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Multi-objective Shape and Flow Optimization of Finned Double-Tube Heat Exchanger Filled with Nanofluid: A CFD and RSM Study

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Abstract

In the present study, the thermal attributes and hydrodynamic characteristics of a finned double-tube heat exchanger involving six design variables (\(\mathrm{Re}, (\frac{H}{D}),(\frac{p}{D}),(\frac{t}{D}),{\varnothing }_{p},(\frac{{T}_{c}}{{T}_{h}}))\) were numerically investigated and optimized by simultaneous use of computational fluid dynamics and response surface methodology. Ninety numerical designs proposed based on the face-centered central composite design (FCCD) technique were utilized to generate mathematical regression models of response functions. The accuracy and reliability of the obtained regression models including \({\eta }_{\left(t-h\right)}, {\eta }_{\mathrm{II}}, \frac{\mathrm{Nu}}{{\mathrm{Nu}}_{s}}\) and \(\Delta p\) were investigated through analysis of variance (ANOVA). Furthermore, the significance of model terms was also analyzed by considering F values larger than the critical F value for each response functions and a P value smaller than the selected level of significance (i.e. 0.05). Multi-objective shape and flow optimization of the finned double-tube counter-flow heat exchanger was carried out using the composite desirability function approach to maximize the thermo-hydrodynamic performance index, exergetic efficiency and Nusselt number and to minimize the pressure drop across the heat exchanger. The optimum design variables resulting in the highest desirability function (i.e. 0.8886) were found to be \(\mathrm{Re}=4000,(\frac{H}{D})=0.154, (\frac{p}{D})=9.840, (\frac{t}{D})=8.610, {\varnothing }_{p}=0\%, ( \frac{{T}_{c}}{{T}_{h}})= 0.968\), which correspond to the maximum predicted value of \({\eta }_{(t-h)}=1.193, {\eta }_{\mathrm{II}}=8.367\%, \frac{\text{Nu}}{{\mathrm{Nu}}_{s}}=1.771,\Delta p=7461.1 (\mathrm{Pa})\). The value of \({\eta }_{(t-h)}\) can be further increased up to 1.261 where the composite desirability function reaches to 0.8514.

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Abbreviations

A :

Heat transfer surface area (m2)

C 2 :

Model constant

C p :

Specific heat at constant pressure (J/kg K)

C µ :

Model parameter

D i :

Inner tube diameter (m)

D o :

Outer tube diameter (m)

D h :

Hydraulic diameter (m)

f :

Friction factor

h :

Heat transfer coefficient (W/m2 K), fin height (m)

H:

Fin height (m)

k :

Turbulent kinetic energy (m2/s2), thermal conductivity (W/mK)

L :

Length of tube (m)

\(\dot{m}\) :

Mass flow rate (kg/s)

Nu:

Nusselt number \((hD_{{\text{h}}} /{\mathrm{K}})\)

p :

Pressure Pa, Fin pitch (m)

Pr:

Prandtl number \(\left( {C_{{\text{p}}} \mu /{\mathrm{K}}} \right)\)

q :

Heat flux (W/m2)

Q :

Heat transfer rate (W)

Re:

Reynolds number \(\left( {\rho uD_{h} /\mu } \right)\)

s :

Specific entropy (J/K)

t :

Fin thickness (m)

T :

Temperature (K)

u :

Velocity component in flow direction (m/s)

W :

Work (J)

\(Y^{+}\) :

Dimensionless distance from wall

Δ:

Difference operator

\(\delta_{ij}\) :

Kronecker delta

\(\varepsilon\) :

Turbulent energy dissipation rate (m2/s3)

\(\mu\) :

Dynamic viscosity (kg/m s)

\(\nu\) :

Kinematic viscosity (m2/s)

\(\rho\) :

Density (kg/m3)

\(\alpha\) :

Thermal diffusivity (m2/s)

\(\nu\) :

Kinematic viscosity (m2/s), Specific volume (1/m3)

\(\sigma_{\tau }\) :

Turbulent Prandtl number in energy equation

\(\sigma_{k}\) :

Diffusion Prandtl number for \(k\)

\(\sigma_{\varepsilon }\) :

Diffusion Prandtl number for \(\varepsilon\)

\(\emptyset\) :

Nanoparticle volume concentration

\(\psi\) :

Specific flow exergy

\(\dot{X}\) :

Exergy rate

\(\eta_{\text{II}}\) :

Second-law efficiency

\(\eta_{t - h}\) :

Thermo-hydrodynamic performance index

Avg:

Average

hw:

Hot water

b:

Bulk quantity

bf:

Base fluid

fr:

Freezing

in:

Inlet

IT:

Inner tube

i, j, k :

Spatial indices

l:

Laminar property

m:

Mean value

nf:

Nanofluid

out:

Outlet

p:

Nanoparticle

s:

Smooth, surface area

t:

Turbulent quantity

t-h:

Thermo-hydrodynamic

w:

Wall

CFD:

Computational fluid dynamics

DTCHEX:

Double-tube counter-flow heat exchanger

RSM:

Response surface methodology

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  1. Department of Mechanical Engineering, Islamic Azad University-Nour Branch, Nour, Iran

    Morteza Mohammadi

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  1. Morteza Mohammadi
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Mohammadi, M. Multi-objective Shape and Flow Optimization of Finned Double-Tube Heat Exchanger Filled with Nanofluid: A CFD and RSM Study. Iran J Sci Technol Trans Mech Eng 48, 1–27 (2024). https://doi.org/10.1007/s40997-023-00641-1

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