A Parametric Study of Functionally Graded Variable Thickness Longitudinal Fin Under Fully Wet Condition

  • Upendra Bajpai
  • Vivek Kumar GabaEmail author
  • Shubhankar Bhowmick
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


Thermal analysis and comparison of the functionally graded longitudinal fin, having a different profile with an insulated tip in fully wet condition, are reported in the present work. In many air-conditioning and refrigeration equipments, the performance of the cooling coil is affected due to vapor condensation on its surface. In this work, the thermal conductivity of the longitudinal fin is varied with exponential law. For analysis and comparison of a fin having different profiles, their weight is assumed to be constant. With the help of the psychometric chart, a nonlinear cubic polynomial relationship is established between specific humidity and corresponding fin surface temperature. Considering a volume element of fin under steady state, energy balance concept is used to derive nonlinear differential heat transfer equation. This differential equation is solved using bvp4c command in MATLAB®. This technique is very useful to solve boundary value problems by collocation method. Further for a different combination of grading parameters, geometry parameters, and relative humidity, a differential equation is solved and results are shown in graphical form. The formulation is verified with standard results, and relative error obtained between these two results is negligible. These results give a better understanding of the thermal performance of functionally graded longitudinal wet fin, and generated data can be used for design purpose.


Functionally graded Longitudinal fin Fully wet 


  1. 1.
    Kuehn TH, Ramsey JW, Threlkeld JL (1998) Thermal environmental engineering, 3rd edn. Prentice-Hall Inc., Upper Saddle River, New JerseyGoogle Scholar
  2. 2.
    McQuiston FC (1975) Fin efficiency with combined heat and mass transfer. ASHRAE Trans 81(1):350–355Google Scholar
  3. 3.
    Chilton TH, Colburn AP (1934) Mass transfer (absorption) coefficients. Ind Eng Chem 26:1183–1187CrossRefGoogle Scholar
  4. 4.
    Elmahdy AH, Biggs RC (1983) Efficiency of extended surfaces with simultaneous heat and mass transfer. ASHRAE Trans 89:135–143Google Scholar
  5. 5.
    Coney JE, Sheppard CG, El-Shafei EA (1989) Fin performance with condensation from humid air: a numerical investigation. Int J Heat Fluid Flow 10:224–231CrossRefGoogle Scholar
  6. 6.
    Wu G, Bong TY (1994) Overall efficiency of a straight fin with combined heat and mass transfer. ASHRAE Trans 100(1):367–374Google Scholar
  7. 7.
    Lin YT, Hsu KC, Chang YJ (2001) Performance of rectangular fin in wet conditions: visualization and wet fin efficiency. ASME J Heat Transf 123:827–836CrossRefGoogle Scholar
  8. 8.
    Xu X, Xia L, Chan M, Deng S (2008) A modified McQuiston model for evaluating efficiency of wet fin considering effect of condensate film moving on fin surface. Energy Convers Manag 49:2403–2408CrossRefGoogle Scholar
  9. 9.
    Kundu B (2007) Performance and optimum design analysis of longitudinal and pin fin with simultaneous heat and mass transfer: unified and comparative investigation. Appl Therm Eng 27:976–987CrossRefGoogle Scholar
  10. 10.
    Kundu B (2009) Approximate analytic solution for performances of wet fin with a polynomial relationship between humidity ratio and temperature. Int J Therm Sci 48:2108–2118CrossRefGoogle Scholar
  11. 11.
    Sharqawy MH, Zubair SM (2011) Efficiency and optimization of straight rectangular fin with combined heat and mass transfer. Heat Transf Eng 29:1018–1026CrossRefGoogle Scholar
  12. 12.
    Gaba VK, Bhowmick S, Tiwari AK (2014) Thermal performance of functionally graded parabolic annular fins having constant weight. J Mech Sci Technol 28:4309–4318CrossRefGoogle Scholar
  13. 13.
    Udupa G, Rao SS, Gangadharan KV (2014) Functionally graded composite materials: an overview. Proc Mater Sci 5:1291–1299CrossRefGoogle Scholar
  14. 14.
    Bhavar V, Kattire P, Thakare S, Patil S, Singh RKP (2017) A review on functionally gradient materials (FGMs) and their applications. Mater Sci Eng 229Google Scholar
  15. 15.
    Subramaniam SK, Gaba VK, Bhowmick S (2018) Temperature distribution in functionally graded longitudinal fins of varying geometry. In: Hierarchical composite materials, 1st edn, pp 90–97Google Scholar
  16. 16.
    Shampine LF, Reichelt MW, Kierzenka J (2010) Solving boundary value problems for ordinary differential equations in Matlab with bvp4c.

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Upendra Bajpai
    • 1
  • Vivek Kumar Gaba
    • 1
    Email author
  • Shubhankar Bhowmick
    • 1
  1. 1.Department of Mechanical EngineeringNational Institute of Technology, RaipurRaipurIndia

Personalised recommendations