Convection–radiation heat transfer in solar heat exchangers filled with a porous medium: Exact and shooting homotopy analysis solution

Soltani, L. Ahmad; Shivanian, Elyas; Ezzati, Reza

doi:10.1016/j.applthermaleng.2016.04.107

Cited by 28 publications

(4 citation statements)

References 31 publications

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“…The functions f 1 and f 2 are C ∞ . Thus, according to the Cauchy-Lipschitz theorem [21], Equation ( 5) has a unique positive solution (S, I) on the infinite time horizon, whenever S 0 > 0, I 0 > 0. Proof.…”

Section: Proofmentioning

confidence: 99%

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Numerical Solution of an Interval-Based Uncertain SIR (Susceptible–Infected–Recovered) Epidemic Model by Homotopy Analysis Method

Bakare

Chakraverty

Potůček

2021

Axioms

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This work proposes an interval-based uncertain Susceptible–Infected–Recovered (SIR) epidemic model. The interval model has been numerically solved by the homotopy analysis method (HAM). The SIR epidemic model is proposed and solved under different uncertain intervals by the HAM to obtain the numerical solution of the model. Furthermore, the SIR ODE model was transformed into a stochastic differential equation (SDE) model and the results of the stochastic and deterministic models were compared using numerical simulations. The results obtained were compared with the numerical solution and found to be in good agreement. Finally, various simulations were done to discuss the solution.

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Section: Proofmentioning

confidence: 99%

“…where A is a linear operator, t denotes the time, and v(t) is an unknown function. Let v 0 (t) denote an initial approximation of v(t) and Z denote an auxiliary linear operator [21]. We construct the zero-order deformation equation…”

Section: Lemma 3 ([20]mentioning

confidence: 99%

Numerical Solution of an Interval-Based Uncertain SIR (Susceptible–Infected–Recovered) Epidemic Model by Homotopy Analysis Method

Bakare

Chakraverty

Potůček

2021

Axioms

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“…Shivanian and Abbasbandy [11] discussed PHAM for two points second order boundary value problems. Homotopy analysis method has been applied in a study of combined conduction-convectionradiation heat transfer [12]. Odibat and Bataineh constructed homotopy polynomials by introducing an adaptation of HAM [13].…”

Section: Introductionmentioning

confidence: 99%

An improved adaptation of homotopy analysis method

Sadaf

Akram

2017

Math Sci

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An improved adaptation of the well-known homotopy analysis method (HAM) is proposed to approximate the solutions of strongly nonlinear differential problems in terms of a rapidly convergent series. The proposed method involves simpler integrals and less computations than the standard HAM. The method is illustrated using different numerical examples. The comparative analysis confirms the applicability and efficiency of the proposed technique.

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“…In view of applications and importance, the authors are motivated to take this problem. Homotopy analysis method (HAM) [14][15][16][17][18][19][20][21][22][23] has been used for the solution of the present problem. Convergence of the resulting series solution is explained.…”

Section: Introductionmentioning

confidence: 99%

Homotopy analysis for the influence of Navier slip flow in a vertical channel with cross diffusion effects

Kaladhar

Komuraiah

2017

Math Sci

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This research is to examine the laminar, incompressible free convective Navier slip flow between vertical plates with cross diffusion effects. This investigation includes the first order chemical reaction also. The resulting equations with boundary conditions are reduced into dimensionless form using suitable transformations. Homotopy analysis method has been applied to solve the system. The influence of emerging parameters on fluid flow quantities have been presented graphically. In addition, the nature of physical quantities are shown in tabular form.

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Convection–radiation heat transfer in solar heat exchangers filled with a porous medium: Exact and shooting homotopy analysis solution

Cited by 28 publications

References 31 publications

Numerical Solution of an Interval-Based Uncertain SIR (Susceptible–Infected–Recovered) Epidemic Model by Homotopy Analysis Method

Numerical Solution of an Interval-Based Uncertain SIR (Susceptible–Infected–Recovered) Epidemic Model by Homotopy Analysis Method

An improved adaptation of homotopy analysis method

Homotopy analysis for the influence of Navier slip flow in a vertical channel with cross diffusion effects

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