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Heat Transfer Research
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Heat Transfer Research

DOI: 10.1615/HeatTransRes.2017016039
pages 1047-1068

EFFECTS OF FRACTIONAL ORDER ON CONVECTIVE FLOW OF AN OLDROYD-B FLUID ALONG A MOVING POROUS HOT PLATE WITH THERMAL DIFFUSION

Constantin Fetecau
Academy of Romanian Scientists, Bucharest 050094, Romania; Department of Mathematics, Technical University of Iasi 700050, Romania
Dumitru Vieru
Department of Theoretical Mechanics, Technical University of Iasi 700050, Romania
Corina Fetecau
Department of Theoretical Mechanics, Technical University of Iasi 700050, Romania
Itrat Abas Mirza
Abdus Salam School of Mathematical Sciences, GC University Lahore 54000, Pakistan

ABSTRACT

Time-fractional convective flow over a dusty incompressible Oldroyd-B fluid over a moving infinite porous vertical plate is investigated in the presence of a heat source. At time t = 0+ the plate, whose temperature is time-variable, begins to move in its plane with a time-dependent velocity uwf(t). Exact solutions for dimensionless temperature and Nusselt number are determined using Laplace transforms. The influence of fractional parameter on the fluid temperature is graphically emphasized for small and large values of time. Its effects on the Nusselt number are also brought to light. The fluid velocity, as well as the dust particles velocity, are determined by combining the Laplace transform technique with the homotopy analysis method, and the Stehfest numerical algorithm is used for the inverse Laplace transform. As a check of the results, a closed form solution for the fluid velocity in the transformed domain is determined by both methods. Finally, the influence of fractional parameter and Prandtl number on the fluid and dust particles velocities is graphically underlined and discussed. Generally, in practical problems, these results can be used to determine suitable values for the fractional parameter so that the theoretical results to be in agreement with the experimental data.