This research article explor es on the steady of the two-dimensional buoyancy effects on MHD Casson fluid flow over a stretching of permeable sheet thr ough a porous medium in the occurrence of suction/injection. The central PDEs are changed into ODEs by applying similarity transformat ions and the changed equations’ solutions are got by Runge -Kutta fourth order along with a shooting technique. The working fluid flow is considered for numerous different parameters graphically. It has been observed that velocity decreases, temperature and concentration increase when magnetic field and permeability of porous parameter increases. Keywords: MHD, Chemical react ion, Porous medium, Buoyancy effects, Stretching sheet, Suction/injection . Cite this Article: Nagaraju Vellanki , Dr. K. Hemalatha and Dr. G. Venkata Ramana Reddy , Radiation and Chemical Reaction Effects on MHD Casson Fluid Flow of a Porous Medium with Suction/Injection , International Journal of Mechanical Engineering and Technology 11(2), 2020, pp. 99-116. http://www.iaeme.com/IJMET/i ssues.a sp?JType=IJMET&VType=11&ITy pe=2 1. INTRODUCTION Owing to the badly need for good understanding of associate transfer phenomena heat transfer through a porous medium has become an interesting subject for last three decades. There is large number of practica l applications in modell ing transport through porous media in literature insensible heat storage beds and beds of fossil fuels such as oil shale and coal, salt leaching in soils, packed sphere beds, chemical, high performan ce insulation for buildings, chem ical catalytic reactors, mechanical, environmental, grain storage, migration of moisture through their contained in fibrous insulations, geological, heat exchange between soil and atmosphere, Radiation and Chemical Reaction Effects on MHD Casson Fluid Flow of a Porous Medium with Suction/Injection http://www.iaeme.com/ IJMET/index. asp 100 editor@iaeme.com solar power collectors, electrochemical processes, insulation of nuclear reactors, regenerative heat exchangers and geothermal energy systems , petroleum and many other areas . Kuznetsov et.al [1] has examined the normal convection limit layer stream of a nanofluid past a vertical plate. Nabil et.al [2] examined in his p aper on MHD stream of non -Newtonian visco -versatile liquid through a permeable med ium close to a quickened plate. Nabil et.al [3] represents Non -Darcy couette course through a permeable mode of MHD visco -flexible liquid with warmth and mass exchange. M. Ha meedet.al [4] contemplated Unsteady MHD stream of a non -Newtonian liquid on a permeable plate . Rajesh [5] broke down MHD impacts on free convection a nd mass change course through a permeable medium with variable temperatures. Sengupta [6] studied Thermal dis persion impact of free convection mass exchange stream past a consistently quickened permeable plate with warmth sink. Bhattacharya [7] talked about impacts of warmth source/sink on MHD stream and warmth move over a contracting sheet with mass suction. Tur kyilmazogluet.al [8] have examined Soret and warmth source impacts on an insecure radiative MHD free convection stream from a rashly begun endless v ertical plate. Narahari [9] contemplated a precise arrangement of precarious MHD free convection stream of an emanating gas past an interminable slanted isothermal plate . Nadeem et.al [10] has displayed MHD three -dimensional Casson liquid stream past a permeable straightly extending sheet. Haqet.al [11] has contemplated convective warmth move and MHD impacts on Casson nanofluid stream over a contracting sheet. Kameswaraniet.al [12] broke down double arrangements of Casson liquid stream over an extending or contracting sheet. Babuet.al [13] talked about radiation impact on MHD warmth and mass exchange stream over a contracting sheet with mass suction. Kirubhashankar et.al [14] examined Casson liquid stream and warmth move over a shaky permeable extending surface. Maboodet.al [15] has contemplated MHD limit layer stream and warmth move of nanofluids over a nonlinear extending sheet. Kataria et.al [16] examined radiation and synthetic response consequences for MHD Casson liquid stream past a swaying vertical plate implanted in permeable medium. Raju et.al [17] additionally examined warmth and mass exchange in magnetoh ydrodynamic Casson liquid over an exponentially penetrable extending surface. Mabood et.al [18] displayed impacts of Soret and non -uniform warmt h source on MHD non -Darcian convective stream over an extending sheet in a dissipative micropolar liquid with ra diation. Yasin et.al [19] examined MHD warmth and mass exchange stream over a porous extending/contracting sheet with radiation impact. Bhattiet .al [20] examined head -on impact between two hydroelastic single waves in shallow water. Katariaet.al [21] exami ned warmth and mass exchange in MHD Casson liquid stream past over a wavering vertical plate implanted in permeable medium with inclined divider temperature. In this warmth and mass exchange numerous creators [22] -[26] talked about. 