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Mixed convection enhancement by using optimized porous media and nanofluid in a cavity with two rotating cylinders

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Abstract

Mixed convection inside a square cavity with internal rotating heater and cooler is analyzed numerically by simultaneous application of porous media and nanofluid as a heat transfer enhancement technique. Optimized multi-block porous foams are utilized to enhance the heat transfer. This type of medium could improve the heat transfer rate with manipulation and selection of porous regions’ pore size (or permeability) by amplifying the flow in critical regions and weakening it in non-effective areas. The whole cavity domain is assumed to be made of 25 distinct porous blocks. At first, the effects of the various rotation directions have been investigated and then the optimum distribution of pore size in the porous media is determined in a manner to maximize the heat transfer rate using the pattern search optimization algorithm. Finally, simultaneous effects of application of multi-block porous media and nanoparticle addition to the base fluid on the average Nusselt number are studied in various conditions. For this purpose, various volume fractions of the nanoparticles are implemented to investigate the effects of the different values of the volume fraction on Nu number. The optimization has done for different Ri and Ra numbers for achieving to the best distribution in each condition. In the best condition, 20.4% increase in the heat transfer is obtained.

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Abbreviations

\(\vec{V}\) :

Velocity

C 1 :

Inertia resistance

C 2 :

Viscous resistance

C d :

Inertia coefficient

d p :

Pore diameter of porous media (m)

F :

Inertia coefficient

f :

Function

H :

Side length of cavity (m)

K :

Permeability

k :

Thermal conductivity (\({\text{W m}}^{ - 1} {\text{ K}}^{ - 1}\))

\(\dot{m}\) :

Mass flow rate (kg s1)

n :

Perpendicular direction

Nu:

Nusselt number

\(\theta\) :

Non dimensional temperature

P :

Pressure (kPa)

Pr:

Prandtl number

\(\vec{r}\) :

Radial direction

Ra:

Rayleigh number

Re:

Reynolds number

Ri:

Richardson number

T :

Temperature (K)

x :

Horizontal direction

y :

Vertical direction

c:

Cold

dr:

Drift

eff:

Effective

f:

Fluid

h:

Hot

k:

Secondary phase

m:

Mixture

p:

Secondary phase

s:

Solid

\(\varphi\) :

Nanoparticle volume fraction

\(\beta\) :

Thermal expansion coefficient

\(\varepsilon\) :

Porosity

\(\rho\) :

Density (kg m3)

\(\eta\) :

Efficiency (%)

\(\mu\) :

Dynamic viscosity (Pa s)

\(\vec{\omega }\) :

Angular velocity

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Tahmasbi, M., Siavashi, M., Abbasi, H. et al. Mixed convection enhancement by using optimized porous media and nanofluid in a cavity with two rotating cylinders. J Therm Anal Calorim 141, 1829–1846 (2020). https://doi.org/10.1007/s10973-020-09604-z

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