Abstract
The partial differential equations of integer order describes only
the models of classical nanofluids and do not consider the memory effects.
For the description of the influence of memory on the nanofluids, differential equations with non-integer derivatives are used for the modeling of
fractional nanofluids. This investigation explores the unsteady mixed convection fractional nanofluids flow of Brinkman type near a plate placed
vertically in a permeable medium. Mass and heat transfer investigation
is carried out under the thermal and chemical reaction effects. Four different nanoparticles named Silver (Ag), Aluminium Oxide (Al2O3), Copper (Cu), Titanium Oxide (T iO2) are dispersed in water which is a base
fluid. The modeled system of partial differential equations are transformed
into dimensional form through suitable dimensionless variables. By using
Laplace transformation, the semi analytic solutions for velocity, temperature and concentrations field are developed. Then by using MATHCAD,
inverse Laplace transform has been computed numerically. The acquired
solutions meet all imposed initial and boundary conditions and change to
similar solutions for ordinary nanofluid when fractional parameter value is
taken as one. Influence of distinct physical parameters such as Brinkman
parameter, fractional parameter, radiation parameter and volume fraction
on the velocity, temperature and concentration profiles are shown through
graphs. The tables for Sherwood number, Nusselt number are also calculated for different values of emerging parameters. The major result
of our study is ordinary nanofluid flow is decelerator than the fractional
nanofluid. Also, the fractional parameter has strong influence over heat
transfer phenomena. It is also explored in this study that heat transfer rate
is high for fractional nanofluid as compared to ordinary nanofluid.
Aneela Razzaq, Nauman Raza. (2019) Heat and mass transfer analysis of Brinkman type fractional nanofluid over a vertical porous plate with velocity slip and Newtonian heating, Punjab University Journal of Mathematics, Volume 51, Issue 9.
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