Sains Malaysiana 51(7)(2022): 2223-2235

http://doi.org/10.17576/jsm-2022-5107-23

Mass Transfer of a Thermally Radiative MHD Cattaneo-Christov Nanofluid between Two Stretchable Spinning Disks

(Pemindahan Jisim Radiatif Terma Bendalir MHD Cattaneo-Christov antara Dua Cakera Berputar Meregang)

PETER NGBO HABU^1,3, SHARIFAH NURIZA AL’AIDRUS¹, NOOR FADIYA MOHD NOOR^1,2,*& ZAILAN SIRI^1,2

¹Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, Federal Territory, Malaysia

²Center for Data Analytics Consultancy & Services, Faculty of Science, Universiti Malaya,

50603 Kuala Lumpur, Federal Territory, Malaysia

³Department of Mathematics, Faculty of Science, Federal University of Lafia, 950101 Nasarawa State, Nigeria

Diserahkan: 17 September 2021/Diterima: 6 Januari 2022

Abstract

The investigation on the impacts of magnetic field, thermal radiation, generation of heat and mass transfer in a porous-medium-embedded homogenous nanofluid flow between two stretchable spinning disks is crucial since spinning disks are prevalent in many engineering and technological applications. The objective of this research was to analyze the influences of these parameters using the Cattaneo-Christov heat flux model against the flow’s temperature, velocity and concentration profiles. Temperature profile is a decreasing function of thermal relaxation time parameter due to the particles require a longer period to transfer heat to the next particles. The rates of heat transfer at both spinning disks decrease as values of heat generation, Eckert number, Prandtl number, Brownian diffusion, thermophoresis diffusion and rotation ratio increase. The disks’ rates of mass transfer decrease with more thermophoresis diffusion, heat generation, heat transfer dissipation, and momentum diffusivity, but they increase with thermal radiation parameter. The current work attempts to include the transport profile of a Buongiorno’s nanofluid embedded in a Darcian porous medium between dual spinning disks with magnetic field, thermal radiation and generation of heat using the heat flux model of Cattaneo-Christov’s. Von Karman transformations are utilized to transform the nonlinear partial differential equations of fluid dynamics into coupled nonlinear ordinary differential equations (ODEs). These coupled ODEs are later solved by employing a shooting method with MATLAB bvp4c algorithm. All numerical evidences from this investigation are conferred through tables and figures after validation of present computations.

Keywords: Heat generation; mass transfer; MHD Cattaneo-Christov nanofluid; thermal radiation; two stretchable spinning disks

Abstrak

Kajian kesan medan magnet, radiasi terma, penjanaan haba dan pemindahan jisim dalam medium berliang yang dialiri oleh bendalir nano homogen di antara dua cakera meregang yang berputar adalah penting kerana cakera berputar lazimnya terdapat dalam banyak aplikasi kejuruteraan dan teknologi. Objektif penyelidikan ini ialah untuk menganalisis pengaruh parameter menggunakan model fluks haba Cattaneo-Christov terhadap profil suhu, halaju dan kepekatan aliran. Profil suhu adalah fungsi yang menyusut dengan parameter masa keredaan terma kerana zarah memerlukan jangka masa yang lebih lama untuk memindahkan haba ke zarah seterusnya. Kadar pemindahan haba pada kedua cakera berputar menyusut apabila nilai penjanaan haba, nombor Eckert, nombor Prandtl, penyebaran Brownian, penyebaran termoforesis dan nisbah putaran meningkat. Kadar pemindahan jisim cakera berkurang dengan penyebaran termoforesis, penjanaan haba, pelesapan pemindahan haba dan penyebaran momentum, tetapi meningkat dengan parameter radiasi terma. Kajian ini cuba memasukkan profil pengangkutan bendalir nano Buongiorno melalui medium berliang Darcy di antara dua cakera berputar dengan medan magnet, radiasi terma dan penjanaan haba menggunakan model fluks haba Cattaneo-Christov. Transformasi Von Karman digunakan untuk mengubah persamaan pembezaan separa tak linear bagi dinamik bendalir supaya menjadi persamaan pembezaan biasa (PPB) tak linear. Gandingan PPB ini kemudiannya diselesaikan dengan menggunakan kaedah pembedilan dengan algoritma MATLAB bvp4c. Semua bukti berangka daripada penyelidikan ini dinyatakan dalam jadual dan rajah setelah pengiraan semasa disahkan.

Kata kunci: Bendalir nano MHD Cattaneo-Christov; dua cakera meregang yang berputar; pemindahan jisim; penjanaan haba; radiasi terma

RUJUKAN

Ahmed, J., Khan, M. & Ahmad, L. 2019. MHD swirling flow and heat transfer in Maxwell fluid driven by two coaxially rotating disks with variable thermal conductivity. Chin. J. Phys. 60: 22-34.

Das, A. 2015. Analytical solution to the flow between two coaxial rotating disks using HAM. Procedia Eng. 127: 377-382.

