Investigating radiative heat transfer, varied wall thickness, and slip effects on Casson nanofluid flow over a stretched sheet with heat source

ABSTRACT

Understanding the intricate interplay between variable fluid properties such as slip and thermal conductivity when flowing over porous surfaces is of utmost importance for a wide range of engineering applications. This investigation delves into this uncharted territory, connecting the analytical capabilities of HAM (Homotopy Analysis Method) to reveal captivating insights into the impact of these variables on the dynamics of Casson nanofluid flow. Besides, we documented the flow aspects which include thermal radiation, heat source, variable wall thickness and chemical reaction. We alter the partial differential flow-related conditions into nonlinear ordinary ones employing the similarity transformation approach. Then, using a popular semi-analytical technique known as the Homotopy Analysis Method (HAM), we were able to untangle them. This method yields to power series solutions to nonlinear differential equations. To illustrate the impact of the velocity, temperature and concentration profiles, parametric research has been done using tables and diagrams. In the limiting sense, the numerical results of our methodology are in great association with the outcomes of previous research. Finally, it is noted that higher values of the velocity slip parameter cause an enhancement in fluid velocity, while escalating values of the thermal slip parameter cause a decline in temperature distribution.

KEYWORDS:

• Casson nanofluid
• variable wall thickness
• slip conditions
• thermal radiation
• HAM

Nomenclature

$\mathit{x},\mathit{y}$	=	directions along and normal to the surface
$\mathit{u},\mathit{v}$	=	velocity components in $\mathit{x},\mathit{y}$ directions
$\mathit{B}$	=	magnetic field
$\mathit{T}$	=	temperature of the fluid
$\mathit{k}$	=	thermal conductivity
$C_p$	=	specific heat at constant pressure
$D_B$	=	Brownian diffusion coefficient
$\mathit{C}$	=	nanoparticle volume fraction
$D_T$	=	Thermophoretic diffusion coefficient
$T_{\mathrm{\infty }}$	=	ambient temperature
$Q_0$	=	heat source coefficient
$C_{\mathrm{\infty }}$	=	ambient nanoparticle volume fraction
$U_0$	=	constant
$U_w$	=	stretching velocity,
$T_w\left(\mathit{x}\right)$	=	temperature at the surface
$C_w\left(\mathit{x}\right)$	=	nanoparticle concentration at the surface
$\mathit{A}$, b1	=	Constants
$\mathit{f}$	=	dimensionless stream function.
Le	=	Lewis number
A1	=	Constant
$\mathit{m}$	=	velocity power index parameter
$\mathit{M}$	=	Magnetic parameter
$\mathit{Pr}$	=	Prandtl number
$\mathit{Nb}$	=	Brownian motion parameter
$\mathit{Nt}$	=	thermophoresis parameter
$q_r$	=	radiative heat flux
$\mathit{\beta }$	=	Casson parameter
$\mathit{R}$	=	radiation parameter
$\mathit{\gamma }$	=	Dimensionless chemical reaction parameter
K	=	permeability parameter
Q	=	Heat source
Kr	=	Dimensional chemical reaction parameter
$q_r$	=	radiative heat flux
$q_w$	=	surface heat flux
$C_f$	=	local skin friction factor
$\mathit{N}{u}_x$	=	local Nusselt number
$\mathit{S}{h}_x$	=	local Sherwood number
$\mathit{Q}$	=	heat source parameter
$\mathit{Sc}$	=	Schmidt number
$\mathit{R}{e}_x$	=	local Reynolds number
Greek symbols	=
$\mathit{\nu }$	=	kinematic viscosity
$\mathit{\rho }$	=	fluid density
$\mathit{\sigma }$	=	Electrical conductivity
$\mathit{\kappa }$	=	temperature dependent thermal conductivity
$\mathit{\psi }$	=	stream function
$\mathit{\zeta }$	=	similarity variable
$\mathit{\theta }$	=	dimensionless temperature
${\lambda }_0$	=	wall thickness parameter
$\mathit{\varphi }$	=	dimensionless nanoparticle volume fraction
$\mathit{\mu }$	=	dynamic viscosity
${\mu }_{\mathrm{\infty }}$	=	ambient dynamic viscosity
${\tau }_w$	=	wall shear stress
$j_w$	=	surface mass flux
${\sigma }^{\ast }$	=	Stefan-Boltzman constant
$k^{\ast }$	=	mean absorption coefficient
Subscripts	=
$\mathit{w}$	=	condition at the surface
$\mathrm{\infty }$	=	condition at the free stream
${\lambda }_1$	=	Dimensional velocity slip parameter
${\lambda }_2$	=	Dimensional temperature slip parameter
${\lambda }_3$	=	Dimensional nanoparticle fraction slip factors
$\mathit{\epsilon }$	=	Thermal conductivity parameter
${\delta }_1$	=	Dimensionless velocity slip parameter
${\delta }_2$	=	Dimensionless temperature slip parameter
${\delta }_3$	=	Dimensionless nanoparticle fraction slip factors

Acknowledgments

The authors thank the Deanship of Scientific Research, Islamic University of Madinah, Madinah, Saudi Arabia, for supporting this research.

