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Double-diffusion Cattaneo-Christov model for oldroyd-b nanofluid with motile microorganisms under Arrhenius reaction and mixed convection

M. O. Mohammed1, O. A. Ajala2, A. K. Jimoh1, A. O. Akindele2, A. A. Waheed3, S. O. Sangoniyi4, M. O. Afolabi2, A. O. Areo2
1Department of Mathematics and Statistics, Kwara State University, Malete, Nigeria
2Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Oyo State Nigeria
3Department of Mathematics, Lead City University, Ibadan, Oyo State, Nigeria
4Department of Mathematics, Emmanuel Alayande University of Education, Oyo, Nigeria
Copyright © M. O. Mohammed, O. A. Ajala, A. K. Jimoh, A. O. Akindele, A. A. Waheed, S. O. Sangoniyi, M. O. Afolabi, A. O. Areo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The growing thermal demands of modern energy conversion, chemical processing, and micro-scale electronic devices necessitate advanced heat and mass transfer strategies, particularly for smart fluids operating in reactive environments. In this work, the flow behavior of an electrically conducting Oldroyd-B nanofluid containing motile microorganisms is analyzed within the Cattaneo-Christov double-diffusion (CCDD) paradigm, which accounts for finite thermal and solutal relaxation times beyond the classical Fourier-Fick theory. The model incorporates mixed convection, and Arrhenius-type chemical reactions to capture complex transport interactions. By employing the Chebyshev Collocation Method (CCM), the coupled nonlinear ordinary differential equations governing the system are solved with high spectral accuracy. The parametric analysis reveals that buoyancy-induced forces significantly strengthen convective transport. Distinct and contrasting influences of relaxation and retardation parameters are observed in the velocity field, highlighting the viscoelastic nature of the fluid. Moreover, thermophoresis and Dufour mechanisms promote thermal and concentration diffusion, while increasing Prandtl and Schmidt numbers, thermal relaxation time, and chemical reaction rate diminish the associated boundary layers. The combined effects of non-Fourier diffusion, and chemical activity lead to transport characteristics unattainable under classical assumptions. These findings offer valuable physical insight for the design and optimization of nanofluid-based thermal systems in advanced industrial and technological applications.

Keywords: Cattaneo-Christov double-diffusion, motile microorganisms, non Newtonian fluids, solar radiation, Chebyshev collocation method