Dogonchi, A. & Ganji, D. 2017. Impact of Cattaneo-Christov heat flux on MHD nanofluid flow and heat transfer between parallel plates considering thermal radiation effect. J. Taiwan Inst. Chem. Eng. 80: 52-63.

El-Mistakawy, T.M., Attia, H.A. & Megahed, A.A. 2000. Asymptotic solution for the flow due to an infinite rotating disk in the case of large magnetic field. Trans. Can. Soc. Mech. Eng. 24: 515-523.

Hayat, T. & Nadeem, S. 2018. Flow of 3D Eyring-Powell fluid by utilizing Cattaneo-Christov heat flux model and chemical processes over an exponentially stretching surface. Results Phys. 8: 397-403.

Hayat, T., Khan, M.I., Qayyum, S., Khan, M.I. & Alsaedi, A. 2018a. Entropy generation for flow of Sisko fluid due to rotating disk. J. Mol. Liq. 264: 375-385.

Hayat, T., Javed, M., Imtiaz, M. & Alsaedi, A. 2018b. Effect of Cattaneo-Christov heat flux on Jeffrey fluid flow with variable thermal conductivity. Results Phys. 8: 341-351.

Hayat, T., Khan, M.W.A., Khan, M.I., Waqas, M. & Alsaedi, A. 2018c. Impact of chemical reaction in fully developed radiated mixed convective flow between two rotating disk. Physica B Condens. 538: 138-149.

Hayat, T., Muhammad, T., Mustafa, M. & Alsaedi, A. 2017a. Three-dimensional flow of Jeffrey fluid with Cattaneo-Christov heat flux: An application to non-Fourier heat flux theory. Chin. J. Phys. 55(3): 1067-1077.

Hayat, T., Khan, M.I., Farooq, M., Alsaedi, A. & Khan, M.I. 2017b. Thermally stratified stretching flow with Cattaneo-Christov heat flux. Int. J. Heat Mass Transfer 106: 289-294.

Hayat, T., Qayyum, S., Imtiaz, M. & Alsaedi, A. 2017c. Flow between two stretchable rotating disks with Cattaneo-Christov heat flux model. Results Phys. 7: 126-133.

Imtiaz, M., Hayat, T., Alsaedi, A. & Ahmad, B. 2016. Convective flow of carbon nanotubes between rotating stretchable disks with thermal radiation effects. Int. J. Heat Mass Transfer 101: 948-957.

Jyothi, K., Reddy, P.S. & Reddy, M.S. 2018. Influence of magnetic field and thermal radiation on convective flow of SWCNTs-water and MWCNTs-water nanofluid between rotating stretchable disks with convective boundary conditions. Powder Tech. 331: 326-337.

Karman, T.V. 1921. Über laminare und turbulente Reibung. ZAMM 1(4): 233-252.

Khan, W., Irfan, M. & Khan, M. 2017. An improved heat conduction and mass diffusion models for rotating flow of an Oldroyd-B fluid. Results Phys. 7: 3583-3589.

Khan, W.A., Khan, M. & Alshomrani, A.S. 2016. Impact of chemical processes on 3D Burgers fluid utilizing Cattaneo-Christov double-diffusion: Applications of non-Fourier's heat and non-Fick's mass flux model. J. Mol. Liq. 223: 1039-1047.

Mahanthesh, B., Gireesha, B. & Raju, C. 2017. Cattaneo-Christov heat flux on UCM nanofluid flow across a melting surface with double stratification and exponential space dependent internal heat source. Inform. Med. Unlocked 9: 26-34.

Mahmood, A., Jamshed, W. & Aziz, A. 2018. Entropy and heat transfer analysis using Cattaneo-Christov heat flux model for a boundary layer flow of Casson nanofluid. Results Phys. 10: 640-649.

Muhammad, N., Nadeem, S. & Mustafa, T. 2017. Squeezed flow of a nanofluid with Cattaneo-Christov heat and mass fluxes. Results Phys. 7: 862-869.

Mustafa, M. 2017. MHD nanofluid flow over a rotating disk with partial slip effects: Buongiorno model. Int. J. Heat Mass Transfer 108: 1910-1916.

Qayyum, S., Khan, M.I., Hayat, T., Alsaedi, A., Tamoor, M. 2018. Entropy generation in dissipative flow of Williamson fluid between two rotating disks. Int. J. Heat Mass Transfer 127: 933-942.

Stewartson, K. 1953. On the flow between two rotating coaxial disks. Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University Press: Cambridge, UK. pp. 333-341.

Turkyilmazoglu, M. 2016. Flow and heat simultaneously induced by two stretchable rotating disks. Phys. Fluids 28(4): 043601.

Upadhya, S.M., Raju, C. & Saleem, S. 2018. Nonlinear unsteady convection on micro and nanofluids with Cattaneo-Christov heat flux. Results Phys. 9: 779-786.

^*Pengarang untuk surat-menyurat; email: drfadiya@um.edu.my