J. Nig. Soc. Phys. Sci. 4 (2022) 924 Journal of the Nigerian Society of Physical Sciences Eyring-Powell MHD nanoliquid and entropy generation in a porous device with thermal radiation and convective cooling S. O. Salawua,∗, R. A. Kareemb, J. O. Ajilorec aDepartment of Mathematics, Bowen University, Iwo, Nigeria. bDepartment of Mathematics, Lagos State University of Science and Technology, Ikorodu, Nigeria. cDepartment of Mathematics, Lagos State University of Science and Technology, Ikorodu, Nigeria. Abstract This study investigates the flow of magnetohydromagnetic (MHD) Eyring-Powell chemical reaction nanoliquid in a permeable boundless device with wall cooling and thermal radiation. The fully developed Cauchy non-Newtonian fluid model is stimulated by species reaction and the stretch- ing sheet under gravity influence. Using the Rosseland radiation approximation model with an appropriate similarity variable, the dimensionless coupled derivatives are obtained. A shooting numerical technique is utilized to determine the thermophysical effects on the flow characteristics. The solution results are computed and given in graphs and tables for clear demonstration and clarification. The results show that entropy is minimized by augmenting the magnetic field, porosity, and thermodynamic equilibrium. Also, parameters that enhance internal heat must be monitored to prevent chemical reaction nanoliquid blowup. DOI:10.46481/jnsps.2022.924 Keywords: Entropy generation; Nanoliquid; Non-Newtonian; Hydromagnetic; Porosity Article History : Received: 07 July 2022 Received in revised form: 20 August 2022 Accepted for publication: 22 August 2022 Published: 08 October 2022 c© 2022 The Author(s). Published by the Nigerian Society of Physical Sciences under the terms of the Creative Commons Attribution 4.0 International license (https://creativecommons.org/licenses/by/4.0). Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Communicated by: S. Fadugba 1. Introduction The dynamical flow of conducting fluid (hydromagnetic) has presently dominated the scientific research and discussion because of its many applications in power generation, agricul- tural technology, medicine and others, Hassan et al. [1]. The flow mechanics also assist in managing flow fluid velocity and improving lubricants [2,3]. However, magnetohydrodynamic liquid flow in a stretching plate will continue to be relevant in technology and industry due to its various usages in poly- mer extrusions, liquid condensation, photographic coasting, etc ∗Corresponding author tel. no: +2348032056439 Email address: kunlesalawu2@gmail.com (S. O. Salawu ) [4,5]. Therefore, to improve the significance and worth of elec- trically conducting liquid flow in a stretching surface, it be- comes necessary to consider its effect on non-Newtonian fluids. Among these liquids is Powell-Eyring material that was formu- lated from the theory of liquids kinetic, and at small or huge shearing rate, it behaves like a Newtonian fluid. The fluid de- fines shear thinning properties; of such is toothpaste, ketchup, human blood and so on. Thus, accompany with heat trans- port, Salawu et al. [6,7] discussed the heat stability of Eyring- Powell with the impact Lorentz force, variable conductivity and electromagnetic heat. Parameters dependent flow character- istics and irreversibility were reported in the study. Nadeem and Saleem [8] examined in a rotating cone, the flow of en- 1 Salawu et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 924 2 ergy and mass transport of Eyring-Powell mixed convection. It was offered that the buoyancy ratio encouraged skin friction, but species and heat gradient are opposite to it. Akbar et al. [9] studied in a stretching plate, the Powell-Eyring MHD in- compressible fluid with a report on the effects of some terms on the shear stress