Heat and mass transfer in Maxwell fluid with nanoparticles past a stretching sheet in the existence of thermal radiation and chemical reaction

ABSTRACT

The objective of this work is to examine the distinctive features of heat and mass transfer in a 2-dimensional Maxwell fluid that is incompressible and contains electrically conducting nanoparticles. They are illustrated by using a stretched sheet with convective boundary conditions and a heat source/sink in the presence of thermal radiation and chemical interaction. Studies of hydromagnetic flow and heat transfer across a stretched sheet have lately attracted a great deal of attention as a result of its numerous industrial applications and a huge impact on a broad variety of manufacturing processes. Power plants, heat exchangers, MHD generators, aerodynamics, plastic sheet extrusion, condensation processes, and metal spinning are examples of these processes. The partial differential equations (PDEs) that govern the flow and the boundary conditions that correspond with them may be non-dimensionalized by using the appropriate similarity variables. The resulting transformed ordinary differential equations (ODEs) are solved using the Runge-Kutta-Fehlberg scheme of the fourth and fifth order. By assuming a value for the boundary condition, the shooting approach transforms the boundary value problem (BVP) into an initial value problem (IVP), which is subsequently solved using the RKF45 algorithm. Graphical representations of how such embedded thermo-physical parameters significantly impact the velocity, temperature, and concentration are assessed and shown. A comparison case study is made with previously published literature, and a great correlation between the results exists. The primary results of the research are that raising estimates of the chemical reaction parameter minimises the concentration distribution while increasing the thermal radiation parameter raises the temperature. As the quantity of thermophoresis rises, the thickness of the boundary layer increases, causing the surface temperature to rise, resulting in a temperature rise.

GRAPHICAL ABSTRACT

KEYWORDS:

• Stretching sheet
• nanoparticles
• thermal radiation
• Maxwell fluid

Nomenclature

$Bi$	=	Biot number
$c$	=	positive constant
$C$	=	Concentration of the fluid $\left(mol{m}^{-3}\right)$
$C_w$	=	Fluid concentration at the wall $\left(mol{m}^{-3}\right)$
$C_{\mathrm{\infty }}$	=	Fluid Concentration at infinity $\left(mol{m}^{-3}\right)$
$C_s$	=	Concentration susceptibility
$C_p$	=	Specific heat at constant pressure $\left(J.K{g}^{-1}.K\right)$
$C_f$	=	Skin friction
$D_B$	=	Brownian diffusion
$D_T$	=	Coefficient of thermophoretic diffusion
$D_M$	=	Mass diffusivity $\left(m^2.s^{-1}\right)$
$f$	=	Dimensionless velocity stream function
$h_f$	=	Heat transfer coefficient
$k$	=	Thermal conductivity $\left(\omega .m^{-1}.K^{-1}\right)$
$k_0$	=	Maxwell fluid relaxation time
$K_T$	=	Thermal-diffusion ratio parameter
$K_r$	=	Chemical reaction parameter
$Le$	=	Lewis Number
$Nb$	=	Brownian Motion Parameter
$Nt$	=	Thermophoresis parameter
$Nr$	=	Radiation Parameter
$N{u}_x$	=	local Nusselt number
$Pr$	=	Prandtl number
$S{h}_x$	=	local Sherwood number
$T$	=	Temperature of fluid near the plate $\left(K\right)$
$T_w$	=	Fluid temperature closer to the wall$\left(K\right)$
$T_{\mathrm{\infty }}$	=	fluid Temperature at infinity $\left(K\right)$
$T_f$	=	The temperature of hot fluid
$u$	=	Dimensionless velocity along $x$-axis$\left(m.s^{-1}\right)$
$v$	=	Dimensionless velocity along of y- axis$\left(m.s^{-1}\right)$
$x,y$	=	Cartesian coordinates
Greek letters	=
$\alpha$	=	Thermal diffusivity
$\beta$	=	Maxwell parameter
$\sigma$	=	Electrical conductivity $\left({\mathrm{\Omega }}^{-1}{m}^{-1}\right)$
$\rho$	=	Fluid density $(kg/m^3$)
${\rho }_p$	=	Density of the particles
${\rho }_f$	=	Density of the base fluid
$\mu$	=	Dynamic viscosity
$\eta$	=	Dimensionless similarity variable
$\nu$	=	Kinematic viscosity $(m^2{s}^{-1}$)
$\theta$	=	Dimensionless temperature of the fluid
$\phi$	=	Dimensionless fluid concentration
$\psi$	=	Stream function
Subscripts	=
$w$	=	condition at the stretching sheet
$\mathrm{\infty }$	=	conditions at infinity
Superscript	=
$\prime$	=	differentiation with respect to $\eta$

