Study of heat flow in a rod using homotopy analysis method and homotopy perturbation method

Gupta, Neelam; Kanth, Neel

doi:10.1063/1.5086635

Cited by 4 publications

(8 citation statements)

References 7 publications

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“…Jean Baptiste Joseph Fourier was first who described heat conduction process. Solution of heat conduction process is obtained by many analytical and numerical methods [1,18]. In this paper, one dimensional heat conduction equation is solved using new perturbation method.…”

Section: Application Of Heat Transfer Modelmentioning

confidence: 99%

“…To solve such kind of partial differential equations (PDE), many methods are used to find the numerical or exact solutions. Homotopy perturbation method (HPM) is one of the methods used in recent years to solve various linear and non-linear PDE [1][2][3]. Initial and boundary value problems can be solved using HPM extensively.…”

Section: Introductionmentioning

confidence: 99%

“…HPM is applicable to linear and non-linear boundary value problems [12]. The solution obtained by HPM gives the solution approximately near to the universally accepted method of separation of variable [1,13]. Recently, Biazar and Eslami proposed the new homotopy perturbation method (NHPM) [14,15].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analytical Approximate Solution of Heat Conduction Equation Using New Homotopy Perturbation Method

Gupta¹,

Kanth²

2019

Matrix sci. math.

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In this paper, the analytic solution of one-dimensional heat conduction equation is obtained by means of new homotopy perturbation method. This method is effectively applied to obtain the exact solution for the problems on hand. Some problems related to one dimensional heat equation have been discussed, which reveals the effectiveness and simplicity of the method. Numerical results have also been analysed graphically to show the rapid convergence of infinite series expansion.

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Section: Application Of Heat Transfer Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analytical Approximate Solution of Heat Conduction Equation Using New Homotopy Perturbation Method

Gupta¹,

Kanth²

2019

Matrix sci. math.

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“…The above partial differential equation is parabolic in nature and can be solved analytically and numerically …”

Section: The Mathematical Model For Heat Conduction Inside the Nipmentioning

confidence: 99%

Analysis of heat conduction inside the nip of a machine calender for the same and different roll temperatures

Kanth

Ray

2019

Heat Trans. Asian Res.

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Calendering is a mechanical leveling and segmenting process at the final stage in many industries, like paper, printing, leather, and textile, where a thin sheet of material passes through the nips formed by two or more rolls in contact. The material composition of rolls varies for different types of calenders. Depending on the quality of products required for the end usage, the rolls can be hard or soft. Furthermore, they may be heated to a certain degree of temperature, using different heat transfer processes, such as induction, hot water passage, or heated oil passage. In this paper, the effect of roll temperature and time of contact (dwell time) on the temperature of newsprint paper in the thickness direction has been discussed using a single hard nip calender (machine calender), when the paper web is inside the calender nip formed by two rolls having the same and different temperature levels. The case of temperature gradient calendering has also been discussed.

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“…The classical heat conduction equation is second order linear partial differential equation. The solutions of which are obtained by using various analytical and numerical methods [1][2][3]. This equation describes the heat distribution in each domain over some time.…”

Section: Introductionmentioning

confidence: 99%

Application of Perturbation Theory in Heat Flow Analysis

Gupta¹,

Kanth²

2021

A Collection of Papers on Chaos Theory and Its Applications

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Many physical and engineering problems can be modeled using partial differential equations such as heat transfer through conduction process in steady and unsteady state. Perturbation methods are analytical approximation method to understand physical phenomena which depends on perturbation quantity. Homotopy perturbation method (HPM) was proposed by Ji Huan He. HPM is considered as effective method in solving partial differential equations. The solution obtained by HPM converges to exact solution, which are in the form of an infinite function series. Biazar and Eslami proposed new homotopy perturbation method (NHPM) in which construction of an appropriate homotopy equation and selection of appropriate initial approximation guess are two important steps. In present work, heat flow analysis has been done on a rod of length L and diffusivity α using HPM and NHPM. The solution obtained using different perturbation methods are compared with the solution obtained from most common analytical method separation of variables.

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Study of heat flow in a rod using homotopy analysis method and homotopy perturbation method

Cited by 4 publications

References 7 publications

Analytical Approximate Solution of Heat Conduction Equation Using New Homotopy Perturbation Method

Analytical Approximate Solution of Heat Conduction Equation Using New Homotopy Perturbation Method

Analysis of heat conduction inside the nip of a machine calender for the same and different roll temperatures

Application of Perturbation Theory in Heat Flow Analysis

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