Analysis of MHD Richardson Flow Past An Exponentially Stretched Infinite Plate with Suction and Cross-Diffusion Effects

Year 2023, Volume: 5 Issue: 2, 74 - 88, 29.12.2023

Uchenna Uka , Promise Mebıne , Samson Agunbıade

https://doi.org/10.55979/tjse.1356407

Abstract

The present paper investigate the effects of magnetic field (MHD), Richardson and suction on an exponentially expanded infinite plate by studying the convective heat and mass transfer of a non-Newtonian incompressible viscous and electrically conducting fluid. Cross-diffusion impacts are also taken into consideration. The governing partial differential equations (PDEs) are transformed into ordinary differential equations through the application of well-posed similarity transformation variables (STVs). Thus, the transformed dimensionless equations are solved analytically by integrating factor approach and the resulting solutions are simulated with an efficient stability numerical algorithm known as Mathematica. The results are displayed in tabular and graphical forms while the effects of various parameters on the velocity, temperature, concentration, skin–friction coefficient, Nusselt and Sherwood numbers are discussed in details. It was found that velocity falls when magnetic field and suction parameters increase. Also, the temperature and nanoparticle concentration decreases as suction number rises but are enhanced as diffusion-thermo and thermal-diffusivity parameters rise. An increase in Richardson and Prandtl numbers leads to a decrease in skin-friction and upsurge in the rate of heat transportation. The results of this study can be used to advance the design, operation, and performance of various systems encountered in industrial and scientific applications.

Keywords

Energy flux, Mass diffusion, Nanofluidic, Wolfram Mathematica

Supporting Institution

None.

Thanks

Thank you.

MHD Richardson Akışının Emiş ve Çapraz Difüzyon Etkileri ile Üstel Olarak Gerilmiş Sonsuz Bir Plakadan Geçmesinin Analizi

Abstract

Bu makale, Newtonyen olmayan sıkıştırılamaz viskoz ve elektriksel olarak iletken bir akışkanın konvektif ısı ve kütle transferini inceleyerek, manyetik alanın (MHD), Richardson ve emmenin üstel olarak genişleyen sonsuz bir plaka üzerindeki etkilerini araştırmaktadır. Çapraz difüzyon etkileri de dikkate alınır. Geçerli kısmi diferansiyel denklemler (PDE'ler), iyi konumlanmış benzerlik dönüşüm değişkenlerinin (STV'ler) uygulanması yoluyla sıradan diferansiyel denklemlere dönüştürülür. Böylece, dönüştürülen boyutsuz denklemler, entegre faktör yaklaşımıyla analitik olarak çözülmekte ve elde edilen çözümler, Mathematica olarak bilinen etkin kararlılık sayısal algoritmasıyla simüle edilmektedir. Sonuçlar tablo ve grafik formlarında gösterilirken, çeşitli parametrelerin hız, sıcaklık, konsantrasyon, yüzey sürtünme katsayısı, Nusselt ve Sherwood sayıları üzerindeki etkileri ayrıntılı olarak tartışılmaktadır. Manyetik alan ve emme parametreleri arttıkça hızın düştüğü bulunmuştur. Ayrıca emme sayısı arttıkça sıcaklık ve nanopartikül konsantrasyonu azalır, ancak difüzyon termo ve termal yayılma parametreleri yükseldikçe artar. Richardson ve Prandtl sayılarındaki artış, cilt sürtünmesinin azalmasına ve ısı aktarım hızının artmasına neden olur. Bu çalışmanın sonuçları, endüstriyel ve bilimsel uygulamalarda karşılaşılan çeşitli sistemlerin tasarımını, işletimini ve performansını geliştirmek için kullanılabilir.

Keywords

Enerji akısı, Kütle difüzyonu, Nanoakışkan, Wolfram Mathematica

Supporting Institution

None.

Thanks

The authors wish to acknowledge Professor Ekaka-a E. N for his well recognized input towards the realization of this work.

