期刊
JOURNAL OF THERMAL ANALYSIS AND CALORIMETRY
卷 143, 期 5, 页码 3667-3676出版社
SPRINGER
DOI: 10.1007/s10973-020-09312-8
关键词
Mittage-Leffler and exponential kernels; Rotational second-grade fluid; Exact solutions; Heat transfer
资金
- Mehran university of Engineering and Technology, Jamshoro, Pakistan
This paper explores the temperature change and thermal stratification of rotational second-grade fluid through fractional analysis and mathematical modeling. The results indicate that fractional solutions are more stable and faster than classical solutions.
This manuscript predicts the change in temperature at a different epilimnion to the change in temperature at a different hypolimnion. The fractional analysis on rotational second-grade fluid with sinusoidal boundary conditions is performed for knowing thermal stratification. The mathematical modeling is also proposed by means of modern fractional differential operators, namely Caputo-Fabrizio and Atangana-Baleanu derivatives, for rotational second-grade fluid. Most of authors have proposed the classical solutions of rotational second-grade fluid, which are obtained by the Laplace transform only. Our fractionalized mathematical model of rotational second-grade fluid has been solved via Fourier sine and Laplace transform techniques simultaneously. The solutions of velocity and temperature have been investigated and expressed in the format of Mittag-Leffler and Fox-H functions. Both fractional solutions are presented for comparison of velocity and temperature through Caputo-Fabrizio and Atangana-Baleanu derivatives. Finally, our results showed that the fractional solutions investigated for the velocity and temperature via Fourier sine and Laplace transform methods are stable and rapid than classical solutions.
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