The flow of a boundarylayer across a wedge is important in recent years due to its numerous applications like geothermal systems, crude oil extraction, heat exchangers, nuclear power plants, as polymer extrusion process, wire drawing, plastic film drawing, production of plastic sheet, metal spinning, friction drag of a ship, etc. The significant aspect of the Eyring Powell fluid is obtained from the kinetic theory of gases relatively ^{1, 2}^{. }An analytical study on entropy analysis on the magnetohydrodynamic flow of boundarylayer across a moving wedge.^{ }^{3} The steady MHD Newtonian boundarylayer flow towards a stretching sheet with Navier’s slip conditions was analytically investigated.^{ }^{4 }An MHD boundarylayer flow past a stretching surface in a micropolar fluid in presence of Joule heating, viscous dissipation, and heat source/sink.^{ }^{5}^{}
The DufourSoret effects play an essential role in the transfer of mass and heat due to its vast applications such as chemical reactors, oil reservoirs, a mixture of gases, binary alloys solidification etc. The transfer of mass caused due to temperature gradient is called Soret [ThermalDiffusion]. On the other hand, the transfer of heat generated due to concentration gradient is called Dufour [DiffusionThermo]. Furthermore, the DufourSoret phenomenon has great significant effects on the fluids of very lightweight molecular as well as mediumweight molecular. The twodimensional unsteady flow of EyringPowell magneto nanofluid on a vertical plate under SoretDufour impacts.^{ }^{6}^{.} The mass and heat transfer effect by SoretDufour on the sheet in an EyringPowell fluid with magnetic dipole and radiation.^{ }^{7}^{.} An effect of SoretDufour over boundarylayer flow due to porous wedge for radiation and suction/injection was studied.^{ }^{8}^{.} Unsteady flow on a vertical plate within the porous matrix in a micropolar fluid by considering heat absorption, DufourSoret, and chemical reaction of first order with an MHD.^{ }^{9}^{.}
The process of transfer of heat due to melting has gained much attention by researchers due to its multifarious applications such as magma solidification, oil extrusion, melting of permafrost, thermal insulation and so on. Moreover, the melting process gives the substance transition from a solid to a liquid state that causes the physical change of the body due to the transfer of heat. An influence of melting process under magnetohydrodynamic flow on a wedge in a Casson nanofluid embedded in the porous stratum.^{ }^{10}^{ }A study on the melting process of nanofluid flow past a wedge with a magnetic field was examined.^{ 11}^{}
An effect of radiation is prominent in controlling the process of heat transfer and it leads to the desired product with a sought quality. The thermal radiation heat transfer has numerous engineering and industrial applications like nuclear plants, aircraft, space vehicles, gas turbines etc. An MHD flow of nanofluid with binary chemical process and radiation was examined.^{ 12 }The impact of an aligned magnetic field in a Newtonian fluid with the effects of radiation and Stefan blowing through a stretching/shrinking sheet was examined.^{ }^{13}^{. }The study presented the heat transfer characteristics of Casson fluid across a stretching curved surface accompanied by thermal radiation and convective boundary conditions under a magnetic field.^{ }^{14}^{. }HAM is one of the most wellknown analytical methods to tackle highly nonlinear differential equations. A study by using HAM to tackle the differential equations formulated for the Casson fluid across a porous wedge can be found.^{ 15}^{. }^{}
To the extent of our knowledge, no attempts have been made to report the combined impacts of SoretDufour and melting process in an electricallyconducting fluid flow due to a wedge analytically as far. Therefore, in this study, we extended the problem of ^{16} accompanied by the melting process and SoretDufour effects. Hence, the present work scrutinized the DufourSoret and melting process in boundarylayer magnetohydrodynamic fluid flow in an Eyring Powell across a wedge along with the chemical reaction of first order and radiation. The solutions are obtained analytically by HAM. In addition, an effect of physical parameters like wedge angle parameter, Schmidt number, magnetic parameter, fluid parameters, Prandtl number, Soret and Dufour parameters along the flow was examined. The paper was presented as follows: A mathematical modelling of the problem was given in section 2. The solution procedure and convergence analysis are presented in sections 3 and 4. The graphical representation and discussions are included in section 5. Sections 6 and 7 consist of concluding remarks and references.
Consider the laminar boundarylayer flow of nonNewtonian Eyring Powell fluid through the wedge. The velocity components
boundary constraints are,
and
Here
The following similarity transformations will be introduced as follows;
Here,
The stream function satisfies the continuity equation (1) such that;
By using Eq. (7) into Eqs. (2)(6) takes the form;
and
where,
The coefficient of skinfriction, Nusselt number and Sherwood number are written as;
where
By Eqs. (7) and (14) in Eq. (13) becomes,
Here,
Shijun Liao 1992 introduced an analytical method called the Homotopy Analysis Method to tackle nonlinear differential equations. The system of Eqs. (8)(10) along with (11) and (12) are solved by utilizing HAM by choosing appropriate linear operators and initial guesses are as follows,
with the properties;
Here,
Let
where, N_{1}, N_{2}, and N_{3 }are nonlinear operators chosen below,
subject to boundary constraints,
and
If
and using Taylor's series w. r. t.
where,
The series Eqs. (37)(39) are converging hence the solution of the series is obtained as follows,
The deformation equations of
and
where,
The general solutions of Eqs. (46)(48) are given by,
The Eqs. (9)(11) accompanied by the boundary constraints (12) and (13) are coupled and nonlinear which are tackled by HAM. The velocity, thermal, and concentration are plotted in
An influence of
The effect of






0.2 




1.7264 
0.4 




1.8466 
0.6 




1.9638 
0.4 
0.5 



1.8466 

1 



1.7321 

1.5 



0.4549 

0.5 
1 


1.8466 


2 


2.1540 


3 


2.4027 


1 
0.5 

1.5486 



1 

1.8466 



1.5 

2.1524 



1 
0.4 
1.8466 




0.8 
1.8680 




1.2 
1.8980 








0.4 
1 
6 
4 
0.2 
0.3 
0.7315 
0.1378 
0.6 





0.8353 
0.0764 
1.2 





0.9945 
0.0093 
0.4 
0.5 




0.7315 
0.1378 

1 




0.7519 
0.2366 

1.5 




0.7617 
0.2768 

1 
6.2 



0.7430 
0.2463 


7.2 



0.6977 
0.2935 


8.2 



0.6517 
0.3389 


6 
5 


0.7519 
0.3247 



6 


0.7519 
0.4082 



7 


0.7519 
0.4870 



4 
0.2 

0.7519 
0.2366 




0.4 

0.1840 
0.4784 




0.6 

0.0284 
0.2366 




0.2 
0.2 
0.7519 
0.1578 





0.4 
0.7519 
0.3155 





0.6 
0.7519 
0.4733 
One of the authors Umadevi K B would like to thank the financial assistance received from the "University Grant Commission" below the program of National fellowship for higher education: 201920NFSTKAR01277.