Punjab University Journal of Mathematics, Vol 51, No 9 (2019)

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Heat and mass transfer analysis of Brinkman type fractional nanofluid over a vertical porous plate with velocity slip and Newtonian heating

Aneela Razzaq, Nauman Raza


The partial differential equations of integer order describes onlythe models of classical nanofluids and do not consider the memory effects.For the description of the influence of memory on the nanofluids, differentialequations with non-integer derivatives are used for the modeling offractional nanofluids. This investigation explores the unsteady mixed convectionfractional nanofluids flow of Brinkman type near a plate placedvertically in a permeable medium. Mass and heat transfer investigationis carried out under the thermal and chemical reaction effects. Four differentnanoparticles named Silver (Ag), Aluminium Oxide (Al2O3), Copper(Cu), Titanium Oxide (TiO2) are dispersed in water which is a basefluid. The modeled system of partial differential equations are transformedinto dimensional form through suitable dimensionless variables. By usingLaplace transformation, the semi analytic solutions for velocity, temperatureand concentrations field are developed. Then by using MATHCAD,inverse Laplace transform has been computed numerically. The acquiredsolutions meet all imposed initial and boundary conditions and change tosimilar solutions for ordinary nanofluid when fractional parameter value istaken as one. Influence of distinct physical parameters such as Brinkmanparameter, fractional parameter, radiation parameter and volume fractionon the velocity, temperature and concentration profiles are shown throughgraphs. The tables for Sherwood number, Nusselt number are also calculatedfor different values of emerging parameters. The major resultof our study is ordinary nanofluid flow is decelerator than the fractionalnanofluid. Also, the fractional parameter has strong influence over heattransfer phenomena. It is also explored in this study that heat transfer rateis high for fractional nanofluid as compared to ordinary nanofluid.

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