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### Nonlinear and Transient Heat Transfer in the Fin by a Truly Meshless Method

#### Affiliations

• SOE, Gautam Buddha University, Greater Noida – 201312, Uttar Pradesh, India
• Rajasthan Technical University, Kota – 324009, Rajasthan, India

#### Abstract

In this article, Meshless Local Petrov- Galerkin (MLPG) method is used to solve the nonlinear and transient one- dimensional heat transfer equation of a fin with the power- law temperature- dependent heat transfer coefficient. Moving least square approximants are used to approximate the unknown function of temperature T(x) with Th (x). These approximants are constructed by using a linear basis, a weight function and a set of non- constant coefficients. Essential boundary conditions are enforced by direct method of interpolation and Penalty Method (PM) respectively. Temperature variation along the fin length over the different time range till the attainment of steady state has been demonstrated for the convective and insulated tip conditions.

#### Keywords

Convective Tip, Direct Method, Fins, Insulated Tip, Meshless Local Petrov-Galerkin (MLPG) Method, Penalty method, Transient

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#### References

• Atluri SN, Zhu T. A new meshless local Petrov- Galerkin (MLPG) approach in computational mechanics,
• Computational Mechanics. 1998a; 22:117-27. https://doi.org/10.1007/s004660050346.
• Atluri SN, Zhu T. A new Meshless Local Petrov- Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation, Computer Modeling and Simulation in Engineering. 1998b; 3(3):187-96.
• Atluri SN, Shen S. The basis of meshless domain discretization: the Meshless Local Petrov- Galerkin (MLPG) method, Advances in Computational Mathematics. 2005; 23:73-93.https://doi.org/10.1007/s10444-004-1813-9.
• Thakur HC, Singh KM, Sahoo PK. MLPG analysis of nonlinear heat conduction in irregular domains, CMES. 2010; 68(2):117-49.
• Qi-Fang W, Bao-Dong D, Zhen-Feng L. A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems, Chin. Phys. B. 2013; 22(8):1-7.
• Zhang T, He Y, Dong L, Li S, Alotaibi A, Atluri SN. Meshless local Petrov- Galerkin mixed Collocation method for solving Cauchy inverse problems of steady state heat transfer, CMES. 2014; 97(6):509-33.
• Singh IV, Sandeep K, Prakash R. Heat transfer analysis of two- dimensional fins using a meshless element free galerkin method, Numerical Heat Transfer, Part A. 2003; 44:73-84. https://doi.org/10.1080/713838174.
• Singh T, Shrivastava S, Ber HS. Analysis of unsteady heat conduction through short fin with applicability of quasi theory, Int. J. Mech. Eng. and Rob. Res. 2013; 2(1):269-83.
• Taler D, Taler J. Steady-state and transient heat transfer through fins of complex geometry, Archives of Thermodynamics. 2014; 35(2):117-33.
• Sao AK, Banjare YP. Analysis of thermal characteristics of transient heat conduction through long fin and comparison with exact fin theory and quasi steady theory, International Journal of Emerging Technology and Advanced Engineering. 2014; 4(11):157-66.
• Sadri S, Raveshi MR, Amiri S. Efficiency analysis of straight fin with variable heat transfer coefficient and thermal conductivity, Journal of Mechanical Science and Technology.2012; 26(4):1283-90. https://doi.org/10.1007/s12206-0120202-4.
• Torabi M, Yaghoobi H. Thermal analysis of the convective radiative fin with a step change in thickness and temperature dependent thermal conductivity, Journal of Theoretical and Applied Mechanics. 2013; 51(3):593-602.
• Kader AHA, Latif MSA, Nour HM. General exact solution of the fin problem with variable thermal conductivity, Propulsion and Power Research. 2016; 5(1):63-69. https:// doi.org/10.1016/j.jppr.2016.01.007.
• Ganji DD, Ganji ZZ, Ganji HD. Determination of temperature distribution for annular fins with temperature dependent thermal conductivity by HPM, Thermal Science.2011; 15(Suppl. 1):S 111-15.
• Mhlongo MD, Moitsheki RJ. Some exact solutions of nonlinear fin problem for steady heat transfer in longitudinal fin with different profiles, Advances in Mathematical Physics.2014; 1-16. https://doi.org/10.1155/2014/947160.
• Sobamowo MG. Thermal analysis of longitudinal fin with temperature dependent properties and internal heat generation using Galerkin's method of weighted residual, Applied Thermal Engineering. 2016; 99:1316-30. https:// doi.org/10.1016/j.applthermaleng.2015.11.076.
• Sun Y, Ma J, Li B, Guo Z. Prediction of nonlinear heat transfer in a convective radiative fin with temperature dependent properties by the collocation spectral method, Numerical Heat Transfer, Part B: Fundamentals. 2016; 69(1):68-73.https://doi.org/10.1080/10407782.2015.1081043.
• Holman JP. Unsteady heat conduction (Chapter 4). Heat Transfer, 10th Edition, McGrawHill Higher Education; 2010.

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