Investigation of a hyperbolic annular fin with temperature dependent thermal conductivity by two step third derivative b
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TECHNICAL PAPER
Investigation of a hyperbolic annular fin with temperature dependent thermal conductivity by two step third derivative block method (TSTDBM) Oluwaseun Adeyeye1 • Ali Aldalbahi2 • Zurni Omar1 • Jawad Raza3 • Mostafizur Rahaman2 Alibek Issakhov4 • Mohammad Rahimi-Gorji5 • S. Nadeem6,7
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Received: 19 July 2020 / Accepted: 22 August 2020 Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Block methods in general have proven to be an efficient approach for the numerical approximation of ordinary differential equations as a whole. Therefore, it is important to investigate the suitability of adopting block methods with the presence of higher derivatives in solving heat transfer models. The presence of the higher derivative in the method gives room for improved accuracy when solving these models. The block method adopted in this article is the two step third derivative block method which is developed using a novel linear block approach. The resultant schemes for the block method were combined as simultaneous integrators for the solution of the differential equation model. The method is seen to adequately provide solutions to the problem of annular fins with hyperbolic profile under the influence of various physical parameters.
1 Introduction Fins with annuals region are often coincide with the cylindrical surfaces to boost up the rate of heat transfer. Control systems, internal combustions engines, heat exchangers and compressors are including in traditional applications. Triangular profiles become popular when angular fins equipped
& S. Nadeem [email protected] Mohammad Rahimi-Gorji [email protected]; [email protected] 1
School of Quantitative Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah, Malaysia
2
Department of Chemistry, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
3
Department of Mathematics and Statistics, Institute of Southern Punjab (ISP), Multan, Pakistan
4
Al-Farabi Kazakh National University, Almaty, Kazakhstan
5
Faculty of Medicine and Health Sciences, Ghent University, 9000 Ghent, Belgium
6
Mathematics and its Applications in Life Sciences Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam
7
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
with space radiators and space age. Finite difference method used by Schnurr and Cothran (1974) for the study of fin-andtube radiator fixed with fin of trapezoidal and triangular profiles which included all effects of analysis for fin-to-base and fin-to-fin radiative exchange. Different values of fin radii ratio and radiation parameter in heat dissipation are calculated by design charts. Electronic devices cooled by using fins as a heat sink. Transistor heat sink use in capped hollow tube where radial fin served by cap (Kraus 1958; Aziz et al. 2006). The research work related to radial fins has gained abundant appeal to the researchers till year 2000 and it has
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