2. MATHEMATICAL FORMULA TION Let us take a steady 2D, electrically conducting non -Newtonian Casson fluid flow of a viscous and incompressible over a permeable stretching sheet is considered. The stretching sheet ’s velocity is taken in the form () ux with ()0, for a stretching surface . Here horizontal and vertical axes are taken on the stretching surface and the normal to it, respectively . Beside the flow is being confined to ()0, . It is considered that the surface is pe rmeable and the mass flux velocity 0v . For suction and injection 0v is negative and positive respectively . Nagaraju Vellanki, Dr. K. Hemalatha and Dr. G. Venkat a Ramana Reddy http://www.iaeme.com/ IJMET/index. asp 101 editor@iaeme.com The rheological properties of Casson fluid for an isotropic and incompressible flow is given by Eldabe e t al [27] and Mustafa et al [28]. ( ) ( )2 / 2 , 2 / 2 ,B y ij c ij B y c ij cpe pe        += + where B is the plastic dynamic viscosity of the non -Newtonian fluid, yp is the yield stress of the fluid ,  - the product o f the component of deformation rate with itself, ,ij ij ije e e= is the (),thij component of the deformation rate , and c - the critical value of  based on non - Newtonian model. The following are taken into consideration: wT =constant temperature at surface of the sheet wC =concentration at the surface of the sheet T =constant temperature of ambient fluid .C =concentration of ambient fluid Yasin et al. [19] in their research article proposed the system of equations which model the flow as: 0,xyuu+= (1) ()()2 0 11x y yy T CBuu vu u u g T T g C Ck   + = + − + + − + −     (2) ()() ()0 p x y p yy ryC uT vT C T q Q T T   + = − + − (3) ()0 x y B yyuC vC D C k C C + = − − (4) Here u =velocity component in x− axes direction v = the velocity component in y− axes direction , T = the fluid temperature, C = the concentration,  = kinematic viscosity of the fluid,  =thermal diffusivity of the fluid,  = the density of the fluid, BD =Brownian diffusion coefficien t, pC =specific heat at constant pressure,  =electric conductivity of the fluid, 0B =applied uniform magnetic field normal to the surface of the sheet, Radiation and Chemical Reaction Effects on MHD Casson Fluid Flow of a Porous Medium with Suction/Injection http://www.iaeme.com/ IJMET/index. asp 102 editor@iaeme.com 0 0heat source if Q >0 heat sink if Q <0rq=  g=acceleration due to gravit y T = the coefficient of thermal expansion, C =the coefficient of solutal expansion k =porous medium permeability coefficient and 0k = the constant chemical reaction rate. We consider that constrains (1)–(4) are subjected to the boundary conditions: ()0, , , , 0 0,w w w v v u u x T T C C at y u T T C C as y = = = = = → → → → (5) where we assume that () ,wu x ax= with 0.a The energy Equation (3) i s expressed as (by applying Rosseland approximation (Brewster, 1992) and Suneetha et al. [ 22]): ()( )()()1 1* * 3 01 3 16x y yy puT vT kk T T Q C T T   − −  + = + − − (6) here k = thermal conductivity, *= Stefan -Boltzmann constant and *k= mean absorption coefficient. The similarity solution of (1), (2), (4) and (6) are obtained as : ()()()() ()()() ()()1/2 1/2, , , / wwT T C Cav xf y a vT T C C       −−= = = =−− (7) Here (),xy = stream function, which is defined in the usual way as /, uy=  and /.x =−  Thus, we have: ()()()1/2, u axf v a f  = =− (8) Hence the parameter S having no dimension is described by : ()1/2 0 S v a−=− (9) S is the constant mass flux with positive, for suction negative, for injectionS=  The followin g ODEs are got by putting (7) in (2), (6) and (4) () () ( )210 f ff f M K f Gr Gc      + + − − + + + = (10) 3403PrRfQ  + + + =  (11) 0. Scf ScKr   + − = (12) Nagaraju Vellanki, Dr. K. Hemalatha and Dr. G. Venkat a Ramana Reddy http://www.iaeme.com/ IJMET/index. asp 103 editor@iaeme.com The corresponding boundary conditions : ()()()() ()()(), , 1, 1 0 0, 0, 0f S f at f as             = = = = = → → → → (13) The constants Pr, , , , , , ,Sc M R Gr Gc Q K and Kr are not possessing any dimension and their description are given below Constants Description Pr Prandtl number Sc Schmidt number M Magnetic parameter R Radiation parameter Gr Thermal Grashof number Gc Solutal Grashof number Q Heat source/sink parameter K Permeability parameter Kr Chemical re action parameter () ()()()()() ()11 1 2 1 * * 3 0 11 122 0 1 1 0Pr , , , 4 , , , , ,,B T w c w p w T wSc D M B R kk T Gr a x g T T Gc a x g C C Q a C Q TT DK k a Kr a k SrCC        −− − −  −− −  − −  = = = = = − = − = −= = = − (14) The most important quantities in the above phenomenon