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Effect of elliptical dimples on heat transfer performance in a shell and tube heat exchanger

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Abstract

The numerical simulation of a shell-and-tube heat exchanger (STHE) depends on a large number of computational cells. The number of computational cells increases dramatically with increasing heat transfer surfaces in heat exchangers, such as increasing the number of tubes or using dimples as modified surfaces. Computational cost is one of the critical parameters in many industrial applications for heat exchanger analysis. The present study uses the P-NTU thermal analysis method, proposes correlations to predict heat transfer inside and outside the tubes, and then analyzes the STHE with elliptical dimples. The analytical approach shows 0.8% and 9% errors for two STHEs with specified heat performance, which is entirely acceptable. Also, for the STHE with elliptical dimples, the results indicate a 40.6% increase in the heat capacity of STHE. Increasing the heat capacity of STHE by using modified surfaces such as dimples significantly reduces the dimensions and weight of STHE in industrial applications. Furthermore, the analytical method can be used for different types of dimples with different geometries and arrangements.

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Abbreviations

A :

elliptic minor axis (m)

a :

constant (dimensionless)

A c :

Cross section area (\({\mathrm{m}}^{2})\)

B :

elliptic major axis (m)

b :

constant (dimensionless)

C :

Heat capacity (kJ/K)

C c :

clearance (m)

C p :

specific heat capacity (kJ/kg.K)

D :

diameter (m)

d :

constant (dimensionless)

G k :

production of turbulent kinetic energy

G ω :

generation of ω

H :

depth (m)

h :

heat transfer coefficient (W/m2.K)

K :

conductivity (W/m.K)

LMTD :

Log Mean Temperature Difference

L bi :

inlet baffle spacing (m)

L bo :

outlet baffle spacing (m)

L tp :

tube pitch (m)

N b :

Baffles number

N p :

number of tube passes

N t :

number of tubes

P :

dimple longitudinal pitch (m)

q” :

heat flux (W/m2)

R t :

The ratio of tube side to shell side heat capacity

S :

distance

T :

Temperature (K)

t :

Time (s)

U :

Overall heat transfer coefficient (W/\({\mathrm{m}}^{2}\) K)

u :

Velocity (m/s)

Y k :

Dissipation of k

Y ω :

Dissipation of \(\upomega\)

Γ :

Production of turbulent kinetic energy

\({\delta }_{ij}\) :

Kronecker delta

\(\varepsilon\) :

Turbulent dissipation rate (\({\mathrm{m}}^{2}/{\mathrm{s}}^{3}\))

μ :

Velocity (m/s)

\(\nu\) :

Kinematic viscosity (\({\mathrm{m}}^{2}/\mathrm{s})\)

\(\rho\) :

Dynamic viscosity (kg/m.s)

\(\tau\) :

Stress tensor (kg/m.\({s}^{2}\))

\(\omega\) :

Specific rate of dissipation (1/s)

\({\sigma }_{\varepsilon }\) :

constant

\({\sigma }_{k}\) :

constant

e :

equivalent

i :

inlet

o :

outlet

\(s\) :

shell

\(t\) :

tube

\(tu\) :

turbulence

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Funding

This work has been funded by ANID/FONDAP 15110019 SERC-Chile project.

Author information

Authors and Affiliations

  1. Independent Researcher, Tehran, Iran

    Seyed Ali Abtahi Mehrjardi

  2. Department of Mechanical Engineering, York University, Toronto, ON, Canada

    Alireza Khademi

  3. Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Alireza Khademi

  4. Sustainable Energy Development Research Group, College of Engineering, University of Sharjah, Sharjah, United Arab Emirates

    Zafar Said

  5. U.S.-Pakistan Center for Advanced Studies in Energy (USPCAS-E), National University of Sciences and Technology (NUST), Islamabad, Pakistan

    Zafar Said

  6. Department of Industrial and Mechanical Engineering, Lebanese American University (LAU), Byblos, Lebanon

    Zafar Said

  7. Center for Advanced Study of Lithium and Industrial Minerals (CELiMIN) and Departamento de Ingeniería Química y Procesos de Minerales, Universidad de Antofagasta, Campus Coloso, Av. Universidad de Antofagasta, 02800, Antofagasta, Chile

    Svetlana Ushak

  8. Faculty of Engineering, Kuwait College of Science and Technology, Doha District, 35004, Kuwait

    Ali J. Chamkha

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  1. Seyed Ali Abtahi Mehrjardi
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Correspondence to Alireza Khademi.

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Mehrjardi, S.A.A., Khademi, A., Said, Z. et al. Effect of elliptical dimples on heat transfer performance in a shell and tube heat exchanger. Heat Mass Transfer 59, 1781–1791 (2023). https://doi.org/10.1007/s00231-023-03367-7

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