and flow velocity. It was noticed that magnetic field and material terms resists flow velocity. Zaidi et al. [10] investigated the stream of thermal dissipation of Poewll-Eyring in a wall jet. The study analysis was done using shooting proce- dures and found that the heat dissipation term boosted the over- all flow dimensions. Some other analysis on Eyring-Powell can be obtained in [11-13]. Recently, due to technological advancement and its appli- cations, nanoliquid has become the central of attraction to the engineers and scientists. The fluid with base liquid made-up of infinitesimal nanoparticles dimension, an example of such is metal, nanotubes carbon, and oxide, Idowu and Falodun [14]. When the base liquid is used, nanofluid is useful in improving the coefficient of heat conduction and heat convection trans- fer. Coupled with magnetic fields, magneto-nanomaterial is re- markably applicable in design of filters wavelength, filters opti- cal fiber, optical switches and modulators, etc, Ishaq et al. [11]. As such, Hayat et al. [15] presented computed outcomes for a flow of squeezing magneto-nanofluid past a far stream do- main. The Lorentz force is seen to have obviously impacted the flow velocity and thermal dispersion in the flow device. Alao et al. [16] carried out simulation on the radiative heat and species transport of chemically reacting flow with soret and dufour. The thermophoretic and Brownian terms are seen to respectively in- crease the temperature and species distribution in the chemi- cal reaction region. Combining nanoliquid and Eyring-Powell fluid is of great importance in enhancing the effectiveness of technological devices for the best possible performance. As a result, Agbaje et al. [17] demonstrated the impact of radia- tive and thermal generation on the nanomaterial Eyring-Powell non-Newtonian fluid in a dwindling plate. The radiation and heat generation was observed to have significantly impacted the heat conduction and convective heat transport in a moving sheet. Malik et al. [18] used numerical scheme to compute the Eyring-Powell mixed convection nanomaterial MHD flow past a widening surface. It was observed that the chemical reaction and the Lewis number term reduces the fluid chemical distribu- tion. In a vertical stretching plate, the hydromagnetic Powell- Eyring nanoliquid with radiation was investigated by [12,19]. Homotopy analytic technique was used and the results show that the radiation, Lewis and heat dissipation terms remarkably influenced the flow characteristics. However, despite the numerous utilization of nanofluid and Eyring-Powell liquid, entropy generation in the system can sig- nificantly affect and diminish the efficiency of the thermal tech- nological tools if no properly managed, Salawu et al. [20]. In thermodynamic structure, energy is lost due to the force of fric- tion, the chemical reaction, the viscosity of the fluid and diffu- sion which resulted in entropy generation. The entropy genera- tion measures the degree of irreversibility in a structure; this is determined using thermodynamic second law, Salawu and Oke [21]. Therefore, to optimize technology tools, entropy genera- tion due to irreversible process should be minimized. As such, Rashidi et al. [22] discussed entropy generation of hydromag- netic swarm particle in a moving gyratory disk. The authors used optimization procedure and the neural artificial system to solve the problem and found that increasing magnetic field min- imized irreversible process. Hayat et al. [23] presented silver and copper nanomaterials with minimization of entropy genera- tion. The solution to the model was analytically obtained. Khan et al. [24] offered a declination of entropy generation for radia- tive nanoparticles in a stretching thin needle. It was seen that Nusselt number and wall drag