are given by fC = skin friction coefficient , xNu = local Nusselt number xSh =local Sherwood number, () () ()2/ , / , /f w w x w w x m B wC u x Nu xq k T T Sh xq D C C = = − = − (15) here w =skin friction or shear stress ,wq =heat flux and mq = mass flux from the sheet, which are given by: ()0 0 0 0, , ,w w r m B y y y yu T Cq q q Dy y y= = = =       = =− + =−             (16) here  =fluid’s dynamic viscosity. By (7), (15) and (16), one can get: () () ()34Re 0 , 0 , 0 ,3 Re Rexx xf xxNu Sh RCf +  = =− =−  (17) Where () Re /xwu x x v= is the local Reynolds number. Radiation and Chemical Reaction Effects on MHD Casson Fluid Flow of a Porous Medium with Suction/Injection http://www.iaeme.com/ IJMET/index. asp 104 editor@iaeme.com 3. RESULTS AND DISCUSSION The similarity transformation changes the non -linear PDEs (2)–(4) into ODEs . The set of non - linear ODEs (10)–(12) with boundary conditions in (13) can be solved numerically using 4thorder Runge –Kutta method along with shooting method and the corresponding MATLAB softwar e is provided. Figure (2) - (4) speak to the velocity , temperature and focus profiles for various estimations of attractive parameter. It is seen that an augmentation of an attractive parameter gets an improvement Lorentz power so velocity profiles diminis hes with increme nt in attractive parameter. It is additionally seen that the temperature and fixation increment as the attractive parameter increment in both the instances of suction and infusion fundamentally after certain separation ordinary to the sheet . Figure (5) - (7) portray the velocity , temperature and fixation profiles for various estimations of Permeability parameter (K). It is seen that the velocity diminishes with expanding K and it is likewise seen that the temperature and focus profiles increm ent with expandi ng estimations of K for both the instance of suction and infusion separately. Physical parts of velocity , temperature and focus profiles are thought with the guide of figures (8), (9) and (10) individually. It is seen that the velocity profiles increment w ith an expansion in Grashof number (Gr) due to Gr impact of warm lightness power to the gooey hydrodynamic power in the limit layer thickness. Here Gr expands the temperature and focus decline for both the instances of suction and infusion parameter. The e ffect of the changed Grashof number (Gm) on the velocity , temperature and fixation profiles are appeared in figures (11) - (13). It was discovered that the expansion in the Gm expands the velocity . Be that as it may, turn around pattern is s een in the tempe rature and fixation profiles for the instances of suction and infusion. Figures (14) and (15) demonstrate the varieties in velocity and temperature profile separately. It is seen that the velocity and temperature fields are expanding for ri sing estimations of the warm radiation because of this expansion the limit layer broadness in both the instances of suction and infusion. Impact of Prandtl number (Pr) on the velocity , temperature and focus profile are exhibited in figures (16),(17) and (1 8) individually. It is seen that the velocity is diminished with expanding Prandtl number. Physically, it is genuine in light of the fact that an addition in the Pr is because of an expansion in the consistency of the liquid, which makes the liquid thick a nd subsequently it diminishes in the liquid of the velocity both the instances of suction and infusion. It is seen that the temperature just as the warm limit layer thickness decline because of the expansion of Pr. The switched pattern is seen on the focu s field both the cases suction and infusion. Impacts of warmth source parameter on the velocity , temperature and fixation profiles are appeared in figures (19), (20) and (21) separately. It is seen that as warmth source parameter increment, velocity and te mperature increm ent. However, turn around pattern is seen in the focus profiles for both the instances of suction and infusion. Impact of the Schmidt number (Sc) on the velocity , temperature and focus profiles are appeared in the figures (22), (23) and (24 ) separately. It tends to be reason that the velocity and fixation profiles decline with the expansion in Schmidt number and furthermore it is seen that temperature increments with the expansion in Sc. Figures (25), (26) and (27) speak to the velocity , tem perature and foc us profiles for various estimations of concoction response parameter. It is seen that the velocity and fixation profiles decline with the expansion in concoction response parameter. It is additionally seen that the temperature field increme nts with the exp ansion in substance response parameter. Figs (28), (29),(30) shows the impact of Casson liquid parameter(β) on the velocity , mild and focus profiles. It was