The authors have declared that no competing interests exist.

This study aims to numerically investigate the Marangoni convective flow of nanoliquid initiated by surface tension and heading towards a radiative Riga surface. The surface tension appears in the problem due to the gradients of temperature and concentration at the interface. The influence of first order chemical reaction is involved in the system with sufficient boundary conditions. Set of governing nonlinear PDEs is transformed into highly nonlinear ODEs using suitable transformations. HAM is applied for convergent series solutions. Impact of various pertinent fluid parameters on momentum, thermal and solutal boundary layers is analyzed graphically. The chemical reaction plays vital role in saturation of nanoparticles in the base fluid near the surface as well as away from it. The Lorentz forces originated by the Riga surface become powerful when the radiation parameter comes into effect. The significance of Riga plate is thus more prominent through thermal radiation. However, the magnetic effect dampens down for higher radiation parameter. Fluid parameters, Nusslt and Sherwood numbers are analyzed with detailed discussion and concluding remarks.

Carlo Marangoni, an Italian scientist introduced the concept of surface tension gradients driven fluid. This surface tension is popped up in the surface due to gradients of temperature and concentration on the occurrence of a liquid to liquid or liquid to air interface. A liquid with higher surface tension attracts more liquid from a region with low surface tension that ultimately results in fluid flow away from the regions having low surface tension. The gradients of temperature and concentration are therefore, critical factors for such convections under Marangoni effect. A significant interest developed in investigation of heat and mass convection under this phenomenon for its vast applications in industries such as welding, crystals, melting of electronic beams etc. Consequently, numerous researchers contributed in this field after Marangoni. Lin et al

Engineers, Scientists working in the field of Nuclear energy, and Pharmaceutics come across the problem of rise in temperature in the working machine at a high speed performance. This situation was a big reason to worry in fluid mechanics before the introduction of Nanoliquids. The Idea of nanoliquid was introduced by Choi

Fluid flow analysis in the field of fluid mechanics has always been dependent on various external influencing agents. Researchers working in the field of Astrology and Geo physics always need such kind of external agents to ease the movement of fluid in their processing. Most of the fluids for example plasma are typically dependent on the magnetic induction for their flow phenomena. Reason of this dependence of fluids on external agents is poor conductivity of fluids. The problem was somehow reduced with the introduction of Riga plate, an array of permanently mounted magnets and alternating electrodes as displayed in the model of this paper. Gailitis and Lielausis

Numerous articles on nanoliquids are available in the literature in the context of heat and mass flux with different variables and different systematic approaches. However, the use of Riga plate for generation of magnetic effect together with effect of chemical reaction is not found in the literature as for as to the knowledge of the author that assures the novelty of this research work. In this study, firstly we have involved the Riga plate to generate Lorentz forces in the system. The chemical reaction effect and thermal radiation effect are considered. Secondly, the set of PDEs is converted into set of nonlinear ODEs with transformations using the technique of non-dimensionalization

A two dimensional steady and in-compressible nanoliquid is considered under Marangoni effect heading towards a radiative Riga surface. The flow is driven by tension appearing in the surface due to the temperature and concentration gradients. Thermal radiation and chemical reaction effects are utilized. The Brownian motion factor and Thermphoresis phenomena are of significant importance in this study. The temperature _{f}relates the temperature gradient whereas _{f} relates the concentration gradient with base fluid. The heat-mass flux is considered along x-axis in Cartesian coordinates.

The surface tension s, being a function of

where

with following boundary conditions,

Here _{f} represents the density of fluid, _{0} and _{0} are temperature and concentration on the surface, α is representing thermal diffusivity of the fluid, _{p} and heat capacity of base fluid, _{f , }_{B} is Brownian diffusion, _{T} is Thermophoresis, and _{r} is the typical radiative heat flux that can be written through Rosseland's approximation as follows:

where ∑^{*}are Stefan-Boltzmann's constant and coefficient of mean absorption, respectively. Using Taylor's series and omitting second and higher order terms, we get,

which upon substitution in (8) yields

Equation (10) in (3) gives,

Define,

We obtain,

With,

where 𝜸 = (C_{o}𝜸_{C}) / (T_{o}𝜸_{T}) is the ratio of thermal to solutal surface tension s.t. R=((C_{0}-C_{∞})γC)/((T_{0}-T_{∞})γT) and Ma|_{L,T}=(L𝝙T𝜸_{T}|_{C})/ να , Ma|_{L,C}=(L𝝙Cγ_{C}|_{T})/να are thermal and solutal Marangoni numbers resulting 𝜸^{4}_{0}_{0}^{2}_{b}_{p}_{B}_{0}^{2}^{}_{f}^{2}_{t}_{p}_{T}^{2}_{f}^{2}_{∞}^{3}

where _{x}

The efficiency of Homotopy analysis method (HAM) for solving non-linear ODEs has been witnessed through literature. Researchers have given preference to this technique over various other famous methods. The method starts with assumption of some suitable initial guess subject to the boundary conditions given in the problem. Let,

One can see that (16) is satisfied. Define,

such that,

Where _{i} are constants for. i = 1-7.The ^{th}order deformation problems are:

subject to,

Resulting the following system,

where _{f}_{,}_{θ}, _{ϕ }are so-called auxiliary parameters with _{f}_{θ}_{ϕ} are the non-linear operators. For

Using Taylor's expansion,

The convergence of (24) is purely dependent on the choice of ĥ. For p such that the system (24) converges, we write,

The m^{th} order deformation problems are,

where _{m}

with following general solutions to the problem,

where _{i} are constants for _{m}^{*}_{(}_{η), }_{m}^{*}_{(}_{η),}_{m}^{*}_{(}_{η)}are special solutions.

The auxiliary parameters used for the flow profiles in series solutions in HAM are typically considered for controlling the convergence. These parameters significantly moderate the convergence rates thus are vital in achieving the convergence of final solutions. Convergence interval of ^{th} iteration for velocity profile and ^{th} iteration for temperature and concentration profiles, respectively.

We examine the behavior of a surface tension driven nanofluid under the action of Lorentz forces generated by Riga surface and the chemical reaction inside the fluid. The flow is assumed in two dimensions such that x-axis is parallel to the fluid flow and y-axis is normal to the surface of the Riga plate. Influence of pertinent fluid parameters on flow profiles is plotted graphically and the discussion on these graphs is as follows. ^{}

movement of nanoparticles from the surface of Riga.

This subsection summarizes the result with a precise comparison of present results with

We examine the behavior of a surface tension driven nanofluid under the action of Lorentz forces generated by Riga surface and the chemical reaction inside the fluid. The flow is assumed in two dimensions such that x-axis is parallel to the fluid flow and y-axis is normal to the surface of the Riga plate. The final governing equations after application of suitable transformations with sufficient boundary conditions have been solved by HAM. The convergent series solutions are presented and analyzed graphically. Following are salient conclusions

Velocity profiles receives prominent enhancement with stronger Marangoni factor (r) however, the elevated values of dimensionless parameter

Prandtl number is an enhancing factor for the temperature distribution.

Both the radiation and thermophoresis are increasing factors of temperature distribution.

Chemical reaction forces the away movement of nanoparticles from Riga surface. A prominent decreasing behavior is witnessed with elevated values of

Heat flux enhances with augmented values of Thermophoretic factor (Nt).

Mass flux declines with augmented values of Thermophoretic factor (Nt) and the Prandtl factor (Pr).