force stimulated higher volume of fraction nanoliquid. Bhatti et al. [19] studied Powell-Eyring nanoparticles entropy generation in a porous moving plate. In the considered thermophysical terms, an enhancing function of irreversible process is observed. Some other studies on thermo- dynamic second law can be found in [25-28]. The present analysis examines the thermodynamic second law of chemical reactive Eyring-Powell nanoliquid with Joule heat and radiation in stretching convective cooling plate. This study is being motivated by the positive achieved results and the applications of non-Newtonian nanoliquid. Despite many re- lated studies, no mathematical post or study on Eyring-Powell nanomaterial has been examined with Ohmic heating, heat gen- eration, natural convection, heat radiation and chemical species. In the study, the entropy generation, irreversibility ratio, and heat and species distributions is examined in a cooling porous device to prevent the materials from distortion. The dimension- less quasilinear coupled derivatives are solved by shooting tech- niques to investigate the thermodynamic flow characteristics of the parameters dependent. The study is significant in reducing irreversibility process in order to enhance the utilization and ef- ficiency of nano Eyring-Powell liquid. Also, the reaction flow behaviour to variation in parameters for proper monitored of technological devices. 2. Mathematical Formulation Examine a hydromagnetic chemical reactive Eyring-Powell nanoliquid flow in permeable media. The flow is gravity-driven past a vertical stretching convective cooling plate at y = 0 and at y > 0, the MHD dominance takes place. The flow is inspired by induced Lorentz force and non-Newtonian material terms. As demonstrated in Figure 1, the flow is offered in x-axis and y-axis is normal to it. The homogenous chemical species occurs in a boundless domain and the stretching wall is exposed to thermal convective cooling satisfying the Newton’s of law of cooling. Due to small effect of Reynolds number, the magnetic induction impact is ignored. The liquid viscoelastic behaviour is encour- aged by the Eyring-powell non-Newtonian Cauchy formulation as presented below. The non-Newtonian Eyring-Powell viscoelastic Cauchy for- mulation is described as [10,29] Ci j = 1 δ sinh−1 ( 1 αr ∂wi ∂x j ) + µ ∂wi ∂x j . (1) The term Ci j denotes Cauchy tensor, αr and δ represents the 2 Salawu et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 924 3 working fluid material term of Powell-Eyring while µ depicts the fluid coefficient viscosity. Thus, sinh−1 ( 1 αr ∂wi ∂x j ) � 1 αr ∂wi ∂x j − 1 6 ( 1 αr ∂wi ∂x j )3 , ∣∣∣∣∣ 1αr ∂wi∂xi ∣∣∣∣∣ < 1.(2) The velocity of the flow is not created by species reaction but influenced by gravity and moving plate. Taking from all the as- sumptions, the approximated equations for the boundary layer mass conservation, momentum, temperature and chemical re- action balance of Eyring-Powell nanoliquid flow in permeable media are given as [6,9,11,13]: ∂u ∂x + ∂v ∂y = 0, (3) u ∂u ∂x + v ∂u ∂y = ( νn f + 1 ρn f αrδ ) ∂2u ∂y2 − 1 2ρn f αrδ3 ( ∂u ∂y )2 ∂2u ∂y2 − σB20 ρn f u − νn f K u + gβt (T − T∞) + gβc(C − C∞), (4) u ∂T ∂x + v ∂T ∂y = Qa (ρcp)n f (T − T∞) + α ∂2T ∂y2 + 16σsT 3∞ 3k∗ ∂2T ∂y2 + τ DB ( ∂C ∂y ∂T ∂y ) + ( DT T∞ ) ( ∂T ∂y )2 + σB 2 0 ρn f u2 + ν K u2, (5) u ∂C ∂x + v ∂C ∂y = DB ( ∂2C ∂y2 ) + DT T∞ ( ∂2T ∂y2 ) − R0(C − C∞) n. (6) The sustaining employed boundary conditions are accord- ing to [10,29]: u = uw(x) = ax, v = 0, − k ∂T ∂y = h f (T f − T ), C = Cw at y = 0, u −→ 0, T −→ T∞, C −→ C∞ at y −→∞. (7) Here, the terms u, u denote the velocity modules in x and y, C, C∞ and T , T∞ are the fluid concentration, far stream con- centration and fluid temperature, far stream temperature respec- tively. The terms νn f , µn f and ρn f are the nanofluid