References

• Abd El-Aziz, M. (2009). Radiation effect on the flow and heat transfer over an unsteady stretching sheet. International Communications in Heat and Mass Transfer, 36, 521-524.
• Abd El-Aziz, M. (2010). Flow and heat transfer over an unsteady stretching surface with Hall Effect. Meccanica, 45, 97-109.
• Abd El-Aziz, M., & Salem, A. M. (2007). MHD-mixed convection and mass transfer from a vertical stretching sheet with diffusion of chemically reactive species and space or temperature dependent heat source. Canadian Journal of Physics, 85, 359-373.
• Abo-Eldahab, E. M., & Abd El-Aziz, M. (2005). Flow and heat transfer in a micropolar fluid past a stretching surface embedded in a non-Darcian porous medium with uniform free stream. Applied Mathematics and Computation, 162, 881-899.
• Ali, M., & Al-Yousef, F. (2004). Laminar mixed convection boundary layers induced by a linearly stretrching permeable surface. International Journal of Heat and Mass Transfer, 45, 4241-4250.
• Awucha, U. U., & Okechukwu, A. (2022). Soret dissipation effect on heat and mass transmission of non-Newtonian Casson Radiative nanofluid Flow with Lorentz drag and Rosseland radiation. Journal of Pure and Applied Sciences, 21(2), 120-127. https://doi.org/10.51984/jopas.v21i2.2059
• Bachok, N., Ishak, A., & Nazar, R. (2011). Flow and heat transfer over an unsteady stretching sheet in a micropolar fluid. Meccanica, 46(9), 935-942.
• Bestman, A. R. (1990). The boundary-layer flow past a semi-infinite heated porous plate for two-component plasma. Astrophysics and Space Science, 173, 93-100.
• Bhattacharyya, K. (2012). Steady boundary layer flow and reactive mass transfer past an exponentially stretching surface in an exponentially moving free stream. Journal of the Egyptian Mathematical Society, 20, 223-228.
• Bhattacharyya, K., & Layek, G. C. (2014). Magnetohydrodynamic boundary layer flow of nanofluid over an exponentially stretching permeable sheet. Physics Research International, 592536. https://doi.org/10.1155/2014/592536
• Boussinesq, J. (1877). Analytical Theory of Heat. Gauthier-Villars. Paris. Dandapat, B. S., Singh, S. N., & Singh, R. P. (2004). Heat transfer due to permeable stretching wall in the presence of transverse magnetic field. Archives of Mechanics, 56, 87-101.
• Das, K. (2012). Influence of thermophoresis and chemical reaction on MHD micropolar fluid flow with variable fluid properties. International Journal of Heat and Mass Transfer, 55, 7166-7174.
• Elbashbeshy, E. M. A., & Bazid, M. A. A. (2004). Heat transfer over an unsteady stretching surface. Heat Mass Transfer, 41, 1-4.
• Ene, R. D., & Marinca, V. (2015). Approximate solutions for steady boundary layer MHD viscous flow and radiative heat transfer over an exponentially porous stretching sheet. Applied Mathematics and Computation, 269, 389-401.
• Fauzi, E. L. H., Ahmad, S., & Pop, I. (2012). Mixed convection boundary layer flow from a vertical cone in a porous medium filled with a nanofluid. Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 6, 10-22.
• Jain, S., & Choudhary, R. (2015). Effects of MHD on boundary layer flow in porous medium due to exponentially shrinking sheet with slip. Procedia Engineering, 127, 1203-1210.
• Liu, I. C., Wang, H. H., & Peng, Y. F. (2013). Flow and heat transfer for three-dimensional flow over an exponentially stretching surface. Chemical Engineering Communications, 200, 253-268.
• Mukhopadhyay, S., Bhattacharyya, K., & Layek, G. C. (2014). Mass transfer over an exponentially stretching porous sheet embedded in a stratified medium. Chemical Engineering Communications, 201, 272-286.
• Nadeem, S., Haq, R. U., & Khan, Z. H. (2014). Heat transfer analysis of water-based nanofluid over an exponentially stretching sheet. Alexandria Engineering Journal, 53, 219-224.
• Rabeti, M. (2014). Mixed convection heat transfer of nanofluids about a horizontal circular cylinder in porous media. SOP Transaction on Nano Technology, 1(1), 1-4.
• Rosseland, S. (1936). Theoretical Astrophysics. Clarendon Press, Oxford.
• Turkyilmazoglu, M. (2014). A note on micropolar fluid flow and heat transfer over a porous shrinking sheet. International Journal of Heat and Mass Transfer, 72, 388-391.