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Effect of Reynolds asymmetry and use of porous media in the counterflow double-pipe heat exchanger for passive heat transfer enhancement

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In order to enhance the heat transfer in a double-pipe counterflow heat exchanger, the use of porous media and nanofluid is analyzed. The effect of complete filling of one or both channels of the heat exchanger with porous metal foams on the heat transfer and pumping power has been studied, considering laminar flow with various Reynolds numbers (Re = 100 to 2000) and porous media (Da = 0.1 to 10−4). As a novelty, in order to select proper porous media with an appropriate Reynolds number in each channel, this study focused on the coupling of Re asymmetry and porous medium properties used in the inner and outer channels of the heat exchanger. Flow through porous media is simulated by the non-Darcy law and two-phase mixture model used for the nanofluid flow. Results are presented and investigated in terms of the effectiveness (ε-NTU method) and the performance evaluation criterion (PEC). It is shown that the effectiveness could only depict the thermal performance, while the PEC reflects the influences of the porous media on both the pumping power and the heat transfer. Use of porous media in both channels (case D) has led to the highest effectiveness (between 0.6 and 1). In addition, PEC study reveals that the optimal Re values exist for flow in each one of the channels and that case D has the highest PEC (more than 4). To maximize the PEC, for the cases with only one porous channel (B and C), the channel which does not include porous media should have the highest Re, while a low or moderate Re should be selected for the porous channel. However, for case D, Rei should have its highest value, while Reo has an optimal value in the range of 500 to 1000.

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C d :

Drag coefficient

C p :

Specific heat at constant pressure

D :

Diameter (m)

D h :

Hydraulic diameter (m)

D np :

Nanoparticles diameter (nm)


Darcy number

\(f_{\text{drag}}\) :

Drag function

F p :

Drag force induced by porous (N)

g :

Acceleration due to gravity (ms−2)

k :

Thermal conductivity (Wm−1 K−1)

K :

Permeability of porous medium (m2)


Number of transfer units

p :

Pressure (Pa)


Performance evaluation criterion

\(\dot{Q}\) :

Heat transfer rate (W)


Reynolds number

T :

Temperature (K)

u m :

Mixture velocity (ms−1)

U :

Velocity (ms−1)

ε :


ε p :


φ :

Nanoparticles volume fraction

ϕ :

Phase volume fraction

μ :

Dynamic viscosity (kg m−1 s−1)

ρ :

Density (kg m−3)


Base configuration


Base fluid


Cold fluid






Hot fluid










Porous region


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Miri Joibary, S.M., Siavashi, M. Effect of Reynolds asymmetry and use of porous media in the counterflow double-pipe heat exchanger for passive heat transfer enhancement. J Therm Anal Calorim 140, 1079–1093 (2020).

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