Comparative study of hybrid and nanofluid flows over an exponentially stretched curved surface with modified Fourier law and dust particles

Abstract

Hybrid nanofluids are the prospective liquids that possess improved heat transfer enactment and thermophysical characteristics than conventional heat transfer fluids (water, oil, ethylene glycol) and single-particle nanoparticle immersed nanofluids. Here, a comparison of the hybrid nanofluid comprising copper, copper oxide nanosized particles with ethylene glycol (Cu-CuO/C₂H₆O₂) as the customary liquid, with nanofluid copper-ethylene glycol (Cu/C₂H₆O₂) is made. The flow of hybrid nanofluid is considered over an absorbent curved sheet which is stretched exponentially with dust particles with modified Fourier law. The modeled problem is assisted by the melting heat and second-order slip boundary conditions. The system of equations is coped numerically after applying the boundary layer theory to the system of governing equations. It is witnessed that dust phase and temperature are augmented for escalating estimations of the curvature parameter. It is also perceived that an escalation in the thermal relaxation and concentration parameter values results in a lowering temperature of the fluid. Furthermore, it is remarked that fluid velocity is enhanced for large disk curvature. The hybrid nanofluid in case of heat transfer comparison is far ahead of the nanofluid. The acquired outcomes are also endorsed by making a comparison with a published study. An outstanding agreement is attained.

KEYWORDS:

• Hybrid nanofluid
• curved stretched surface
• modified Fourier law
• dusty fluid

Acknowledgment

This research was supported by Taif University Researchers Supporting Project Number (TURSP-2020/304), Taif University, Taif, Saudi Arabia.

Disclosure statement

No potential conflict of interest was reported by the authors.

Authors’ contributions

M. R. did conceptualization, H. A. worked on graphical illustrations, and worked on the revised manuscript.

Nomenclature

Symbols	=	Description
$u,v$	=	Fluid velocity component
${\tau }_v$	=	Time for the dust phase to relax
$T_{\mathrm{\infty }}$	=	free stream temperature
$E_c$	=	Eckert number
$l_m$	=	Mass concentration of particles
${\rho }_{hnf}$	=	Density of nanofluid
$\gamma$	=	Specific heat ratio
$nf$	=	Nanofluid
$L_2$	=	Second-order slip parameter
$C_m$	=	Specific heat for dust phase
$R{e}_s$	=	Reynolds number
$T_p$	=	Dust phase temperature
$T$	=	Fluid
$S$	=	Number density for the dust phase
$\lambda$	=	Latent heat of the fluid
$T_{\mathrm{\infty }}$	=	Temperature away from the surface
$K$	=	Curvature parameter
$S$	=	Dust particle density number
${\epsilon }_t$	=	Thermal relaxation time parameter

Greek symbols

$L_1$	=	First-order slip parameter
$\beta$	=	Fluid-particle interaction parameter
${\varphi }_i$	=	Nanoparticle volume fraction
${\lambda }_E$	=	heat flux relaxation time
${\beta }_C$	=	fluid-particle interaction parameter for concentration
${\lambda }_2$	=	Second-order slip coefficient
$Me$	=	Melting parameter
$K$	=	Curvature parameter
$(\rho C_p{)}_{hnf}$	=	Hybrid nanofluid heat capacity
${\mu }_{hnf}$	=	dynamic viscosity of hybrid nanofluid
$Pr$	=	Prandtl number
${\beta }_T$	=	fluid-particle interactive temperature parameter
$hnf$	=	Hybrid nanofluid
${\beta }_v$	=	Fluid particle interactive velocity parameter
$S_c$	=	Schmidt number
${\lambda }_1$	=	First-order slip coefficient
$l_m$	=	Mass concentration
$T_w$	=	Wall temperature