kinematic viscosity, fluid viscosity and density separately. Also, DT , σ, DB, βt,c, K, g, Qa, cp, B0, α, R0 and n are correspondingly the thermophoretic diffusion, electric conductivity, Brownian diffu- sion, thermal expansion, porosity, gravity, heat generation, heat capacity, magnetic strength, thermal conduction, chemical re- action and reaction index. Meanwhile, α and δ are the Powell- Eyring terms. The second term on the right hand side of equation (5) represent the approximated thermal Rosseland radiation, where σs and k∗ are the Stefan-Boltzman and mean absorption terms. Using the succeeding associated variables for the transformation of equa- tions (3)-(7) θ(η) = T − T∞ T f − T∞ , φ(η) = C − C∞ Cw − C∞ , η = ( a ν ) 1 2 y, u = ax f ′(η), v = − √ aν f (η),ψ(x, y) = (xν)1/2 f (η). (8) Here, ψ is the stream function and its satisfied (u, v) = ( ∂ψ ∂y ,− ∂ψ ∂x ) . By applying the similarity variables of equation (8) on equa- tions (3) to (7), equation (3) is spontaneously gratified while equations (4) to (7) gives (1 + �) f ′′′ + f f ′′ − ( f ′ )2 − �λ( f ′′ )2 f ′′′ −(M + P) f ′ + Grθ + Gcφ = 0, (9)( 1 + 4 3 Ra ) θ ′′ + Pr f θ ′ + PrNbθ ′ φ ′ + BrPr(M + P)( f ′ )2 + PrNr(θ ′ )2 + PrQθ = 0, (10) φ ′′ + Le f φ ′ + Nb Nr θ ′′ − LeΛφn = 0. (11) With boundary conditions gives f (0) = 0, f ′ (0) = 1, θ ′ (0) = −Bi(1 − θ(0)), φ(0) = 1, f ′ (∞) = 0, θ(∞) = 0, φ(∞) = 0. (12) where the terms � = 1 µαrδ and λ = a 3 x2 2α2r ν are the working fluid ma- terials, M = σB20 ρn f a is magnetic field, P = νaK is the porosity, Gr = gβt (T f −T∞) a2 x and Gc = gβc (C f −C∞) a2 x are the heat and species buoy- ancy number, Nr = τDT (T f −T∞) T∞ν denotes thermophoretic, Pr = ν α is Prandtl number, Ra = 4σs T 3 ∞ 3νkn f is the radiation, Nb = τDB (C f −C∞) ν defines Brownian motion, Le = νDb connotes Lewis number, Q = Q0a(ρc)n f the heat source, Λ = Rn (C f −C∞)n−1 a is chemical reac- tion and Br = u 2 w C p(T f −T∞) denotes the heat term. The wall drag (C f ), heat gradient (Nu) and mass gradient (S h) are the engineering thermophysical quantities of inquisi- tiveness which are given as: C f = Gw ρu2w ; where Gw = ( µ + 1 αrδ ) ∂u ∂y − 1 2α3r δ ( ∂u ∂y )3 ,(13) Nu = aQw (T − T∞)kn f ; where Qw = −kn f ( ∂T ∂y ) , (14) S h = aS w (C − C∞)DB ; where S w = DB ( ∂C ∂y ) . (15) Using the variables in equation (8) on equations (13)-(15), the equations reduces to dimensionless for as: C f = (1 + �) f ′′ (0) + �λ 3 ( f ′′ (0) )3 , Nu = − ( 1 + 4 3 Ra ) θ ′ (0), S h = −φ ′ (0). (16) 3. Entropy generation A continuous irreversibility process is created in the flow of Eyring-Powell nanoliquid simulated by heat conduction, fluid 3 Salawu et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 924 4 friction and diffusive irreversibility, this process defined en- tropy generation. Entropy is generated when there is an ex- change of heat between device wall and the Eyring-Powell hy- dromagnetic nanoliquid. The entropy volumetric rate for the considered non-Newtonian fluid with the impact of electric field, porosity, and magnetic field is defined according to [25-27]: EG = kn f T 2∞  ( ∂T ∂y )2 + 16σsT 3∞ 3kn f ( ∂T ∂y )2 + µn f T∞  ( 1 + 1 ρn f αrδ ) ( ∂u ∂y )2 − 1 6ρn f αrδ ( ∂u ∂y )4 + σB20 T∞ u2 + ν KT∞ u2 + RD C0 ( ∂C ∂y )2 + RD T∞ ( ∂C ∂x ∂T ∂x + ∂C ∂y ∂T ∂y ) , (17) the characteristics of entropy production is denoted as EH = (kn f∇T )2 T 2∞a2 . (18) Applying equation (8) on equation (17), the non-dimensional entropy generation takes the form Nc = EG EH = ( 1 + 4 3 Ra ) (θ ′ )2 + Reϕγ Ω ( ϕ Ω (φ ′ )2 + φ ′ θ ′ ) + BrRe Ω [ (1 + λ)( f ′′ )2 − λ� 3 ( f ′′ )4 + (M + P)( f ′ )2 ] , (19) where Ω = ∆TT∞ , γ = C∞RD kn f , ϕ = ∆CC∞ , Re = Uw a2 ν . Taken Np = ( 1 + 43 Ra ) ( θ ′ )2 and Nq = BrRe Ω [ (1 + λ)( f ′′ )2 − λ�3 ( f ′′ )4 + (M + P)( f ′ )2 ] + Reϕγ Ω ( ϕ Ω (φ ′ )2 + φ ′ θ ′ ) , The Bejan number (Be) is expressed as Be = ( 1 + 43 Ra ) ( θ ′ )2 BrRe Ω [ (1 + λ)( f ′′)2 − λ�3 ( f ′′)4 + (M + P)( f ′)2 ] +( 1 + 4 3 Ra ) (θ ′ )2 + Reϕγ Ω ( ϕ Ω (φ ′ )2 + φ ′ θ ′ ) . (20) Here, Np + Nq = Nc, and Np represents the energy irreversibil- ity, Nq connotes irreversibility due to diffusion, conduction and Joule heating. Be defines the ratio of irreversibility. The irre- versibility of nanoliquid Powell-Eyring is dominated with chem- ical diffusion, Joule heat and heat transfer when Be = 0 but when Be = 1, the irreversibility of non-Newtonian nanoliquid is controlled by thermal conducting of the fluid with changes in the temperature. Figure 1. Flow schematic diagram Figure 2. Flow rate field for various � Figure 3. Velocity field for different M 4 Salawu et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 924 5 Figure 4. f (η) against η for various P Figure 5. Heat profile for variation of Br Figure 6. Plot of θ(η) versus η for Nr Figure 7. Temperature field for various Q Figure 8. Rising Ra effect on temperature Figure 9. Reaction field for rising Le 5 Salawu et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 924 6 Figure 10. Effect of Λ on concentration Figure 11. φ(η) versus η for various Nb Figure 12. Entropy profile for different Figure 13. M impacts on entropy field Figure 14. Irreversibility for increasing Br Figure 15. Impact of P on Bejan number 6 Salawu et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 924 7 4. Method of Solution Based on previous analysis, the following values � = 0.5, λ = 0.1, n = 1.0, Λ = 1.0, P = 0.2, M = 0.5, Pr = 0.72, Ra = 0.5, Nb = 0.5, Nr = 0.5, Le = 0.5, Q = 0.5, Gr = 3.0, Gc = 3.0, Br = 0.05, Re = 1.0, Ω = 0.5, ϕ = 0.2, γ = 0.3 are set as default. A numerical shooting techniques is carried out on the MHD Eyring-Powell nanoliquid boundary value equations. The numerical method allows the transformation of boundary value equation to an initial value equation. At far field (η −→ ∞), a finite appropriate boundary value is assumed. Then the derivative of higher order is presented in first order derivative by assuming and substituting the following quantities in equations (9) to (12): a1 = f, a2 = f ′, a3 = f ′′, a4 = θ, a5 = θ ′, a6 = φ, a7 = φ ′, (21) a′3 = −a1a3 + (a2)2 + (M + P)a2 − Gra4 − Gca6 (1 + �) −λ�(a3)2 , (22) a′5 = −Pra1a5 − PrNba5a7 − BrPr(M + P)(a2)2 1 + 43 Ra − PrNr(a5)2 + PrQa4 1 + 43 Ra , (23) a′7 = −Lea1a7 − Nb Nr a′5 + LeΛ(a6) n, (24) The boundary conditions becomes a1(0) = 0, a2 = 1, a5(0) = −Bi(1 − a4(0)), a6 = 1, a2(∞) = 0, a4(∞) = 0, a6(∞) = 0. (25) The reduced initial value equations (21) to (24) are to be solved. The unknown points a2(0) = r1, a5(0) = r2 and a7(0) = r3 are needed for computation. Therefore, the unknown values are initially guessed to allow computation which is carried out using integrating Runge-Kutta procedures with step size ∇η = 0.0001. The same solution procedures is used for the physical quantities and the entropy generation. 5. Results and Discussion The comparison of computed outcomes for the heat gradient and plate drag force is presented in tables 1 and 2. The compar- ison was done with relevant previous related studies in order to confirm the consistency and exactness of the present computed results. Table 1 denotes the compared results for heat gradient with the work of Tawade et al. [4], Ishaq et al. [11] and Salawu and Ogunseye [29]. Also, table 2 represents the skin friction numerical results as compared with the previous study of Hayat et al. [10] and Ogunseye et al. [30]. As seen from the tables, the computational values agreed well with about 10−6 relative error. The computational values for the thermophyscial quantities of engineering interest are presented in table 3. Keeping other Figure 16. M effects on Bejan number Figure 17. Irreversibility ratio field for Br parameters