This work deals with the prediction of unknown parameters and identifying feasible materials for satisfying a given temperature distribution in a rectangular fin geometry involving variable thermal conductivity and surface heat transfer coefficient. The unknown parameters which have been estimated in this work are the thermal conductivity, coefficient of variable conductivity and fin dimensions. For achieving the required objective, an inverse problem is solved by minimization of least squares error using a hybrid evolutionary-nonlinear programming algorithm. Due to correlated nature of the unknowns, many feasible combinations of materials have been found with varying dimensions, which is proposed to offer a wide range of flexibility in selecting the fin material. The present study is proposed to be useful in situations where only few discrete temperatures are available, as it helps to find out feasible materials alongwith relevant dimensions which will yield a prescribed temperature distribution.
KernQDKrausD.A. Extended surface heat transfer, New York, NY: McGraw-Hill, 1972.
2.
DuffinRJ. A variational problem relating to cooling fins. J Math Mech1959; 8: 47–56.
3.
HajmohammadiMRNourazarSSManeshAH. Semi-analytical treatments of conjugate heat transfer. Proc IMechE, Part C: J Mechanical Engineering Science2013; 227: 492–503.
4.
LiawSPYehRH. Fins with surface dependent surface heat flux-I: single heat transfer mode. Int J Heat Mass Transfer1994; 37: 1509–1515.
5.
Dul'kinINGaras'koGI. Analytical solutions of 1D heat conduction problem for a single fin with temperature dependent heat transfer coefficient-I: closed-form inverse solution. Int J Heat Mass Transfer2002; 45: 1895–1903.
6.
SalimpourMRSharifiFMenbariD. Constructal design for cooling a disc-shaped body using incomplete inserts with temperature temperature-dependent thermal conductivities. Proc IMechE, Part E: J Process Mechanical Engineering2011; 227: 231–242.
7.
HajmohammadiMRNourazarSS. Conjugate forced convection heat transfer from a heated flat plate of finite thickness and temperature-dependent thermal conductivity. Heat Transfer Eng2014; 35: 863–874.
8.
KimSHuangCH. A series solution of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. J Phys D Appl Phys2007; 40: 2979–2987.
9.
KhaniFRajiMANejadHH. Analytical solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. Commun Nonlinear Sci Numer Simulat2009; 14: 3327–3338.
10.
HajmohammadiMRPoozeshSHosseiniR. Radiation effect on constructal design analysis of a T-Y-shaped assembly of fins. J Thermal Sci Technol2012; 7: 1463–1469.
11.
HajmohammadiMRPoozeshSNourazarSS. Constructal design of multiple heat sources in a square-shaped fin. Proc IMechE, Part E: J Process Mechanical Engineering2012; 226: 324–336.
12.
BeckJVLitkouhiBClairCSJr.. Efficient sequential solution of the nonlinear inverse heat conduction problem. Numer Heat Transfer A Appl1982; 5: 275–286.
13.
MoreauPLochegniesDOudinJ. An inverse method for prediction of the required temperature distribution in the creep forming process. Proc IMechE, Part E: J Process Mechanical Engineering1998; 212: 7–11.
14.
OzisikMNOrlandeHRB. Inverse heat transfer: fundamentals and applications, New York, NY: CRC Press, 2000.
15.
DasROoiKT. Predicting multiple combination of parameters for designing a porous fin subjected to a given temperature requirement. Energy Convers Manage2013; 66: 211–219.
16.
DasRMallickAOoiKT. A fin design employing an inverse approach using simplex search method. Heat Mass Transfer2013; 49: 1029–1038.
17.
KarlekarBVChaoBT. Mass minimization of radiating trapezoidal fins with negligible base cylinder interaction. Int J Heat Mass Transfer1963; 6: 33–48.
18.
AlebrahimABejanA. Constructal trees of circular fins for conductive and convective heat transfer. Int J Heat Mass Transfer1999; 42: 3585–3597.
19.
