The significance of nonNewtonian fluid importance is being found in several branches of applications and engineering, especially in the design of solid matrix heat transportation, petroleum cooling etc. Haroon et al
Joule heating is representative of Ohmic heating due to its connection to the Ohm’s Law and it is the base for a number of practical applications like electric fuses and so forth. Kumar & Srinivas ^{6} have discussed the magnetohydrodynamic nanofluid flow over a shrinking surface and they have observed that the higher the velocity of the fluid with the lower local Grashof number. Samuel ^{7} investigated the impact of hydromagnetic on Ohmic heating and viscous fluid on a porous sheet. Jagadeeshwar and Srinivasacharya
The Ohmic heating and nonlinear radiation of the heat transporting the hydromagnetic fluid flow over a stretchable surface were presented by Tarakaramu and Narayana
To the best of our knowledge, no author has inquired about the impact of uneven heat sink/source and nonlinear radiation on hydromagnetic Casson fluid flow past an inclined elongating stretching sheet. The governing equations of flow momentum, heat and mass transport are characterized by a set of partial differential equations. Later, these equations are transformed into ordinary differential equations by utilizing proper similarity functions and are thereby resolved numerically by the Runge–Kutta technique. The effects of different relevant physical parameters on the flow, skin friction, Nusselt and Sherwood number designations are discussed through graphical outputs and numerical values are through the tables.
Consider a steady 2D flow of an incompressible Casson fluid flow which is produced by the inclination of the surface at an angle
Where
With initial BCs:
Here
Here
The parameter of nonuniform heat sink/source is,
In the above expression, the time dependent and space of heat sink/source are
The similarity variables are,
Here
Substituting the equations (8)(9) into the equations (3,4,5 and 6) above the transformed equations as becomes,
With BCEs
The nondimensional parameters are Schmidt number, chemical reaction, Eckert number, Grashof and Local Grashof number, magnetic parameter, suction parameter, Grashof number, and Prandtl number.
Where,
The Skin frication, Nusselt and Sherwood numbers respectively,
The effect of governing nondimensionless parameters on nonlinear radiation, Casson parameter, magnetic field, chemical reaction, nonuniform heat source, Schmidt number, thermophoresis, Eckert number and Brownian diffusion are evaluated. And also, the effect of dimensionless governing profile computed on the momentum, thermal and concentration. Using the numerical method with bvp4c embedded in the MATLAB software scheme, in this present study the fixed values of the governing profiles are taken as
The thermal curve that are affected by the nonlinear radiation as cited in
The impact of Brownian diffusion on the concentration and temperature parameters for the various distributions is seen in
The Grashof and local Grashof numbers on momentum parameters are displayed in
The influence of nonuniform heat source /sink on the thermal profile is shown in
The influences of Casson fluid profile are displayed on the momentum field as shown in










1 






0.714724 
0.543365 
0.460178 
2 






0.953325 
0.538723 
0.435217 
3 






1.138898 
0.536769 
0.418481 

0.1 





0.714715 
0.579469 
0.526032 

0.4 





0.714715 
0.613483 
0.420728 

1 





0.714715 
0.644786 
0.401296 


0.0 




0.714715 
0.600136 
0.387370 


0.8 




0.714715 
0.581995 
0.715754 


1 




0.714715 
0.574566 
0.822131 



0.2 



0.714724 
0.501000 
0.466158 



0.4 



0.714724 
0.433288 
0.475426 



0.6 



0.714724 
0.382824 
0.482109 




0.1 


0.714855 
0.343537 
0.495345 




0.2 


0.714855 
0.366157 
0.492034 




0.3 


0.714855 
0.388866 
0.488704 





1 

0.942880 
0.563374 
0.459988 





2 

1.155213 
0.565431 
0.443039 





3 

1.257832 
0.565746 
0.436218 






1 
0.714855 
0.550307 
0.464872 






2 
0.714855 
0.658589 
0.456947 






3 
0.714855 
0.705336 
0.453484 
The study presents the hydromagnetic nonlinear radiation and Casson fluid flow past an inclination of the stretched surface. It considered the nonlinear radiation, Joule heating, chemical reaction, nonuniform heat sink/source and Schmidt number using the RungeKutta method. Some prominent findings are listed below:
Sherwood numbers decrease as Brownian motion and nonuniform heat source and Schmidt number parameters decrease.
The temperature parameter reduces the rate of mass transit and improves the nonuniform heat sink/source.
Increasing the thermophoresis profile decreases the rate of heat transport.
Increasing the magnetic field profile lowers the friction factor, Sherwood number and Nusselt number and it raises the skin factor.
Brownian diffusion increases in the concentration parameter and decreases with the thermal boundary layer.