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This study examines fluid flow within a rectangular porous medium bounded by walls capable of expansion or contraction. It focuses on a non-Newtonian fluid with Casson characteristics, incompressibility, and electrical conductivity, demonstrating temperature-dependent impacts on viscosity.

The flow is two-dimensional, unsteady, and laminar, influenced by a small electromagnetic force and electrical conductivity. The Hybrid Analytical and Numerical Method (HAN method) resolves the constitutive differential equations.

The fluid’s velocity is influenced by the Casson parameter, viscosity variation parameter, and resistive force, while the fluid’s temperature is affected by the radiation parameter, Prandtl number, and power-law index. Increasing the Casson parameter from 0.1 to 50 results in a 4.699% increase in maximum fluid velocity and a 0.123% increase in average velocity. Viscosity variation from 0 to 15 decreases average velocity by 1.42%. Wall expansion (a from −4 to 4) increases maximum velocity by 19.07% and average velocity by 1.09%. The average fluid temperature increases by 100.92% with wall expansion and decreases by 51.47% with a Prandtl number change from 0 to 7.

Understanding fluid dynamics in various environments is crucial for engineering and natural systems. This research emphasizes the critical role of wall movements in fluid dynamics and offers valuable insights for designing systems requiring fluid flow and heat transfer. The study presents new findings on heat transfer and fluid flow in a rectangular channel with two parallel, porous walls capable of expansion and contraction, which have not been previously reported.

The current analysis produces the fractional sample of non-Newtonian Casson and Williamson boundary layer flow considering the heat flux and the slip velocity. An extended sheet with a nonuniform thickness causes the steady boundary layer flow’s temperature and velocity fields. Our purpose in this research is to use Akbari Ganji method (AGM) to solve equations and compare the accuracy of this method with the spectral collocation method.

The trial polynomials that will be utilized to carry out the AGM are then used to solve the nonlinear governing system of the PDEs, which has been transformed into a nonlinear collection of linked ODEs.

The profile of temperature and dimensionless velocity for different parameters were displayed graphically. Also, the effect of two different parameters simultaneously on the temperature is displayed in three dimensions. The results demonstrate that the skin-friction coefficient rises with growing magnetic numbers, whereas the Casson and the local Williamson parameters show reverse manners.

Moreover, the usefulness and precision of the presented approach are pleasing, as can be seen by comparing the results with previous research. Also, the calculated solutions utilizing the provided procedure were physically sufficient and precise.

This study aims to analyze the two-dimensional ferrofluid flow in porous media. The effects of changes in parameters such as permeability parameter, buoyancy parameter, