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Effects of stretching/shrinking on the thermal performance of a fully wetted convective-radiative longitudinal fin of exponential profile

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Abstract

The present investigation focuses on the thermal performance of a fully wet stretching/shrinking longitudinal fin of exponential profile coated with a mechanism like a conveyer belt. The modeled equation is non-dimensionalized and solved by applying the Runge-Kutta-Fehlberg (RKF) method. The effects of parameters such as the wet parameter, the fin shape parameter, and the stretching/shrinking parameter on the heat transfer and thermal characteristics of the fin are graphically analyzed and discussed. It is inferred that the negative effects of motion and internal heat generation on the fin heat transfer rate can be lessened by setting a shrinking mechanism on the fin surface. The current examination is inclined towards practical applications and is beneficial to the design of fins.

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Abbreviations

A :

thermal conductivity parameter

A(x):

cross-sectional area of the fin, m2

A b :

area of the fin base, m2

T a :

ambient temperature, K

b 2 :

variable parameter, K−1

c p :

specific heat at constant pressure, J/(kg·K)

h D :

uniform mass transfer coefficient

h a :

coefficient of convective heat transfer at Ta, W/(m2·K)

h :

coefficient of convective heat transfer, W/(m2·K)

G :

generation number

k a :

thermal conductivity at Ta, W/(m·K)

k :

thermal conductivity, W/(m·K)

L :

fin length, m

m 0 :

m1, constants

m 2 :

wet parameter

N r :

radiative parameter

Pe :

Peclet number

p :

exponential index of h

Q :

non-dimensional heat transfer rate

\(q_{\rm{a}}^ * \) :

rate of internal heat generation at Ta, W/m3

q*:

rate of internal heat generation, W/m3

q :

base heat transfer rate, W

S :

stretching/shrinking parameter of the fin

s* :

stretching/shrinking rate of the fin, m−1

T :

local fin temperature, K

T b :

base temperature, K

t(x):

fin thickness, m

t b :

base thickness of the fin, m

U :

constant velocity of the fin, m/s

W :

width, m

X :

dimensionless length

x :

axial coordinate of the fin, m.

ω :

humidity ratio of the saturated air

ν :

shape parameter of the fin

α :

measure of thermal conductivity variation with temperature, K−1

ω a :

humidity ratio of the surrounding air

ϵ G :

nondimensional internal heat generation parameter

θ a :

nondimensional ambient temperature

θ :

dimensionless temperature

ε :

surface emissivity of the fin

i fg :

latent heat of water evaporation, J/kg

σ :

Stefan-Boltzmann constant, W/(m2·K4)

ρ :

density of the ambient fluid, kg/m3.

a:

ambient

b:

base.

References

  1. KRAUS, A. D., AZIZ, A., and WELTY, J. R. Extended Surface Heat Transfer, John Wiley, New York (2002)

    Google Scholar 

  2. KIWAN, S. Thermal analysis of natural convection porous fins. Transport in Porous Media, 67(1), 17–29 (2007)

    Article  MathSciNet  Google Scholar 

  3. GORLA, R. S. R. and BAKIER, A. Y. Thermal analysis of natural convection and radiation in porous fins. International Communications in Heat and Mass Transfer, 38(5), 638–645 (2011)

    Article  Google Scholar 

  4. TORABI, M. and AZIZ, A. Thermal performance and efficiency of convective-radiative T-shaped fins with temperature dependent thermal conductivity, heat transfer coefficient and surface emissivity. International Communications in Heat and Mass Transfer, 39(8), 1018–1029 (2012)

    Article  Google Scholar 

  5. VAHABZADEH, A., GANJI, D. D., and ABBASI, M. Analytical investigation of porous pin fins with variable section in fully-wet conditions. Case Studies in Thermal Engineering, 5, 1–12 (2015)

    Article  Google Scholar 

  6. DARVISHI, M. T., KHANI, F., and AZIZ, A. Numerical investigation for a hyperbolic annular fin with temperature dependent thermal conductivity. Propulsion and Power Research, 5(1), 55–62 (2016)