fixed, the results demonstrated the effect of some parameters on the stretching wall. As obtained from the table, some terms have an increasing effect on the wall while some have a reducing impact on the stretching wall. The computed values depends on the momentum, thermal and reaction species boundary layers. Th reaction of Eyring-Powell nanoliquid velocity in a verti- cal plate to the rising values of material term �, magnetic term M, and porosity term P are respectively demonstrated in figures 2, 3 and 4. The dimensionless velocity f ′(η) is plotted against the dimensionless distance η as seen in the figures. With fixed values of other terms, the parameters �, M and P show a de- creasing effect on the viscoelastic nanoliquid flow rate near the stretching boundary wall. The reducing effect occurs close to the stretching vertical plate due to a rise in the molecular bond- ing force and lower internal heating. However, the parameters influence on the fluid velocity decreases steadily away from the plate. As the non-Newtonian fluid flows far from the plate, the heat produced in the chemical reaction system upsurges, due to an augmentation in the heat generation and Ohmic heating in- fluencing the reaction rate that in turn reduced the viscoelastic fluid bonding force. Therefore, the flow rate is progressively ex- panded far the velocity field and converged far away the stream. 7 Salawu et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 924 8 Table 1. Results comparison for the heat gradient. λ Pr Nr [4] [11] [30] New results 0.2 1.0 0.1 0.3238 0.32102 0.32186 0.32186 0.3 0.3020 0.30042 0.30071 0.30071 0.4 0.2925 0.29142 0.29092 0.29092 0.5 0.3717 0.37142 0.37129 0.37129 1.5 0.1819 0.18229 0.18210 0.18210 0.4 0.6117 0.61243 0.61238 0.61238 0.6 0.6023 0.69143 0.70016 0.70016 0.8 0.5013 0.50099 0.50083 0.50083 Table 2. Results comparison for the skin friction. Nr Nb [10] [31] Present results 0.5 1.21380 1.21380229 1.21380217 0.2 1.24143 1.24142703 1.24142698 0.5 1.37544 1.37544311 1.37544302 0.0 1.79329 1.79328569 1.79328551 0.2 1.0 1.25874 1.25873960 1.25873893 1.5 1.26916 1.26016234 1.26016222 Table 3. Numerical values for the skin friction (C f ), Nussetl number (Nu) and Sherwood number (S h) M λ � Ra Le Nr Nb C f Nu S h 0.5 0.1 0.5 0.5 0.5 0.5 0.5 0.987613128 0.0567754810 0.937155927 0.7 0.937510305 0.0531214474 0.943378662 1.5 0.763440580 0.0377939599 0.970428985 0.3 1.008526464 0.0567917496 0.937253896 0.7 1.061377860 0.0568290633 0.937472853 1.0 0.759445493 0.0564705972 0.934027849 1.5 0.610097045 0.0562309677 0.931818099 0.03 0.922979767 0.0603941793 0.941008972 0.07 0.927870854 0.0601463768 0.940178666 0.7 0.917559030 0.0532639565 1.108694229 1.0 0.843402030 0.0497823360 1.320808092 1.5 1.069353500 0.0495253726 0.919047457 2.5 1.184217940 0.0407985312 0.920494831 1.0 1.037237502 0.0542505586 0.998303261 2.0 1.124838686 0.0498904892 1.170942782 Hence, the flow rate profiles for the considered fluid rises in the neighboring of the moving plate, but in opposite direction far- off the vertical surface. The effect of some thermophysical terms on the energy dis- tribution is confirmed in figures 5, 6, 7 and 8. The impact of heat dissipation Br, thermophoretic Nb, heat source Q and ra- diation Ra terms on the temperature distribution are separately presented in the plots. At different significance, the parameters vigorously influenced the thermal dispersion rate in the porous device. The strong heat encouragement is due to rises in the chemical reaction rate that leads to random motion and rapid collision of the fluid particles. Also, as heat source parame- ters is boosted, small or no thermal propagation of chemically non-Newtonian viscoplastic mixtures out of the system to the ambient. This is as a result of thermal boundary film is in- spired, which in turn damped the heat