discovered that the Casson liquid parameter expands the liquid thickness builds this causes the re ductions the liquid velocity yet switch pattern saw in the temperature and focus Nagaraju Vellanki, Dr. K. Hemalatha and Dr. G. Venkat a Ramana Reddy http://www.iaeme.com/ IJMET/index. asp 105 editor@iaeme.com profiles increments when expanding the Casson liquid parameter because of warm and mass diffusivity. Figure 2 Velocity profiles for different values of Magne tic Parameter (M) Figure 3 Temperature profiles for different values of Magnetic Parameter (M) Figure 4 Concentration profiles for different values of Magnetic Parameter (M) Radiation and Chemical Reaction Effects on MHD Casson Fluid Flow of a Porous Medium with Suction/Injection http://www.iaeme.com/ IJMET/index. asp 106 editor@iaeme.com Figure 5 Velocity profiles for different values of Permeability parameter (K) Figure 6 Temperature profiles for different values of Permeability parameter (K) Figure 7 Concentration profiles for different values of Permeability parameter (K) Nagaraju Vellanki, Dr. K. Hemalatha and Dr. G. Venkat a Ramana Reddy http://www.iaeme.com/ IJMET/index. asp 107 editor@iaeme.com Figure 8 Velocity profiles for different values of Grashoff number (Gr) Figure 9 Tempe rature profiles for different values of Grashoff number (Gr) Figure 10 Concentration profiles for different values of Grashoff number (Gr) Radiation and Chemical Reaction Effects on MHD Casson Fluid Flow of a Porous Medium with Suction/Injection http://www.iaeme.com/ IJMET/index. asp 108 editor@iaeme.com Figure 11 Velocity profiles for different values of modified Grashoff number (Gm) Figure 12 Temperature profiles f or different values of modified Grashoff number (Gm) Figure 13 Concentration profiles for different values of modified Grashoff number (Gm) Nagaraju Vellanki, Dr. K. Hemalatha and Dr. G. Venkat a Ramana Reddy http://www.iaeme.com/ IJMET/index. asp 109 editor@iaeme.com Figure 14 Velocity profiles for different values of radiation parameter (R) Figure 15 Temperature profiles for di fferent values of radiation parameter (R) Figure 16 Velocity profiles for different values of Prandtl number (Pr) Radiation and Chemical Reaction Effects on MHD Casson Fluid Flow of a Porous Medium with Suction/Injection http://www.iaeme.com/ IJMET/index. asp 110 editor@iaeme.com Figure 17 Temperature profiles for different values of Prandtl numbe r(Pr) Figure 18 Concentration profiles for different values of Prandtl number(Pr) Figure 19 Velocity profiles for different values of heat source parameter(Q) Nagaraju Vellanki, Dr. K. Hemalatha and Dr. G. Venkat a Ramana Reddy http://www.iaeme.com/ IJMET/index. asp 111 editor@iaeme.com Figure 20 Temperature profiles for different values of heat source parameter(Q) Figure 21 Concentration profiles for different values of heat source parameter(Q) Figure 22 Velocity profiles for different values of Schmidt number (Sc) Radiation and Chemical Reaction Effects on MHD Casson Fluid Flow of a Porous Medium with Suction/Injection http://www.iaeme.com/ IJMET/index. asp 112 editor@iaeme.com Figure 23 Temperature profiles for different values of Schmidt number (Sc) Figure 24 Concentration profiles fo r different values of Schmidt number (Sc) Figure 25 Velocity profiles for d ifferent values of chemical reaction (Kr) Nagaraju Vellanki, Dr. K. Hemalatha and Dr. G. Venkat a Ramana Reddy http://www.iaeme.com/ IJMET/index. asp 113 editor@iaeme.com Figure 26 Temperature profiles for different values of chemical reaction(Kr) Figure 27 Concentration profiles for different values of chemical reaction ( Kr) Figure 28 Velocity profiles for different values Casson f luid parameter ( β). Radiation and Chemical Reaction Effects on MHD Casson Fluid Flow of a Porous Medium with Suction/Injection http://www.iaeme.com/ IJMET/index. asp 114 editor@iaeme.com Figure 29 Temperature profiles for different values Casson fluid parameter ( β). Figure 30 Concentration profiles for different values Casson fluid parameter ( β). 4. CONCLUSION S The above research discussion proposed the influence of heat source, mass transfer and radiation on steady 2D MHD flow of Casson fluid over a permeable stretching sheet through porous medium in the presence of suction/injection using Applied Numerical Analysis . The conclusions of the above discourse are: • Velocity increases when Gr, Gm, R and Q increase. • Velocity decreases when M, K, Pr, Sc and Kr increase • M, K, R, Q, Sc and Kr increase with increase in temperature. • Gr, Gm and Pr increase with decrease in temperature. • Concentration increases when M, K and Pr increase. • Concentration d ecreases when Gr, Gm, Q, Sc and Kr decrease. Nagaraju Vellanki, Dr. K. Hemalatha and Dr. G. Venkat a Ramana Reddy http://www.iaeme.com/ IJMET/index. asp 115 editor@iaeme.com