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Heat Transfer Research
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Heat Transfer Research

DOI: 10.1615/HeatTransRes.2018021213
pages 1507-1526

ENTROPY GENERATION DUE TO FRACTIONAL COUETTE FLOW IN A ROTATING CHANNEL WITH EXPONENTIAL HEATING OF WALLS

Waqas Ali Azhar
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
Dumitru Vieru
Department of Theoretical Mechanics, Technical University of Iasi 700050, Romania
Constantin Fetecau
Academy of Romanian Scientists, Bucuresti 050094, Romania

ABSTRACT

The effect of the time-fractional Caputo-Fabrizio derivative on the entropy generation due to unsteady hydromagnetic fractional Couette flow in a rotating channel with the temperature of the channel walls varying exponentially is investigated analytically and numerically. Analytical solutions for primary and secondary velocity are obtained. These solutions are written as the sum of the post-transient solution (steady-state solution) and transient solution. Analytical and numerical solutions for the temperature filed, and local volumetric rate of entropy generation were obtained. Especially, we studied the influence of the fractional order parameter on the velocity components, temperature and entropy generation. It is found that the memory parameter influences only the transient parts of velocities. Therefore, after a critical time the velocity of fractional fluid will be close to that of the ordinary fluid. The fractional parameter significantly influences the temperature field and the local volumetric rate of entropy generation. The fluid temperature increases if the memory parameter decreases. The smallest value of temperature is obtained for ordinary fluids. Analyzing the influence of the fractional parameter on the dimensionless number of entropy generation and on the Bejan number, it is found that the entropy generation can be decreased by reducing the value of memory parameter.