Numerical investigation of MHD radiative heat and mass transfer of nanofluid flow towards a vertical wavy surface with viscous dissipation and Joule heating effects using Keller-box method

In this paper, the effect of viscous dissipation and Joule heating on magneto-hydrodynamic (MHD) nanofluid flow towards a vertical sinusoidal wavy surface has been investigated numerically. The wavy surface is considered to be heated with uniform flux. Effects of radiation and nanoparticle volume concentration are also considered. The fluid flow over the surface geometry is designed through the highly non-linear partial differential equations, and governing equations must be transformed into a dimensionless non-similar system of equations to get a better solution by applying the highly efficient well-known Keller-box scheme. In this regard, the numerical solutions are obtained for a concentration of mass fluid, velocity profile, temperature profile, local skin friction number coefficient, local Nusselt number, and Sherwood number shown graphically. Connected parameters involve in the modelled problem such as heat generation parameter, radiative conduction flow parameter, the amplitude of the waviness of the surface, Prandtl number, Brownian motion parameter, Buoyancy ratio, magnetic parameter, Thermophoresis parameter and the Lewis number for momentum, temperature profile, and concentration profile of the fluid through different graphs are explained. In this process, certain iterations were performed for different step sizes in the direction of η=0.01 and x=0.005, respectively. So, keeping this in view to get the more accurate results with all parameters considered, 0≤M≤1, 0≤Rd≤1,0≤Q≤1,0.01≤α≤0.04, 0≤Le≤40, 0.1≤Nb≤0.7,0.1≤Nt≤0.7,0.1≤Nr≤0.7,0.1≤Ec≤0.4,0.1≤J≤0.4,. The obtained results illustrate that Nusselt number, Sherwood number, and velocity profile decreases respectively with the increase of waviness amplitude, but skin friction changes its behaviour to wavier. Also, temperature and concentration profiles increase respectively with enhancing the value of the amplitude of waviness. Finally, it is noted that Nusselt number and Sherwood number decrease for higher values of the Brownian parameter. But after a specific value of x, the trend of Sherwood number increases. However, the behaviour of skin friction decreases, but in a precise manner, it remains almost unchanged.