Disclosure statement

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

Future scope

We can extend our research to other types of nanofluids and hybrid nanofluids beyond Casson fluids to broaden the applicability of these findings and also integrate this research with other relevant physical phenomena like mass transfer, chemical reactions, or multiphase flows for a more comprehensive understanding of complex fluid systems.

Supplementary Material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/02286203.2024.2345256

Additional information

Notes on contributors

P. Raja Sekhar

P. Raja Sekhar is an energetic researcher in the Department of Mathematics, GITAM School of Science, GITAM (Deemed to be University), Visakhapatnam, Andhra Pradesh- 530045, India. His research focuses on numerical analysis and mathematical modeling. He has many scientific papers published in high-impact journals.

S. Sreedhar

S. Sreedhar is a dynamic researcher in the Department of Mathematics, GITAM School of Science, GITAM (Deemed to be University), Visakhapatnam, Andhra Pradesh- 530045, India. His research focuses on Magnetohydrodynamics, Heat & Mass Transfer Applied Mathematics, Heat Transfer, Energy nonlinear partial differential equations, Artificial neural networks, computational fluid dynamics and fluid mechanics problems.

P. Vijaya Kumar

P. Vijaya Kumar is an active researcher in the Department of Mathematics, GITAM School of Science, GITAM (Deemed to be University), Visakhapatnam, Andhra Pradesh- 530045, India. His research focuses on Engineering, Thermodynamics, Heat Exchangers, Applied Thermodynamics, Numerical Simulation, Computational Fluid Dynamics, Fluid Mechanics, Turbulence, Thermal Conductivity, CFD, Simulation and Convection.

S. Mohammed Ibrahim

S. Mohammed Ibrahim is a researcher in the Department of Mathematics, Koneru Lakshmaiah Education Foundation, Green Fields, Vaddeswaram, A.P. – 522302, India. His research focuses on the effects of nanoparticles, solid-state physics, theoretical physics, machine learning and computational fluid dynamics problems.

Charankumar Ganteda

Charankumar Ganteda is a researcher in Department of Mathematics, Koneru Lakshmaiah Education Foundation, Green Fields, Vaddeswaram, A.P. – 522302, India. His research focuses on the following topics: nanofluids; non-Newtonian fluids, chemical reactions, numerical treatment of nanofluids flow, porous media, and magnetic fields. Numerical Modeling, Computational Fluid Mechanics, FLUENT Modeling and Simulation, Experimental Fluid Mechanics, Heat Capacity, Thermal Management, CFD, Coding, Engineering Thermophysics, Turbulence Modeling, Thermal Physics, Numerical Analysis, Fluid Turbulence, Condensation.

Syed M. Hussain

Syed M. Hussain is full professor in the Department of Mathematics, Faculty of Science, Islamic University of Madinah, 42351, Saudi Arabia. His research focuses on Magnetohydrodynamics, Heat & Mass Transfer Applied Mathematics, Heat Transfer, Energy, Thermal Engineering, Engineering, Thermodynamics, Heat Exchangers, Applied Thermodynamics, Numerical Simulation, Computational Fluid Dynamics, Fluid Mechanics, Turbulence, Thermal Conductivity, CFD, Simulation and Convection.

Wasim Jamshed

Wasim Jamshed is an active researcher in the Department of Mathematics at Capital University of Science & Technology (CUST), Islamabad, Pakistan. His research focuses on effect of nanoparticle, heat and mass transfer in fluid mechanics via porous media. In particular he is studying the following topics: nanofluids; hybrid nanofluids, non-Newtonian fluids, chemical reactions effect, numerical treatments of nanofluids flow, porous media, magnetic field and solar energy applications. For the 2nd year in a row, He has been ranked in the top 2% of the world’s most cited scientists for research conducted by Stanford University in collaboration with Elsevier Publishing and Scopus in the mechanical engineering and Transport fields from 2022 to 2023.

Ayesha Amjad

Ayesha Amjad is a dynamic researcher in the Faculty of transport and aviation engineering, Silesian university of Technology Gliwice, 44-100, Poland. Her research focuses on, Energy nonlinear partial differential equations, Artificial neural networks, computational fluid dynamics and fluid mechanics problems.

Katarzyna Markowska

Katarzyna Markowska is a active researcher in the Faculty of transport and aviation engineering, Silesian university of Technology Gliwice, 44-100, Poland. His research focuses on Applied Thermodynamics, Numerical Simulation, Computational Fluid Dynamics, Fluid Mechanics, Turbulence, Thermal Conductivity, CFD, Simulation and Convection.