Abstract
This research applies fractional time derivatives to fluid flow through a horizontal microchannel. It uses fractional time derivatives with the Laplace transform technique and method of undetermined coefficient to analyze and obtain solutions of the governing equations in the Laplace domain. To this end, the solutions are reversed in the time domain using Riemann-sum approximation methods. In order to obtain the solutions for the pressure-driven flow, the time factional derivative in the Caputo sense is employed. Here, the influence of each governing parameter is explained with a line graph. Results show that with the decreases in fractional order $(\alpha)$, the velocity decreases within the interval $0<\alpha<1$. The fluid velocity increases and decreases as the Knudsen number $(kn)$ changes. Besides, transient wall-skin frictions for different times $(t)$ and Knudsen number $(kn)$ with a fixed value of fractional order $(\alpha)$ are observed.
Keywords
Fractional time derivative pressure-driven flow Knudsen number Laplace transform Couette flow
Thanks
Thank you so much for the opportunity to submit the manuscript
References
- H. M. Srivastava, R. K. Saxena, Operations of fractional integration and their applications, Applied Mathematics and Computation 118 (1) (2001) 1–52.
- D. Kaur, A detail study on fractional calculus, in: S. Negi, A. Kumar, T. Singh (Eds.), International Multidisciplinary Conference, Chandigarh, 2022, pp. 54–59.
- G. Farid, N. Latif, M. Anwar, A. Imran, M. Ozair, M. Nawaz, On applications of Caputo k-fractional derivatives, Advances in Difference Equations 2019 (2019) 439 16 pages.
- F. Ali, Z. Ahmad, M. Arif, I. Khan, K. S. Nisar, A time fractional model of generalized Couette flow of couple stress nanofluid with heat and mass transfer: Applications in engine oil, IEEE Access 8 (2020) 146944–146966.
- V. Djordjevic, Modeling of the slip boundary condition in micro-channel/pipe flow via fractional derivative, Monograph of Academy of Nonlinear Sciences. Advances in Nonlinear Sciences II-Sciences and Applications, Belgrade 2 (2008) 136–158.
- M. Saqib, A. R. M. Kasim, N. F. Mohammad, D. L. C. Ching, S. Shafie, Application of fractional derivative without singular and local kernel to enhanced heat transfer in CNTs nanofluid over an inclined plate, Symmetry 12 (5) (2020) 768 22 pages.
- R. Ellahi, T. Hayat, F. M. Mahomed, Generalized Couette flow of a third-grade fluid with slip: the exact solutions, Zeitschrift für Naturforschung A 65 (12) (2010) 1071–1076.
- M. Farooq, A. Khan, R. Nawaz, S. Islam, M. Ayaz, Y.-M. Chu, Comparative study of generalized couette flow of couple stress fluid using optimal homotopy asymptotic method and new iterative method, Scientific Reports 11 (2021) 3478 20 pages.
- M. Arif, P. Kumam, W. Kumam, M. B. Riaz, D. Khan, A comparative analysis of multiple fractional solutions of generalized Couette flow of couple stress fluid in a channel, Heat Transfer 51 (8) (2022) 7348–7368.
- S. Maiti, S. Shaw, G. C. Shit, Fractional order model for thermochemical flow of blood with Dufour and Soret effects under magnetic and vibration environment, Colloids and Surfaces B: Biointerfaces, 197 (2021) 1–18.
- M. L. Kaurangini, B. K. Jha, Unsteady generalized Couette flow in composite microchannel, Applied Mathematics and Mechanics 32 (2011) 23–32.
- S. Chen, L. Zheng, C. Li, J. Sui, Time-space dependent fractional viscoelastic MHD fluid flow and heat transfer over accelerating plate with slip boundary, Thermal Science 21 (6 Part A) (2017) 2337–2345.
Abstract
References
- H. M. Srivastava, R. K. Saxena, Operations of fractional integration and their applications, Applied Mathematics and Computation 118 (1) (2001) 1–52.
- D. Kaur, A detail study on fractional calculus, in: S. Negi, A. Kumar, T. Singh (Eds.), International Multidisciplinary Conference, Chandigarh, 2022, pp. 54–59.
- G. Farid, N. Latif, M. Anwar, A. Imran, M. Ozair, M. Nawaz, On applications of Caputo k-fractional derivatives, Advances in Difference Equations 2019 (2019) 439 16 pages.
- F. Ali, Z. Ahmad, M. Arif, I. Khan, K. S. Nisar, A time fractional model of generalized Couette flow of couple stress nanofluid with heat and mass transfer: Applications in engine oil, IEEE Access 8 (2020) 146944–146966.
- V. Djordjevic, Modeling of the slip boundary condition in micro-channel/pipe flow via fractional derivative, Monograph of Academy of Nonlinear Sciences. Advances in Nonlinear Sciences II-Sciences and Applications, Belgrade 2 (2008) 136–158.
- M. Saqib, A. R. M. Kasim, N. F. Mohammad, D. L. C. Ching, S. Shafie, Application of fractional derivative without singular and local kernel to enhanced heat transfer in CNTs nanofluid over an inclined plate, Symmetry 12 (5) (2020) 768 22 pages.
- R. Ellahi, T. Hayat, F. M. Mahomed, Generalized Couette flow of a third-grade fluid with slip: the exact solutions, Zeitschrift für Naturforschung A 65 (12) (2010) 1071–1076.
- M. Farooq, A. Khan, R. Nawaz, S. Islam, M. Ayaz, Y.-M. Chu, Comparative study of generalized couette flow of couple stress fluid using optimal homotopy asymptotic method and new iterative method, Scientific Reports 11 (2021) 3478 20 pages.
- M. Arif, P. Kumam, W. Kumam, M. B. Riaz, D. Khan, A comparative analysis of multiple fractional solutions of generalized Couette flow of couple stress fluid in a channel, Heat Transfer 51 (8) (2022) 7348–7368.
- S. Maiti, S. Shaw, G. C. Shit, Fractional order model for thermochemical flow of blood with Dufour and Soret effects under magnetic and vibration environment, Colloids and Surfaces B: Biointerfaces, 197 (2021) 1–18.
- M. L. Kaurangini, B. K. Jha, Unsteady generalized Couette flow in composite microchannel, Applied Mathematics and Mechanics 32 (2011) 23–32.
- S. Chen, L. Zheng, C. Li, J. Sui, Time-space dependent fractional viscoelastic MHD fluid flow and heat transfer over accelerating plate with slip boundary, Thermal Science 21 (6 Part A) (2017) 2337–2345.
Details
| Primary Language | English |
|---|---|
| Subjects | Applied Mathematics (Other) |
| Journal Section | Research & Review Articles |
| Authors | |
| Publication Date | December 31, 2023 |
| Submission Date | October 22, 2023 |
| Acceptance Date | December 27, 2023 |
| Published in Issue | Year 2023 Volume: 4 Issue: 2 |
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