Convective flow of a Maxwell hybrid nanofluid due to pressure gradient in a channel
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Convective flow of a Maxwell hybrid nanofluid due to pressure gradient in a channel Rizwan Ali1 · Muhammad Imran Asjad1 · Ali Aldalbahi2 · Mohammad Rahimi‑Gorji3 · Mostafizur Rahaman2 Received: 23 March 2020 / Accepted: 24 September 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract In this work, analytical solution of hybrid Maxwell nanofluid of the vertical channel due to pressure gradient is discussed. By introducing dimensionless variables the governing equations with all levied initial and boundary conditions is converted into dimensionless form. Fractional model for Maxwell fluid is developed by Caputo time fractional differential operator by using the constitutive relation. The dimensionless expression for temperature and velocity are found using Laplace transform. Draw graphs of temperature and velocity by Mathcad software and discuss the behavior of flow parameters and the effect of fractional parameters. As a result, we have found by increasing the volumetric fraction of copper and alumina temperature increases and velocity decreases. Also, fluid flow properties showed dual behavior for small and large time, respectively, by increasing fractional parameters values. Keywords Hybrid nanofluids · Non-Newtonian fluid · MHD · Pressure gradient · Channel flow · Power law memory kernel List of symbols u Velocity (ms−1 ) T Temperature (K) 𝜌hbnf Density of the hybrid nanofluid (kg m−3 ) 𝜇hbnf Dynamic viscosity of hybrid nanofluid (kg m−1 s−1 ) 𝛽t Volumetric thermal expansion coefficient (K−1 ) g Gravitational acceleration (ms−2 ) (Cp )hbnf Heat capacitance of the hybrid nanofluid (J K−1 ) knf Thermal conductivity of nanofluid (W m−1 k−1 ) 𝜙1 Volume fraction of nanoparticles of copper * Muhammad Imran Asjad [email protected]
Mohammad Rahimi‑Gorji [email protected]; [email protected]
1
Department of Mathematics, University of Management and Technology, Lahore, Pakistan
2
Department of Chemistry, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
3
Faculty of Medicine and Health Sciences, Ghent University, 9000 Ghent, Belgium
𝜙2 Volume fraction of nanoparticles of alumina 𝜌f , 𝜌s1 , 𝜌s2 Density of the base fluid and hybrid nanoparticles (kg m−3 ) 𝛽f , 𝛽s1 , 𝛽s2 Volumetric coefficient of thermal expansion of the base fluid and hybrid nanoparticles (K−1 ) (Cp )f , (Cp )s1 , (Cp )s2 Specific heat capacities of the base fluid and hybrid nanoparticles (J K−1 ) kf , ks1 , ks2 Thermal conductivities of the base fluid and hybrid nanoparticles (W m−1 k−1 )
Introduction The Maxwell fluid model has received much attention for being the first and one of the simplest rate type fluid models. It is still used widely specially to describe the response of some polymeric liquids. However, same like other models, Maxwell fluid model has some boundaries. For example, this model does not properly define the typical relation between shear rate and shear stress in a simple shear flow [1, 2]. Most of the existing studies on Maxwell fluid particularly on the analyt
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