    Article  Google Scholar 

  7. OGUNTALA, G., ABD-ALHAMEED, R., and SOBAMOWO, G. On the effect of magnetic field on thermal performance of convective-radiative fin with temperature-dependent thermal conductivity. Karbala International Journal of Modern Science, 4(1), 1–11 (2018)

    Article  Google Scholar 

  8. HOSEINZADEH, S., MOAFI, A., SHIRKHANI, A., and CHAMKHA, A. J. Numerical validation heat transfer of rectangular cross-section porous fins. Journal of Thermophysics and Heat Transfer, 33(3), 698–704 (2019)

    Article  Google Scholar 

  9. SOWMYA, G., GIREESHA, B. J., KHAN, M. I., MOMANI, S., and HAYAT, T. Thermal investigation of fully wet longitudinal porous fin of functionally graded material. International Journal of Numerical Methods for Heat & Fluid Flow, 30(12), 5087–5101 (2020)

    Article  Google Scholar 

  10. KUNDU, B. and YOOK, S. J. An accurate approach for thermal analysis of porous longitudinal, spine and radial fins with all nonlinearity effects-analytical and unified assessment. Applied Mathematics and Computation, 402, 126124 (2021)

    Article  MathSciNet  Google Scholar 

  11. TURKYILMAZOGLU, M. Thermal management of parabolic pin fin subjected to a uniform oncoming airflow: optimum fin dimensions. Journal of Thermal Analysis and Calorimetry, 143, 3731–3739 (2021)

    Article  Google Scholar 

  12. TURKYILMAZOGLU, M. Expanding/contracting fin of rectangular profile. International Journal of Numerical Methods for Heat and Fluid Flow, 31, 1057–1068 (2021)

    Article  Google Scholar 

  13. TORABI, M., AZIZ, A., and ZHANG, K. A comparative study of longitudinal fins of rectangular, trapezoidal and concave parabolic profiles with multiple nonlinearities. Energy, 51, 243–256 (2013)

    Article  Google Scholar 

  14. TORABI, M. and QIAO, B. Z. Analytical solution for evaluating the thermal performance and efficiency of convective-radiative straight fins with various profiles and considering all non-linearities. Energy Conversion and Management, 66, 199–210 (2013)

    Article  Google Scholar 

  15. HATAMI, M. and GANJI, D. D. Thermal behavior of longitudinal convective-radiative porous fins with different section shapes and ceramic materials (SiC and Si3N4). Ceramics International, 40(5), 6765–6775 (2014)

    Article  Google Scholar 

  16. KUNDU, B. and LEE, K. S. Exact analysis for minimum shape of porous fins under convection and radiation heat exchange with surrounding. International Journal of Heat and Mass Transfer, 81, 439–448 (2015)

    Article  Google Scholar 

  17. KUNDU, B., DAS, R., and LEE, K. S. Differential transform method for thermal analysis of exponential fins under sensible and latent heat transfer. Procedia Engineering, 127, 287–294 (2015)

    Article  Google Scholar 

  18. TURKYILMAZOGLU, M. Heat transfer from moving exponential fins exposed to heat generation. International Journal of Heat and Mass Transfer, 116, 346–351 (2018)

    Article  Google Scholar 

  19. SHARQAWY, M. H. and ZUBAIR, S. M. Efficiency and optimization of straight fins with combined heat and mass transfer — an analytical solution. Applied Thermal Engineering, 28(17–18), 2279–2288 (2008)

    Article  Google Scholar 

  20. HATAMI, M., AHANGAR, G. R. M., GANJI, D. D., and BOUBAKER, K. Refrigeration efficiency analysis for fully wet semi-spherical porous fins. Energy Conversion and Management, 84, 533–540 (2014)

    Article  Google Scholar 

  21. KHANI, F., DARVISHI, M. T., GORLA, R. S. R., and GIREESHA, B. J. Thermal analysis of a fully wet porous radial fin with natural convection and radiation using the spectral collocation method. International Journal of Applied Mechanics and Engineering, 21(2), 377–392 (2016)

    Article  Google Scholar 

  22. SOWMYA, G., GIREESHA, B. J., and BERREHAL, H. An unsteady thermal investigation of a wetted longitudinal porous fin of different profiles. Journal of Thermal Analysis and Calorimetry, 143(3), 2463–2474 (2021)

