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Impact of trihybrid nanofluid on the transient thermal performance of inclined dovetail fin with emphasis on internal heat generation

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Abstract

The current study focuses on examining the transient thermal performance of a dovetail fin structure that is completely immersed in a trihybrid nanofluid and is formulated by the combination of \({\text{MWCNT}}, {\text{Ag}}\), and \({\text{Cu}}\) nanoparticles with the hybrid base fluid \({{\text{C}}}_{2}{{\text{H}}}_{6}{{\text{O}}}_{2}-{{\text{H}}}_{2}{\text{O}}.\) The fin's porous medium is modelled using Darcy's law to simulate the interaction between the fluid and the solid. The resulting nonlinear partial differential equation is converted into a non-dimensional form and resolved using the finite difference method (FDM) to understand the physical implications of the model. Factors like surface convection \(({\text{Nc}})\), radiation \(({\text{Nr}})\) and internally generated heat \((Q)\) have been considered in assessing the fin's heat exchange. This investigation highlights the impact of variables such as tip tapering, dimensionless time, inclination angle, full wet condition, porosity, internal heat generation, and ambient temperature on the fin's thermal profile. The efficiency of the fin structure is graphically explored and discussed. Compared to mono and binary hybrid nanofluids, the trihybrid nanofluid demonstrates superior thermal response and notably the introduction of the trihybrid nanofluid significantly enhances the fin's efficiency. Dovetail fin conjunction with the trihybrid nanofluid provides superior heat transfer rate because increase in the surface area is the major finding of this study. These findings are crucial for improving heat transfer in various industrial settings. Moreover, this advancement holds the potential to revolutionize cooling and heating processes in sectors like automotive and aerospace engineering.

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Data Availability Statement

This manuscript has associated data in a data repository. [Author’s comment: All data included in this manuscript are available upon request by contacting with the corresponding author.]

Abbreviations

\({C}_{{\text{p}}}\) :

Specific heat at constant pressure \(({\text{J}}/\mathrm{kg K})\)

\(K\) :

Permeability \(({{\text{m}}}^{2})\)

\(L\) :

Length of the fin \(({\text{m}})\)

\(C\) :

Fin taper ratio

\({\text{Le}}\) :

Lewis number

\(G\) :

Generation parameter

\(M\) :

Thermogeometric parameter

\({\text{Nc}}\) :

Convection parameter

\({\text{Nr}}\) :

Radiative parameter

\(T\) :

Local fin temperature \(({\text{K}})\)

\({T}_{{\text{a}}}\) :

Ambient temperature \(({\text{K}})\)

\({T}_{{\text{b}}}\) :

Base temperature \(({\text{K}})\)

\(X\) :

Dimensionless length

\({b}_{2}\) :

Variable parameter \((1/{\text{K}})\)

\(g\) :

Acceleration due to gravity \(({\text{m}}/{{\text{s}}}^{2})\)

\(h\) :

Heat transfer coefficient \(({\text{W}}/{{\text{m}}}^{2}{\text{K}})\)

\({h}_{{\text{a}}}\) :

Heat transfer coefficient at temperature \({T}_{{\text{a}}}({\text{W}}/{{\text{m}}}^{2}{\text{K}})\)

\({h}_{{\text{D}}}\) :

Uniform mass transfer co efficient \(({\text{kg}}/{{\text{m}}}^{2}{\text{s}})\)

\({i}_{fg}\) :

Latent heat of water evaporation \(({\text{J}}/{\text{kg}})\)

\(k\) :

Thermal conductivity \(({\text{J}}/{\text{kg}})\)

\({n}_{1}\) :

Wet parameter

\(p\) :

Power index of temperature dependent \(h\)

\({t}^{*}\) :

Time \(({\text{s}})\)

\({q}^{*}\) :

Internal rate of heat generation \(({\text{W}}/{{\text{m}}}^{3})\)

\({q}_{{\text{a}}}^{*}\) :

Internal rate of heat generation at temperature \({T}_{{\text{a}}}({\text{W}}/{{\text{m}}}^{3})\)

\(t\left(x\right)\) :

Fin thickness at distance \(x(m)\)

\({t}_{{\text{b}}}\) :

Fin base thickness \(({\text{m}})\)

\(W\) :

Width \(({\text{m}})\)

\(\rho \) :

Density \(({\text{kg}}/{{\text{m}}}^{3})\)

\(\mu \) :

Dynamic viscosity \(({\text{kg}}/{\text{ms}})\)

\(\tau \) :

Dimensionless time

\(\alpha \) :

Angle of inclination

\({\epsilon }_{{\text{g}}}\) :

Internal heat generation parameter \((1/{\text{K}})\)

\({\epsilon }_{{\text{G}}}\) :

Non-dimensional internal heat generation parameter

\(\nu \) :

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

\(\theta \) :

Non-dimensional temperature

\({\theta }_{{\text{a}}}\) :

Dimensionless ambient temperature

\(\omega \) :

Humidity ratio of saturated air

\({\omega }_{{\text{a}}}\) :

Humidity ratio is surrounding air

\(\phi \) :

Solid volume fraction of nanoparticles

\(\varphi \) :

Porosity

\(\delta \) :

A geometrical quantity that defines the tip semi fin thickness \(({\text{m}})\)

\(\sigma \) :

Stefan–Boltzmann constant \(({\text{W}}/{{\text{m}}}^{2}{{\text{K}}}^{4})\)

\(\epsilon \) :

Surface emissivity of fin

\(\beta \) :

Volumetric thermal expansion: coefficient \((1/{\text{K}})\)

\({\text{a}}\) :

Ambient

\({\text{b}}\) :

Fin base

\({\text{f}}\) :

Fluid

\({\text{nf}}\) :

Nanofluid

\({\text{hnf}}\) :

Hybrid nanofluid

\({\text{thnf}}\) :

Trihybrid nanofluid

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Acknowledgements

The authors are thankful to the Department of Science and Technology, Government of India, for financing, as part of the DST-FIST venture for HEIs (Grant No. SR/FST/MS-I/2018/23(C)).

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Authors and Affiliations

  1. Department of PG Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, Shivamogga, Karnataka, 577451, India

    P. L. Pavan Kumar & B. J. Gireesha

  2. Department of Mathematics, Sahyadri Science College, Shimoga, Kuvempu University, Jnana Sahyadri, Shankaraghatta, Karnataka, India

    P. Venkatesh

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Contributions

PLPK contributed to conceptualization, methodology, software, writing—original draft, writing—review and editing. BJG contributed to conceptualization, methodology, writing—review and editing, supervision. PV contributed to conceptualization, methodology, software, writing—review and editing.

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Correspondence to B. J. Gireesha.

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Pavan Kumar, P.L., Gireesha, B.J. & Venkatesh, P. Impact of trihybrid nanofluid on the transient thermal performance of inclined dovetail fin with emphasis on internal heat generation. Eur. Phys. J. Plus 139, 60 (2024). https://doi.org/10.1140/epjp/s13360-023-04848-8

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