Buoyancy Effect on MHD Slip Flow and Heat Transfer of a Nanofluid Flow Over a Vertical Porous Plate

This study investigated the boundary layer flow and heat transfer aspects of a nanofluid over a porous plate with thermal radiation.Using suitable similarity transformations,partial differential equations were converted into ordinary differential equations and then solved numerically with the help of the Runge-Kutta scheme. The effects of various parameters were analyzed such as Prandtl number 𝑃𝑟, Lewis number 𝐿𝑒, Thermophoresis 𝑁𝑡, Mixed convection parameter λ,Brownianmotion 𝑁𝑏, Magnetic parameter M, and Suction/Blowing parameter S. The results were depicted with the help of graphs.


Introduction
A fluid containing nanometer sized particles which are known as nanoparticles are called nanofluid and is typically prepared for metal, oxide, or carbon nanotubes. The common base fluid contains water and oil.
The study of the magnetic properties and behavior of electrically conducting fluid is called magneto-hydro-dynamics. There are many examples of magneto fluids including plasma, liquid metal, salt water, and electrolyte. Alawiet al. [1] focused on determining and modelling the dynamic thermal conductivity of nanofluids. Abbas et al. [2] discussedthe critical view of the influence of nanofluids on the improvement of the PV/T system. Ahmed et al. [3] considered School of Sciences Volume 4 Issue 1, 2020 transverse magnetic lea the transient free convective flow of nanofluids with generalized thermal transport between two vertical and parallel platters. Akbar et al. [4] discussed the peristaltic transport of fluid in human body. Ahmadloo and Azizi [5] comparedthe neural network model for nanofluidswithbase fluids. Arulprakasajothi et al. [6] discussed the flux conditions forthe Nusselt number. Choi et al. [7] investigatedthe thermal conductivity of waterbased nanofluid. Daset al. [8] exploreda nanoparticle that has attracted much attention dueto the increase in heat. Devendiranet al. [9] investigated the heat transfer flow ofthe heat exchanging system. Esfe et al. [10] discussed the thermal conductivity of ferromagnetic nanofluids. Haque et al. [11]analyzed the effect of biting treatment with the help of the physical properties. Hayat et al. [12] analyzedthe flow of carreaunanofluid over a stretching sheet. Kundan and Mallick [13] explored experimentally by using volume fraction based nanofluids. Mansour et al. [14] investigated the proposition that MHD localizes heat sources. Mohammad et al. [15] discussedthe improvement resulting from the combination of nanoparticles. Mahmood et al. [16] analyzed the heat transfer of an incompressible fluid flow on a disc. Nicolas et al. [17] established the theory of thermal condition for obligatory temperatureat the wall. Prakash et al. [18] postulatedthat all fluidsarenanofluidsbecause they contain nanometersized particles known as nanoparticles. Ramzan et al. [19] analyzedthe boundary layer fluidflow of nanofluidson a moving surface. According to the author's best knowledge, the study of the MHD buoyancy effect of a nanofluid flow over a vertical porous platehas not been undertaken yet.Moreover, the effects of thermal and velocity slipshavenot been analyzed. The physical interpretation for several parametersisinspectedwith the support of graphs in this study.Using similarity transformations, non-lineardifferential equationsare solved numerically employing Runge-Kuttashooting technique.

Formulation and Problem
We consideredthe buoyancy effect on MHD slip flow and heat transfer of a nanofluid flow over avertical porous plate. The governing equation's continuity, momentum, and heat transfer are written as follows, (4) where u and v are velocity components, = √ is the non-uniform magnetic field with as a constant,  is fluid viscositycoefficient, is fluid density, is electric conductivity, k is thermal diffusivity, u  is depictsBrownian diffusion, depicts Thermophoresis diffusion, and  is the ratio of heat capacities.
Boundary conditions for this problem are given by the following equation, School of Sciences

Results and Discussion
In order to get a clear insight intothe physical problem, numerical computations were carried out using Runge-Kutta method with shooting technique for various values of different parameters, such as the magnetic parameter M, mixed convection parameter , velocity slip parameter , thermal slip parameter  , suction/blowing parameter S, Prandtl number , Lewis number , Brownian motion , and thermophoresis .

Findings
The buoyancy effect on MHD slip flow and heat transfer of a nanofluid flow over a vertical porous plate were studied numerically.The impact of different physical parameters on velocity profile, temperature profile,Nusselt number,and skin friction coefficient were detected. The main outcomes are given below.