    Article  Google Scholar 

  23. MA, J., SUN, Y. S., and LI, B. W. Simulation of combined conductive, convective and radiative heat transfer in moving irregular porous fins by spectral element method. International Journal of Thermal Sciences, 118, 475–487 (2017)

    Article  Google Scholar 

  24. GIREESHA, B. J., SOWMYA, G., and MACHA, M. Temperature distribution analysis in a fully wet moving radial porous fin by finite element method. International Journal of Numerical Methods for Heat & Fluid Flow (2019) https://doi.org/10.1108/HFF-12-2018-0744

  25. MOSAYEBIDORCHEH, S., FARZINPOOR, M., and GANJI, D. D. Transient thermal analysis of longitudinal fins with internal heat generation considering temperature-dependent properties and different fin profiles. Energy Conversion and Management, 86, 365–370 (2014)

    Article  Google Scholar 

  26. ALKASASSBEH, M., OMAR, Z., MEBAREK-OUDINA, F., RAZA, J., and CHAMKHA, A. Heat transfer study of convective fin with temperature-dependent internal heat generation by hybrid block method. Heat Transfer-Asian Research, 48(4), 1225–1244 (2019)

    Article  Google Scholar 

  27. TURKYILMAZOGLU, M. Stretching/shrinking longitudinal fins of rectangular profile and heat transfer. Energy Conversion and Management, 91, 199–203 (2015)

    Article  Google Scholar 

  28. MOSAVAT, M., MORADI, R., TAKAMI, M. R., GERDROODBARY, M. B., and GANJI, D. D. Heat transfer study of mechanical face seal and fin by analytical method. Engineering Science and Technology, an International Journal, 21(3), 380–388 (2018)

    Article  Google Scholar 

  29. ROY, P. K., MALLICK, A., MONDAL, H., and SIBANDA, P. A modified decomposition solution of triangular moving fin with multiple variable thermal properties. Arabian Journal for Science and Engineering, 43(3), 1485–1497 (2018)

    Article  Google Scholar 

  30. AZIZ, A. and TORABI, M. Convective-radiative fins with simultaneous variation of thermal conductivity, heat transfer coefficient, and surface emissivity with temperature. Heat Transfer-Asian Research, 41(2), 99–113 (2012)

    Article  Google Scholar 

  31. AZIZ, M. and BOUAZIZ, M. N. A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity. Energy Conversion and Management, 52(8–9), 2876–2882 (2011)

    Article  Google Scholar 

  32. TORABI, M., YAGHOOBI, H., and AZIZ, A. Analytical solution for convective-radiative continuously moving fin with temperature-dependent thermal conductivity. International Journal of Thermophysics, 33(5), 924–941 (2012)

    Article  Google Scholar 

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Acknowledgements

One of the authors (M. L. KEERTHI) acknowledges the University Grants Commission (UGC), New Delhi, India for financial support under the UGC-Junior Research Fellowship (No. CSIR-UGC NET DEC. 2019) (Student ID: 191620111468).

Author information

Authors and Affiliations

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

    B. J. Gireesha & M. L. Keerthi

  2. Department of PG Mathematics, The National College (Auto), Bangalore, 560070, India

    G. Sowmya

Authors
  1. B. J. Gireesha
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  2. M. L. Keerthi
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  3. G. Sowmya
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Corresponding author

Correspondence to B. J. Gireesha.

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Citation: GIREESHA, B. J., KEERTHI, M. L., and SOWMYA, G. Effects of stretching/shrinking on the thermal performance of a fully wetted convective-radiative longitudinal fin of exponential profile. Applied Mathematics and Mechanics (English Edition), 43(3), 389–402 (2022) https://doi.org/10.1007/s10483-022-2836-6

Project supported by the Department of Science and Technology, Government of India (No. SR/FST/MS-I/2018/23(C))

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Gireesha, B.J., Keerthi, M.L. & Sowmya, G. Effects of stretching/shrinking on the thermal performance of a fully wetted convective-radiative longitudinal fin of exponential profile. Appl. Math. Mech.-Engl. Ed. 43, 389–402 (2022). https://doi.org/10.1007/s10483-022-2836-6

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  • DOI: https://doi.org/10.1007/s10483-022-2836-6

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