Optimization of dissipative-magneto highly reactive Casson nanoliquid flow with an electric field utilizing response surface methodology

ABSTRACT

The studies of a first-order chemical reaction have been presented in various published investigations, while the nth chemical reaction should be examined. Also, optimizing the effect of process variables is important for a clear understanding of the heat transfer mechanism. Therefore, this paper presents an optimization and sensitivity analysis for the heat transfer and shear rate utilizing response surface methodology (RSM) for dissipative-magneto highly reactive Casson nanoliquid flow with an electric field. The irreversibility property is disclosed, and both active and passively controlled cases are assumed. The governing system is transformed into similar forms and solved using the Blottner technique together with the Finite Difference Method (FDM). The main attraction of the current investigation is to optimize the rate of heat transfer as well as the shear rate by utilizing robust statistical approaches. Further, sensitivity analysis for the significant factors is, also, demonstrated for the proposed responses. The major outcomes revealed that the skin fraction is enhanced as the magnetic parameter is altered, while the electrical coefficient causes a reduction in the velocity gradients. In the active-controlled case, the power index of the chemical reaction reduces the mass transfer rate.

KEYWORDS:

• Electric field
• higher-order chemical reaction
• MHD
• porous medium
• viscous dissipation
• Casson nanoliquid
• Blottner-FDM
• response surface methodology
• central composite design

Nomenclature

$u,v$	=	Velocity components in $x,y$ directions $(m/s)$
$\rho$	=	Density $(kg/m^3)$
$\mu$	=	Dynamic viscosity $\left(kg{m}^{-1}{s}^{-1}\right)$
$\upsilon$	=	Kinematic viscosity $(m^2/s)$
$c_p$	=	Specific heat $(J/Kg/K)$
$k$	=	Thermal conductivity $(W/mK)$
$g$	=	Gravity acceleration
$K$	=	Permeability parameter $(m^2)$
${\beta }_T$	=	Heat expansion coefficient $(K)$
$N$	=	Nanoparticle concentration
$F$	=	Forchheimer number
$T$	=	Temperature $(K)$
$D_B$	=	Brownian diffusion
$D_T$	=	Thermophoresis diffusion
$T_w$	=	The temperature of stretching sheet $(K)$
$T_{\mathrm{\infty }}$	=	The temperature at a distance from sheet $(K)$
$\gamma$	=	Chemical reaction parameter $\left(\gamma =\frac{{\delta }_n{[N_w-N_{\mathrm{\infty }}]}^n}{b}\right)$
$Kr$	=	Porous parameter $\left(Kr=\frac{\upsilon }{kb}\right)$
$Ha$	=	Hartmann number $\left(H{a}^2=\frac{\sigma B_0^2}{\rho b}\right)$
$B$	=	Casson parameter
$Er$	=	Electric parameter$\left(Er=\frac{E_0}{B_{0}bx}\right)$
$Nt$	=	Thermophoresis parameter $\left(Nt=\frac{D_T\rho c_p(T_w-T_{\mathrm{\infty }})}{\upsilon \rho c_f{T}_{\mathrm{\infty }}}\right)$
$Fr$	=	Inertia coefficient
$\lambda$	=	Mixed convection parameter
$Pr$	=	Prandtl number $\left(Pr=\frac{\upsilon \rho c_p}{k}\right)$
$Ec$	=	Eckert number $\left(Ec=\frac{b^2{x}^2}{c_p(T_w-T_{\mathrm{\infty }})}\right)$
$Nb$	=	Brownian motion parameter $\left(Nb=\frac{D_B\rho c_p(N_w-N_{\mathrm{\infty }})}{\upsilon \rho c_f}\right)$
$Sc$	=	Schmidt number$\left(Sc=\frac{\upsilon }{D_B}\right)$
$Cf$	=	Skin friction coefficient
$N{u}_x$	=	Nusselt number
$S{h}_x$	=	Sherwood number
$Br$	=	Brinkman number
$Re$	=	Reynolds number
$Rd$	=	Thermal radiation $\left(Rd=\frac{4\sigma T_{\mathrm{\infty }}^3}{\upsilon k^{\ast }\rho c_p}\right)$
$\mathrm{\Omega }$	=	Dimensionless temperature difference.
Ξ	=	Dimensionless concentration difference.
$N_0$	=	Characteristic entropy generation rate
$\epsilon$	=	Constant parameter.

Acknowledgments

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through a large group Research Project under grant number RGP2/64/44.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the King Khalid University [RGP2/64/44].

Notes on contributors

Abdulaziz Alenazi

Abdulaziz Alenazi obtained his doctorate degree in Statistics from The University of Sheffield, UK. He is currently an assistant professor in Statistics at the Department of Mathematics, College of Science, Northern Border University, Arar, Saudi Arabia. His research interest is in Statistical and Mathematical methods, Compositional data analysis, Statistical and Mathematical modelling, Bayesian Statistics analysis, and Computational Statistics. He has several international publications in reputable journals to his credits.

Thirupathi Thumma

Dr. Thirupathi Thumma is working as an Associate Professor of Computer Science at Vardhaman College of Engineering. He completed his Ph.D. in Applied Mathematics in 2019. His research interests are Heat and Mass Transfer, Hydrodynamic boundary layer flow of mono and hybrid nanofluids, Response Surface Methodology, MHD/EMHD flow within porous media, and advanced numerical, semi-analytical methods. He has more than 50 publications in internationally reputed journals with h-Index 21. Currently, three Ph.D. scholars working under his supervision. He is also an active reviewer in many reputed journals.

Sameh E. Ahmed

Sameh E. Ahmed obtained his doctorate degree in applied Mathematics from South Valley University, Department of Mathematics, Faculty of Science, Egypt. He is currently professor in the department of Mathematics, Faculty of science, King Khalid University. His research interest is in Mathematical methods, Fluid mechanics, and Mathematical modelling. He has several international publications in reputable Journals to his credits.

Zehba A. S. Raizah

Zehba A. S. Raizah obtained her doctorate degree in applied Mathematics from King Khalid University, Department of Mathematics, Faculty of Science, KSA. She is currently a professor in the department of Mathematics, Faculty of science, King Khalid University. Her research interest is in Mathematical methods, Fluid mechanics, and Mathematical modelling. She has several international publications in reputable Journals to her credits.

Mishra S. R.

Dr. Mishra S. R. currently working as a professor, in the Department of Mathematics, Siksha O Anusandhan (Deemed to be University), Bhubaneswar. He did his Ph.D. from Siksha O Anusandhan in 2013 and since then actively engaged in his research work. His area of interest is Heat transfer, Magnetohydrodynamics, Porous media, etc. with the broad area of Fluid Dynamics. He has published nearly 250 papers in international journals of repute. With a huge citation of his work, he took the position of Top 2% World Scientists by Stanford University, USA in the last four consecutive years i.e. 2020-2023. He has guided thirteen research scholars. As a strength, he has edited a book series in Springer Nature for the year 2020 as a leading Editor and Editor/associate editor in several reputed international journals. He is also an active reviewer in many reputed journals.