AlmogbelMBejanA. Cylindrical trees of pin fins. Int J Heat Mass Transfer2000; 43: 4285–4297.
20.
LorenziniGRochaLAO. Geometric optimization of TY-shaped cavity according to constructal design. Int J Heat Mass Transfer2009; 52: 4683–4688.
21.
PouzeshAHajmohammadiMRPoozeshS. Investigations on the internal shape of constructal cavities intruding a heat generating body. Thermal Sci. Epub ahead of print 2012. DOI: 10.2298/TSCI120427164P.
22.
HajmohammadiMRPoozeshSCampoA. Valuable reconsideration in the constructal design of cavities. Energy Convers Manage2013; 66: 33–40.
23.
HajmohammadiMRAlizadeh AbianehVMoezzinajafabadiM. Fork-shaped highly conductive pathways for maximum cooling in a heat generating piece. Appl Thermal Eng2013; 61: 228–235.
24.
HajmohammadiMRJoneydi ShariatzadehOMoulodM. Phi and Psi shaped conductive routes for improved cooling in a heat generating piece. Int J Thermal Sci2014; 77: 66–74.
25.
BanimRSBrettPNTierneyMJ. Application of inverse methods to temperature measurement in internal mixtures. Proc IMechE, Part E: J Process Mechanical Engineering2003; 217: 295–306.
26.
LeeHLChouHMYangYC. The function estimation in predicting heat flux of pin fins with variable heat transfer coefficients. Energy Convers Manage2004; 45: 1749–1758.
27.
Bello-OchendeTMeyerJPBejanA. Constructal multi-scale pin–fins. Int J Heat Mass Transfer2010; 53: 2773–2779.
28.
KunduBBhanjaD. Performance and optimization analysis of a constructal T-shaped fin subject to variable thermal conductivity and convective heat transfer coefficient. Int J Heat Mass Transfer2010; 53: 254–267.
29.
DasROoiKT. Application of simulated annealing in a rectangular fin with variable heat transfer coefficient. Inverse Probl Sci Eng2013; 21: 1352–1367.
30.
HajmohammadiMRPoozeshSNourazarSS. Optimal architecture of heat generating pieces in a fin. J Mech Sci Technol2013; 27: 1143–1149.
31.
SinglaRKDasRBhowmikA. Inverse heat transfer analysis of porous extended surface using simplex search method. In: ASME 2013 gas turbine India conference (GTINDIA2013), Bangalore, India, 05 December–06 December 2013, Paper no. GTINDIA2013-3548, DOI: 10.1115/GTINDIA2013-3548.
32.
BhowmikASinglaRKRoyPK. Predicting geometry of rectangular and hyperbolic fin profiles with temperature-dependent thermal properties using decomposition and evolutionary methods. Energy Convers Manage2013; 74: 535–547.
33.
FainekosGEGiannakoglouKC. Inverse design of airfoils based on a novel formulation of the ant colony optimization method. Inverse Probl Sci Eng2003; 11: 21–38.
34.
LiuFB. A modified genetic algorithm for solving the inverse heat transfer problem of estimating plan heat source. Int J Heat Mass Transfer2008; 51: 3745–3752.
35.
ChopadeRPAgnihotriESinghAK. Application of a particle swarm algorithm for parameter retrieval in a transient conduction-radiation problem. Numer Heat Transfer A Appl2011; 59: 672–692.
36.
StornRPriceK. Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Global Optimization1997; 11: 341–359.
37.
ChopadeRPMohanVMayankR. Simultaneous retrieval of parameters in a transient conduction-radiation problem using a differential evolution algorithm. Numer Heat Transfer A Appl2013; 63: 373–395.
38.
Ouyang A, Zhou Y and Luo Q. Hybrid particle swarm optimization algorithm for solving systems of nonlinear equations. In: Proceedings of the I.E.E.E. international conference on granular computing, (GRC'09), Nanchang, China, 17–19 August 2009, pp.460–465. DOI: 10.1109/GRC.2009.5255079.
