheimer, Z. Ver. D. Ing. 45, 1782 (1901)

M. Sohail, U. Nazir, A. Singh, A. Tulu, M.J. Khan, Sci. Rep. 14, 1520 (2024)

T. Sajid, M. Sagheer, S. Hussain, Math. Prob. Eng. 2020, 9701860 (2020)