# Numerical Investigation of Laminar Forced Convection and Entropy Generation of Nanofluid in a Confined Impinging Slot Jet Using Two-Phase Mixture Model

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## Abstract

In this article, computational fluid dynamics (CFD) simulations is used to investigate the volumetric entropy generation and heat transfer on confined impinging slot jet, with a mixture of water and Al_{2}O_{3} nanoparticles as working fluid. The flow is laminar and a constant temperature is applied on the impingement surface. The governing mass and momentum equations for mixture and dispersed phase and also energy equation for mixture are solved using the finite volume method. This paper studies the effects of different geometric parameters, particle volume concentration and Reynolds number on local and average Nusselt number, stagnation point Nusselt number, entropy generation and stream function contours. The results showed that the intensity and size of the vortex structures depend on jet-to-impingement surface distance ratio (*H/W*), Reynolds number and particle concentrations. As *H/W* ratio increases, average and stagnation point Nusselt number decrease due to flow instability. By increasing Reynolds number and volume concentration, average Nusselt number and exergy loss increase due to stretching of the vortex structure in downstream direction. From the CFD results, it is found that a substantial portion of entropy generation occurs at stagnation and wall jet regions.

## Keywords

CFD Vortex structure Entropy generation Stagnation region Mixture model## List of symbols

- \(\overline{C}_{\text{f}}\)
Average skin friction coefficient

- \(c_{\text{p}}\)
Constant pressure-specific heat, J/kgK

*H*Channel height, m

*H*Convective heat transfer coefficient, W/(m

^{2}k)*d*_{p}Particle diameter, m

- d
*V* Volume element, m

^{3}*K*Thermal conductivity, W/mk

*Nu*Nusselt number

*Pr*Prandtl number

*Re*Reynolds number

*SG*_{C}Volumetric entropy generation due to heat conduction and convection, W m

^{−3}K^{−1}*SG*_{F}Volumetric entropy generation due to fluid friction, W m

^{−3}K^{−1}- \(\mathop {SG_{\text{C}} }\limits^{ \bullet }\)
Entropy generation due to heat conduction and convection, W K

^{−1}- \(\mathop {SG_{\text{F}} }\limits^{ \bullet }\)
Entropy generation due to fluid friction, W K

^{−1}- \(\mathop {SG}\limits^{ \bullet }\)
Total entropy generation, W K

^{−1}*T*Temperature, K

*T*_{b}Bulk temperature, K

*T*_{0}Ambient temperature, K − 293 K

- \(\vec{V}(u,\nu )\)
Velocity vector, m/s

*U*,*v*Velocity components along

*x*,*y*axes, respectively, m/s*W*Jet width, m

*X*,*Y*Spatial coordinates, m

## Greek symbols

- \(\phi\)
Volume fraction of nanoparticles

- \(\mu\)
Dynamic viscosity, Pa s

*Α*Thermal diffusivity

*ρ*Density, kg/m

^{3}- \(\tau\)
Wall shear stress, Pa

- \(\dot{\psi }\)
Exergy loss, W

## Superscripts

- ave
Average at the inlet

- f
Fluid

- C
Continuous phase

- jet
Refers to the reference (inlet) condition

- K
k-th phase

- m
Mixture

- nf
Nanofluid properties

- p
Nanoparticles

- stg
Stagnation point

- w
Wall

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