transport in permeable media. In the temperature equation, the thermal source are pro- pelled to enhance thermal transport in the Eyring-Powell chem- ical nanoliquid mixture, which leads to a complete increase in the temperature profiles. Thus, the parameters Br, Nb, Q and Ra inspires the temperature propagation in the moving vertical plate as depicted in figures 5, 6, 7 and 8. Concentration profiles for various effects of some parame- ters are established in figures 9, 10 and 11. The figures depict the plot of φ(η) versus distance η −→∞ in a boundless domain. In figures 9 and 10, the response of the species concentration to variation in the Lewis number Le and chemical reaction Λ are illustrated. As obtained in the figures, both terms of equal variational values decrease the concentration field at different significant. The reducing impact is momentously noticeable in the Lewis number Le than chemical reaction Λ. The diminish- ing in the profiles is due to lower chemical reaction rate in the 8 Salawu et al. / J. Nig. Soc. Phys. Sci. 4 (2022) 924 9 system that causes the species particles to react slowly and dis- couraged. Hence, increasing the values of both terms enhances nanoliquid chemical diffusion as the concentration boundary layer shrinks. Figure 11 depicts the impact of Brownian move- ment Nr on the reacting species profile. Rising values of the Brownian movement term increases the reaction rate and rapid random motion of the chemical particles, this then causes a rise in the reaction mass field as presented in the figure. The respective influence of variation in the thermophysical terms porosity P, magnetic M and heat dissipation Br on the entropy generation is described in figures 12, 13 and 14. In a process where irreversibility is in existence, entropy generation is defined. This measure the amount of energy loss that causes degradation of technology system performance. As seen, the parameters encourages system irreversibility due to high en- ergy dissipation near the stretching plate as the values of the parameters is raised. However, the irreversibility due chemical diffusive, friction and conducting heat decrease regularly few distance from the moving surface because the fluid thermody- namic equilibrium is rising gradually and continuously toward the free field. The decrease in the entropy generation contin- ues until a balance thermodynamic equilibrium is attained and energy dissipation tends to zero. Hence, irreversibility reduces far the field as portrayed in figures 12, 13 and 14. The effect of porosity P, magnetic M and heat dissipation Br on the irre- versibility ratio is respectively presented in figures 15, 16 and 17. Bejan number is the irreversibility heat transfer ratio to the sum of the irreversibility of fluid friction and heat transfer. The irreversibility ratio rises all over the considered system do- main as demonstrated in figure 15 and 16. The overall rising in the magnitude of the Bejan number is because of the increas- ing rate in the heat transfer irreversibility in the non-Newtonian viscoelastic fluid regime. Meanwhile, heat dissipation term Br completely reduced the irreversibility ratio of the chemical dif- fusive system. The significant impact is very obvious within the chemical reaction due to strong fluid frictional effect that dom- inate the reactive system. Therefore, as depicted in figure 17, the Bejan number decreases momentously over the domain. 6. Conclusion In the study, the entropy generation of Eyring-Powell chem- ical reaction nanoliquid was considered in a porous vertical boundless device with heat distribution. A shooting numerical technique is adopted for the solutions coupled with the Runge- Kutta scheme due to its convergence, consistency, and uncon- ditional stability. 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