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors received no financial support for the research, authorship, and publication of this article.

Notes on contributors

N. Venkatesh

Mr. N. Venkatesh working as an Assistant professor in the Department of Mathematics, at Anurag University. He received his Master of Science (Mathematics) from National Institute of Technology Warangal, in 2011 and is Pursuing Ph.D. in Mathematics from GITAM University Hyderabad. He has over 12 years of teaching and research experience. He has 5 publications to his credit in reputed international journals. He also presented papers at various National and International conferences. He received the patent right in Micropolar fluids from Intellectual Property of India in 2022 He is a member of the Indian Science Congress and Telangana State Mathematical Society. His research areas include Fluid mechanics, Heat, and Mass transfer.

R. Srinivasa Raju

Dr. R. Srinivasa Raju is presently working as an Associate Professor at GITAM School of Science, GITAM (Deemed to be University), Hyderabad Campus, Rudraram, Hyderabad, Telangana state, India. He acquired his Doctorate in Applied Mathematics from Osmania University in 2012, and he also received his Master of Science in Applied Mathematics from Osmania University in 2005. He has over 115 publications in International and National reputed Journals. He also attended and paper presented in various National and International Conferences. He has published a book entitled Finite Element Technique on MHD Fluid Flow Problems by RIGI Publications. He serves as an editorial member for four international journals. He is a member of several National and International Mathematical Societies. He received the Srinivasa Ramanujan Life Time Achievement National Award in the year 2018. He has also received the Prestigious Award for Young Educator and Scholar Award from the National Foundation for Entrepreneurship Development (NFED) in the year 2018. He has produced 4 doctoral candidates. He is currently supervising 10 research scholars.

M. Anil Kumar

Dr. M. Anil kumar working as an Associate professor in the Department of Mathematics, at Anurag University. In the year 2020, he obtained his Doctorate from GITAM (Deemed to be University), Visakhapatnam, India, and in 2005, he received his Master of Science in Applied Mathematics from the National Institute of Technology Warangal. Dr. Anil kumar has over 18 years of teaching experience and over 8 years of research experience. He received the Best Teacher award from Anurag University for the academic year 2022-2023. He has 23 publications to his credit in reputed national and international journals. He received a SEED money project from Anurag University of Rs 2 lakhs for the Academic year 2021-22. He received the patent right in Micropolar fluids from Intellectual Property of India in 2022. He also presented papers at various National and International conferences. He is a member of several National and International Mathematical Societies. His research areas include Fluid mechanics, Heat, and Mass transfer. He is currently supervising one research scholar.

Ch. Vijayabhaskar

Dr. Ch. Vijayabhaskar is an Assistant Professor in the Department of Mathematics, Anurag University, and Hyderabad, India. He received his M.Sc. in Mathematics from Osmania University, Hyderabad, India. He received his Ph.D. degree in Applied Mathematics from GITAM University, Andra Pradesh, India. He qualified in Telangana State Eligibility Test (TS-SET). He is a Life member of APTSMS. He has more than eighteen years of experience in teaching and research. His current area of research studies includes Fluid dynamics, Magneto hydrodynamics, Heat and mass transfer. He has published many research papers in reputed journals and also attended many National and International conferences.