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Article
Publication date: 11 September 2019

Muhammad Ayub, Muhammad Yousaf Malik, Misbah Ijaz, Marei Saeed Alqarni and Ali Saeed Alqahtani

The purpose of this paper is to explore the novel aspects of activation energy in the nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo–Christov…

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Abstract

Purpose

The purpose of this paper is to explore the novel aspects of activation energy in the nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo–Christov double-diffusion model over a permeable stretched sheet. Features of nonlinear thermal radiation, dual stratification, non-uniform heat generation/absorption, MHD and binary chemical reaction are also evaluated for present flow problem. Walter-B nanomaterial model is employed to describe the significant slip mechanism of Brownian and thermophoresis diffusions. Generalized Fourier’s and Fick’s laws are examined through Cattaneo–Christov double-diffusion model. Modified Arrhenius formula for activation energy is also implemented.

Design/methodology/approach

Several techniques are employed for solving nonlinear differential equations. The authors have used a homotopy technique (HAM) for our nonlinear problem to get convergent solutions. The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear coupled ordinary/partial differential equations. The capability of the HAM to naturally display convergence of the series solution is unusual in analytical and semi-analytic approaches to nonlinear partial differential equations. This analytical method has the following great advantages over other techniques:

  • It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

  • It guarantees the convergence of series solutions for nonlinear problems.

  • It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

It guarantees the convergence of series solutions for nonlinear problems.

It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

Brief mathematical description of HAM technique (Liao, 2012; Mabood et al., 2016) is as follows. For a general nonlinear equation:

(1) N [ u ( x ) ] = 0 ,

where N denotes a nonlinear operator, x the independent variables and u(x) is an unknown function, respectively. By means of generalizing the traditional homotopy method, Liao (1992) creates the so-called zero-order deformation equation:

(2) ( 1 q ) L [ u ˆ ( x ; q ) u o ( x ) ] = q h H ( x ) N [ u ˆ ( x ; q ) ] ,

here q∈[0, 1] is the embedding parameter, H(x) ≠ 0 is an auxiliary function, h(≠ 0) is a nonzero parameter, L is an auxiliary linear operator, uo(x) is an initial guess of u(x) and u ˆ ( x ; q ) is an unknown function, respectively. It is significant that one has great freedom to choose auxiliary things in HAM. Noticeably, when q=0 and q=1, following holds:

(3) u ˆ ( x ; 0 ) = u o ( x )andu ˆ ( x ; 1 ) = u ( x ) ,

Expanding u ˆ ( x ; q ) in Taylor series with respect to (q), we have:

(4) u ˆ ( x ; q ) = u o ( x ) + m = 1 u m ( x )q m , whereu m ( x ) = 1 m ! mu ˆ ( x ; q ) q m | q = 0 .

If the initial guess, the auxiliary linear operator, the auxiliary h and the auxiliary function are selected properly, then the series (4) converges at q=1, then we have:

(5) u ( x ) = u o ( x ) + m = 1 + u m ( x ) .

By defining a vector u = ( u o ( x ) , u 1 ( x ) , u 2 ( x ) , , u n ( x ) ) , and differentiating Equation (2) m-times with respect to (q) and then setting q=0, we obtain the mth-order deformation equation:

(6) L [ u ˆ m ( x ) χ m u m 1 ( x ) ] = h H ( x ) R m [ u m 1 ] ,

where:

(7) R m [ u m 1 ] = 1 ( m 1 ) ! m 1 N [ u ( x ; q ) ] q m 1 | q = 0andχ m = | 0m 11m > 1 .

Applying L−1 on both sides of Equation (6), we get:

(8) u m ( x ) = χ m u m 1 ( x ) + hL 1 [ H ( x ) R m [ u m 1 ] ] .

In this way, we obtain um for m ⩾ 1, at mth-order, we have:

(9) u ( x ) = m = 1 M u m ( x ) .

Findings

It is evident from obtained results that the nanoparticle concentration field is directly proportional to the chemical reaction with activation energy. Additionally, both temperature and concentration distributions are declining functions of thermal and solutal stratification parameters (P1) and (P2), respectively. Moreover, temperature Θ(Ω1) enhances for greater values of Brownian motion parameter (Nb), non-uniform heat source/sink parameter (B1) and thermophoresis factor (Nt). Reverse behavior of concentration ϒ(Ω1) field is remarked in view of (Nb) and (Nt). Graphs and tables are also constructed to analyze the effect of different flow parameters on skin friction coefficient, local Nusselt number, Sherwood numbers, velocity, temperature and concentration fields.

Originality/value

The novelty of the present problem is to inspect the Arrhenius activation energy phenomena for viscoelastic Walter-B nanofluid model with additional features of nonlinear thermal radiation, non-uniform heat generation/absorption, nonlinear mixed convection, thermal and solutal stratification. The novel aspect of binary chemical reaction is analyzed to characterize the impact of activation energy in the presence of Cattaneo–Christov double-diffusion model. The mathematical model of Buongiorno is employed to incorporate Brownian motion and thermophoresis effects due to nanoparticles.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 1
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 9 October 2023

Safwan Kamal, Izra Berakon, Abdul Hamid and Zainal Muttaqin

Previous studies described the professional zakat had been limited. Generally, the past authors conducted a quantitative method with general results and did not focus on the…

410

Abstract

Purpose

Previous studies described the professional zakat had been limited. Generally, the past authors conducted a quantitative method with general results and did not focus on the behaviour of people who pay the professional zakat. As a result, the purpose of this study is to provide a comprehensive understanding of how the general public can pay their zakat using Bloom’s theory.

Design/methodology/approach

This research uses primary data with in-depth interviews from five informants, including civil servants (PNS) and private employees. Spiral analysis was used to analyse the data, arrange it, read it frequently, take brief notes, find categories, interpret and summarise it.

Findings

The results show Bloom’s theory can accommodate muzakki’s behaviour by paying professional zakat. It can be seen from the following conclusions: firstly, in the cognitive domain, muzakki’s behaviour of paying the professional zakat was motivated by their memories (experiences), the ability to interpret, the ability to understand the principles of zakat, the ability to understand the relations and the ability to understand the role of zakat from its norms. Secondly, in the affective domain, muzakki’s behaviour in paying the professional zakat was motivated by their ability to receive, give positive value, call others and dare to take risks. Thirdly, in the psychomotor domain, guided practice, mechanised practice and adoption drive muzakki’s behaviour of paying zakat.

Research limitations/implications

This study has limitations regarding the number of samples (informants). In addition, the results of the research are designed to be very subjective so that they cannot be generalised to phenomena that exist in other places and countries that also require zakat in the profession. In the future, the results of this study can be used as a variable development with quantitative methods so that it can involve more samples to get maximum and a broader result.

Practical implications

This research has a valuable managerial impact on the zakat management institutions, particularly in Langsa, Aceh, Indonesia and all zakat institutions worldwide. Therefore, the central government can evaluate the zakat gap through various socialisation activities by promoting the cognitive, affective and psychomotor domains. Socialisation should improve people’s behaviour to pay zakat so that the amount of zakat collected will be higher and will reduce the gap between the potency of zakat and the zakat in reality which has been unequal so far.

Originality/value

This research will contribute to the significant development of zakat in terms of studying the behaviour of muzakki paying the professional zakat. Although the theory of planned behaviour was dominated by previous research, this research reveals other aspects of muzakki behaviour using Bloom’s model by elaborating on cognitive, affective and psychomotor domains.

Details

Journal of Islamic Marketing, vol. 15 no. 3
Type: Research Article
ISSN: 1759-0833

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Article
Publication date: 20 June 2024

Safwan Kamal, Nanda Safarida and Erne Suzila Kassim

The purpose of this study is to develop and assess the effects of unified theory of acceptance and use of technology (UTAUT 2) constructs – effort expectancy (EE), social…

439

Abstract

Purpose

The purpose of this study is to develop and assess the effects of unified theory of acceptance and use of technology (UTAUT 2) constructs – effort expectancy (EE), social influence (SI) and hedonic motivation (HM) – on behavioural intention (BI), as well as the impact of innovation resistance theory (IRT) constructs – usage barrier (UB) and tradition barrier (TB) – on innovation resistance (IR) behavior in the context of digital zakat payment in Aceh. In addition, this study also examines how knowledge of fiqh zakat influences both BI and IR.

Design/methodology/approach

This was a quantitative study including 350 Acehnese persons who paid zakat online. This research used a Likert scale, and the sampling technique was purposive sampling applied for the Acehnese people. The research respondents were civil servants, private employees, BUMN employees (employees of State-Owned Enterprises), merchants, restaurant owners, professionals and other occupations who had paid professional zakat through a digital system mechanism. The data were analysed using partial least squares structural equation modelling.

Findings

This research found that the constructs built through the theory of UTAUT 2 explained the position of the EE variable, which had a significant effect on BI. On the other hand, the variable of SI and HM did not significantly affect BI in digital zakat payment. This finding demonstrated that BI significantly influenced actual usage (AU). UB and TB had no impact on IR, according to the theoretical framework developed by IRT. Yet, the knowledge about the fiqh zakat (KFZ) significantly affected the AU. In terms of the moderation role, the KFZ variable moderated the relationship between BI and AU. However, the KFZ variable did not moderate the relationship between IR and AU.

Research limitations/implications

This research had limitations and could still be investigated further by involving a larger sample. This study does not include all UTAUT 2 and IRT constructs, but only involves UTAUT 2 and IRT constructs based on the phenomenon of digital zakat paying behavior in the people of Aceh.

Practical implications

This research had a managerial contribution and an evaluation of the use of digital zakat collection services in Aceh and zakat management institutions in various countries. The existence of significant EE should be a reference for zakat institutions to produce continuous payment applications with a higher level of convenience in the future. In addition, the government should encourage more organised fiqh zakat education in society to plan a more optimal zakat collection. The reason for this is that KFZ has been shown to moderate zakat intentions towards actual digital zakat payment behaviour.

Social implications

The results of this study were then accommodated by the government to design a digital zakat collection system so that it resulted in optimising the collected zakat funds. The greater the zakat funds collected, the greater the economic impact and social resilience of the community was in the midst of the post-covid and global crisis.

Originality/value

This research provided an essential value in the aspect of collecting zakat funds, especially in the study of the behaviour of paying zakat digitally. The theory of planned behaviour predominated in earlier studies that investigated zakat-paying behaviour. Yet, this research was even more focused as it used the constructs of UTAUT 2 and IRT theory and applied the involvement of a moderator variable like fiqh zakat knowledge that was barely discussed.

Details

Journal of Islamic Marketing, vol. 15 no. 11
Type: Research Article
ISSN: 1759-0833

Keywords

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