On the Formulation of Metaheuristic Algorithm-Based Approximation Approach for Nonlinear Ordinary Differential Equations with Application to Heat Exchanger Problem

Low, Ee Soong; Ong, Pauline

doi:10.47836/pjst.28.4.06

Cited by 2 publications

(1 citation statement)

References 39 publications

(59 reference statements)

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“…Since there is probable danger of smelt explosions, the dry solids content of heavy black liquor (HBL) should be a minimum of 58%. Nowadays, the dry solids content of 70% to75% is normal, and even 80% to 85% is the target value for the dry solids content with wood to increase the chemical recovery furnace thermal efficiency (Naqvi et al, 2010;Nasir et al, 2020;Low & Ong, 2020), with agricultural residues black liquor, is normally in the range of 60% to 65 %.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Infra-Red Evaporation Characteristics of Wheat Straw Black Liquor

Singh¹,

Jawaid²,

Yadav³

et al. 2021

JST

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Infrared (IR) evaporation characteristics of Weak Soda Black Liquor (WSBL) were determined at five different temperatures of 80, 90, 100, 110 and 120oC. The effect of constant temperature on evaporation rate and moisture content (on a dry basis) of 1.5 gm approx. WSBL tests were contemplated and required a careful time frame of IR dissipation to vanish the dampness content at a different consistent temperature. The dissipation rate expanded with expanding infrared temperature. Therefore, different numerical models, such as Page and Logarithmic, Henderson, Pabis and Lewis, were utilised to fit the experimental data properly. A Gaussian model equation was developed for evaporation rate and moisture fraction of black liquor. The probable empirical parameters, along with the relating of reduced chi-square (X2), Residual Sum of Square (RSS), and coefficients of determination (adjusted R2) from non-linear regression analysis of all the numerical model equations, were examined. In addition, the effect of evaporation temperature on the water removal rate, the effective diffusion coefficient and activation energy were also estimated. The effective diffusion coefficient ranges from 2.67 × 10–10 m2/s to 10.4 × 10–10 m2/s, and the activation energy was 39.19 kJ/mol. The statistical indicators (chi-square and determination coefficient) showed that the Decay model equation and Gaussian equation are the most suitable models for describing the evaporation process of WSBL.

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Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Infra-Red Evaporation Characteristics of Wheat Straw Black Liquor

Singh¹,

Jawaid²,

Yadav³

et al. 2021

JST

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show abstract

Homotopy Analysis-Based Hybrid Genetic Algorithm and Secant Method to Solve IVP and Higher-Order BVP

Omar

2021

IEEE Access

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The analytical solution of the Initial Value Problem (IVP) and the Boundary Value Problem (BVP) is an essential issue in numerous engineering applications. However, it cannot usually be realized by simple methods. Accordingly, utilizing semi-analytical solution methods such as the homotopy analysis method (HAM) is an alternative. However, it depends on calculating a dedicated convergence parameter. Different algorithms were proposed to realize this parameter. Thus, converting the residual function into an optimization problem represented a promising solution. The resulted optimization problem can be solved either using traditional analytical methods or meta-heuristic algorithms. In this paper, a new algorithm called Homotopy Analysis Method-based hybrid Genetic algorithm and Secant method (HAMGS) is proposed for solving such optimization problems. The proposed hybridization is based on utilizing the Secant method in the crossover process of the genetic algorithm to improve and accelerate the convergence. Moreover, this hybridization will protect the secant method from divergence in searching for new individuals. As a result, the convergence control parameter can be detected algebraically without drawing the h-curves. This facilitates identifying the minimum number of HAM terms to reach the solution, which reduces the computational burden remarkably. The presumed improvement of pairing the genetic algorithm and Secant method for improving the HAM solver is verified via four IVPs and three higher-order BVPs. The results corroborate the competence of the proposed algorithm and its ability to solve such problems efficiently.

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On the Formulation of Metaheuristic Algorithm-Based Approximation Approach for Nonlinear Ordinary Differential Equations with Application to Heat Exchanger Problem

Cited by 2 publications

References 39 publications

Mathematical Modelling of Infra-Red Evaporation Characteristics of Wheat Straw Black Liquor

Mathematical Modelling of Infra-Red Evaporation Characteristics of Wheat Straw Black Liquor

Homotopy Analysis-Based Hybrid Genetic Algorithm and Secant Method to Solve IVP and Higher-Order BVP

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