Parametric analysis and optimization of convective fin with variable thermal conductivity using semi-analytical solution

Parametric analysis and optimization of convective fin with variable thermal conductivity using semi-analytical solution

Vadivelu M. ArumugamRamesh K. Chidambaram 

Automotive Research Center, Department of Automotive Engineering, School of Mechanical Engineering, VIT University, Vellore 632014, India

Corresponding Author Email: 
vadivelu.m.arumugam@gmail.com
Page: 
677-686
|
DOI: 
https://doi.org/10.18280/ijht.360233
Received: 
6 October 2017
| |
Accepted: 
27 March 2018
| | Citation

OPEN ACCESS

Abstract: 

Due to the temperature dependent properties, evaluation of heat transfer performance parameters of a polymer composite material through experimentation is difficult as it needs sophisticated measurement techniques. In this article, to meet the current requirements, a simple semi-analytical method is proposed to investigate the performance of convective straight fins with temperature dependent thermal conductivity. The Adomian Decomposition Method (ADM) was adopted to solve the non-linear energy equation and Newton-Raphson method was used for optimization of the fin problem. After the analysis, the effect of convective-geometric fin parameter and thermal conductivity parameter is introduced in this problem to interpret the physical significance of such parameters. A parametric analysis was carried out to depict the dependency of heat transfer phenomena on various parameters. The informative plot on the gradient field of the fin efficiency negotiates the direction of maximum performance.

Keywords: 

heat transfer performance, temperature dependent thermal conductivity, straight fins, ADM, optimization and parametric analysis

1. Introduction
2. Mathematical Model and Assumptions
3. Decomposition Method for Nonlinear Equation
4. Parametric Temperature Distribution
5. Performance Analysis and Optimization
6. Results and Discussion
7. Conclusion
Nomenclature
  References

[1] Incropera FP, Dewitt DP. (1996). Introduction to Heat Transfer. Third ed., Wiley, New York.

[2] Kraus AD. (1972). Extended Surface Heat Transfer. McGraw-Hill, New York.

[3] Grimvall G. (1999). Thermophysical properties of materials. Elsevier.

[4] Choi S, Kim J. (2013). Thermal conductivity of epoxy composites with a binary-particle system of aluminum oxide and aluminum nitride fillers. Compos. Part B Eng. 51: 140–147. https://doi.org/10.1016/j.compositesb.2013.03.002

[5] Bigg D, Stickford G, Talbert S. (1989). Applications of polymeric materials for condensing heat exchangers. Polymeric Engineering and Science 29: 1111–1116. https://doi.org/10.1002/pen.760291607 

[6] Vadivelu MA, Ramesh Kumar C, Girish MJ. (2016). Polymer composites for thermal management: A review. Composite Interfaces 847-872. http://dx.doi.org/10.1080/09276440.2016.1176853

[7] Hung HM, Appl FC. (1967). Heat transfer of thin fins with temperature dependent thermal properties and internal heat generation. ASME J Heat Transfer 89: 155-161. https://dx.doi.org/10.1115/1.3614342

[8] Unal HC. (1986). Determination of the temperature distribution in an extended surface with a non-uniform heat transfer coefficient. Int J Heat Mass Transfer 28: 2279-84. https://doi.org/10.1016/0017-9310(85)90046-8

[9] Meyer GE. (1971). Analytical Methods in Heat Conduction, McGraw-Hill, New York.

[10] Muzzio A. (1976). Approximate solution for convective fins with variable thermal conductivity. J Heat Transfer Trans. ASME 98: 680-682. https://doi.org/10.1115/1.3450623

[11] Thongmoon M, Pusjuso S. (2010). The numerical solutions of differential transform method and Laplace method for a system of differential equations. Nonlinear Analysis: Hybrid Systems 4: 425-431. https://doi.org/10.1016/j.nahs.2009.10.006

[12] Ozkan O. (2010). Numerical implementation of differential transformations method for integro-differential equations. International Journal of Computer Mathematics 87: 2786-2797. https://doi.org/10.1080/00207160902795627

[13] Bert CW. (2002). Application of differential transform method to heat conduction in tapered fins. ASME Journal of Heat Transfer 124: 208-209. https://doi.org/10.1115/1.1423316

[14] Chu HP, Lo CY. (2008). Application of the hybrid differential transform-finite difference method to nonlinear transient heat conduction problem. Numerical Heat Transfer Part A 53: 295-307. Https://dx.doi.org/10.1080/10407780701557931

[15] Jang MJ, Chen CL, Liu YC. (2001). Two-dimensional differential transform for partial differential equations. Appl. Math. Comput. 121: 261-270. https://doi.org/10.1016/S0096-3003(99)00293-3

[16] Adomian G. (1988). A review of the decomposition method in applied mathematics. J. Math. Anal. Applications 135(2): 501-544. https://doi.org/10.1016/0022-247X(88)90170-9

[17] Adomian G. (1994). Solving Frontier Problems in Physics: The Decomposition Method. Kluwer Academic Publisher, Dordrecht.

[18] Adomian G. (1985). On the solution of algebraic by the decomposition method. J. Math. Anal. Applications 105(1): 141-166. https://doi.org/10.1016/0022-247X(85)90102-7

[19] Adomian G. (1988). Nonlinear stochastic system theory and application to physics. Kluwer Academic Publisher, Dordrecht.

[20] Adomian G. (1991). Solving frontier problems modeled by nonlinear partial differential equations. Comput. Math. Appl. 22(8): 91-94. https://doi.org/10.1016/0898-1221(91)90017-X

[21] Shih TM. (1984). In: Numerical Heat Transfer. Springer, New York.