ATANGANA – BALEANU FRACTIONAL MODELLING OF OLDROYD–B FLUID FLOW AND HEAT TRANSFER IN A CAPILLARY TUBE
DOI:
https://doi.org/10.62050/fjst2025.v9n1.350Keywords:
ldroyd-B fluid, heat transfer, Atangana-Baleanu fractional derivative, time-fractional modelingAbstract
In this work, the fluid flow and heat performance of Oldroyd-B fluids, through a capillary tube, were analyzed by means of a fractional model based on the Atangana-Baleanu time-fractional derivative. The fluid motion is generated by an arbitrary pressure gradient of a continuous function of the time. Analytical solutions for the velocity and temperature fields were obtained using the Laplace transform and the finite Hankel transform. In order to obtain the physical behavior regarding the velocity and temperature at the variation of the fractional parameters, material time, pulsation frequency effect and Prandtl number we carried out numerical calculations using MathCAD software and results were graphically presented. Numerical results obtained illustrated distinct behaviors of fractional order solutions when compared with classical model solutions. The fluid velocity and heat transfer performance in capillary tube can be controlled by regulating the fractional derivative parameter, relaxation, retardation time and Prandtl number which are very important in capillary devices. This fact can be an important in Biochip technology, thus making it possible to use this analysis technique extremely effective to control bioliquid samples of nanovolumes in capillary fluidic devices used for biological analysis and medical diagnosis
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Ali, M., Abdullahi, I., Yakubu, D. G., Adamu, G. T., Abdulhameed, M. and Baba, A. M. (2024). Transient MHD flow of fractional Burger's fluid
model through a parallel microchannel with heat transfer and slip boundary condition. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 238(2), 774-787.
Altunkaya, A., Aydin, O. and Avci, M. (2023). Pulsating flow and heat transfer of power-law fluid in a circular pipe. Nonlinear Analysis: Modelling and Control, 28(1).
Anwar, T., Kumam, P., Khan, I. and Thounthong, P. (2022). Thermal analysis of MHD convective slip transport of fractional Oldroyd-B fluid over a plate. Mechanics of Time-Dependent Materials, 26(2), 431-462
Dadheech, A., Sharma, S. and Al-Mdallal, Q. (2024). Numerical simulation for MHD Oldroyd-B fluid flow with melting and slip effect. scientific reports, 14(1), 10591
Fati, H. A., Abdulhameed, M. M., Adamu, M. Y. and Abdulhameed, B. M. (2023). Analytical solutions of non-Newtonian fluid flow and heat
transfer over an oscillating capillary tube. International Journal of Scientific Research in Mathematical and Statistical Sciences, 10(76)
Guedri, K., Lashin, M. M., Abbasi, A., Khan, S. U., Tag-ElDin, E. S. M., Khan, M. I., ... and Galal, A. M. (2022). Modelling and mathematical
investigation of blood-based flow of compressible rate type fluid with compressibility effects in a micro-channel. Micro-machines, 13(10), 1750
Liu, T., Chen, T. and Miozzi, M. (2024). Correlation between skin friction and enstrophy convection velocity in near-wall turbulence. uropean Journal of Mechanics-B/Fluids, 104, 224-230.
Martín-Gil, A. and Flores, O. (2024). Predicting the skin friction’s evolution in a forced turbulent channel flow. Computers & Fluids, 106417
Quran, O., Olimat, A. N., Maaitah, H. and Duwairi, H. M. (2024). Computational influences of convection micropolar fluid influx and
permeability on characteristics of heating rate and skin friction over vertical plate. International Journal of Thermofluids, 100885
Rathore, N. and N, S. (2023). A modified thermal flux model to examine the enhanced heat transmission in hybrid blood flow through artery: A comparison between Maxwell and Oldroyd-B models. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of
Process Mechanical Engineering, 237(5), 1846-1853.
Sehra, S., Noor, A., Haq, S. U., Jan, S. U., Khan, I. and Mohamed, A. (2023). Heat transfer of generalized second grade fluid with MHD, radiation and exponential heating using Caputo–Fabrizio fractional derivatives approach. Scientific Reports, 13(1), 5220.
Sidahmed, A. O. (2024). Numerical study for MHD flow of an Oldroyd-B fluid over a stretching sheet in the presence of thermal radiation with Soret and Dufour effects. International Journal of Analysis and Applications, 22, 19-19
Veltkamp, B., Jagielka, J., Velikov, K. P. and Bonn, D. (2023). Lubrication with non-Newtonian fluids. Physical Review Applied, 19(1), 14056.
Wang, X., Qiao, Y., Qi, H. and Xu, H. (2022). Numerical study of pulsatile non-Newtonian blood flow and heat transfer in small vessels under a magnetic field. International Communications in Heat and Mass Transfer, 133, 105930.
Yin D. and Ma H. B. (2013). Analytical solution of oscillating flow in a capillary tube, International Journal of Heat and Mass Transfer, 66, 699–705.
Zhao, Y., Fan, Y. and Li, W. (2024). Reynolds number effects on a velocity–vorticity correlation-based skin-friction drag decomposition in
incompressible turbulent channel flows. Journal of Fluid Mechanics, 979, A20.
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