Calendering is a mechanical finishing technology used in the leather, textile, and paper industry, with the mechanism of reshaping and deforming fibers of the web to be calendered with the help of pressure and heat transfer. In this paper, a comparative study has been done to examine the flow of heat inside the calender nip using an unsteady heat conduction equation with specific initial and boundary conditions. The outcomes achieved by utilizing the new homotopy perturbation method and finite difference method have been compared with the exact solution. The achieved outcomes reveal the accuracy, effectiveness, and reliability of techniques applied. It is observed that the outcomes achieved by the new homotopy perturbation method are more accurate than those obtained by the finite difference method.
Biazar J, Eslami M. A new homotopy perturbation method for solving systems of partial differential equations. Computers and Mathematics with Applications. 2011;225–34.
2.
Biazar J, Asayesh R. A new finite difference scheme for parabolic equations. The 50th Annual Iranian Mathematics Conference. 2019;1–4.
3.
Demir A, Erman S, Ozgur B, Korkmaz E. Analysis of the new homotopy perturbation method for linear and nonlinear problems, Boundary Value Problems. 2013;1–11.
4.
Elbadri M. A New Homotopy Perturbation Method for Solving Laplace Equation. Advances in Theoretical and Applied Mathematics. 2013;237–42.
5.
Elbadri M, Elzaki T. New Modification of Homotopy Perturbation Method and the Fourth-Order Parabolic Equations with Variable Coefficients. Pure Appl Math J. 2015;6.
6.
Fadugba S, Edogbanya O, Zelibe S. Crank Nicolson method for solving parabolic partial differential equations. International Journal of Applied Mathematics and Modeling. 2013;8–23.
7.
Grover D, Kumar V, Sharma D. A Comparative Study of Numerical Techniques and Homotopy Perturbation Method for Solving Parabolic Equation and Nonlinear Equations. International Journal for Computational Methods in Engineering Science and Mechanics. 2012;403–7.
8.
Gupta N, Kanth N. Analysis of Nip Mechanics Model for Rolling Calender Used in Textile Industry. Journal of the Serbian Society for Computational Mechanics. 2018;39–52.
9.
Gupta N, Kanth N. Numerical Solution of Diffusion Equation Using Method of Lines. Indian Journal of Industrial and Applied Mathematics. 2019;(2):194–203.
10.
Gupta N, Kanth N. Study of heat flow in a rod using homotopy analysis method and homotopy perturbation method. AIP Conference Proceedings. 2019;20013–4.
11.
Gupta N, Kanth. Analytical approximate solution of heat conduction equation using new homotopy perturbation method. Matrix Science Mathematic. (2):1–07.
12.
Gupta N, Kanth N. Study of heat conduction inside rolling calender nip for different roll temperatures. Journal of Physics: Conference series. 2019;(1):12044–5.
13.
Gupta N, Kanth N. Analysis of heat conduction inside the calender nip used in textile industry. AIP Conference Proceedings. 2020;(1):20008.
14.
Gupta N, Kanth N. Application of Perturbation Theory in Heat Flow Analysis. A Collection of Papers on Chaos Theory and Its Applications. 2021;173.
15.
He J. A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International of non-linear mechanics. 2000;37–43.
16.
He J. Homotopy perturbation method: a new nonlinear analytical technique. Applied Mathematics and computation. 2003;73–9.
17.
He J. Homotopy perturbation method for solving boundary value problems. Physics letters A. 2006;87–8.
18.
He J. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern physics B. 2006;1141–99.
19.
Kanth N, Ray A. Analysis of heat conduction inside the nip of machine calender for the same and different roll temperatures. Heat Transfer Asian Research. 2019;1–17.
20.
Mirzazadeh M, Ayati Z. New homotopy perturbation method for system of Burgers equations. Alexandria Engineering Journal. 2016;1619–24.
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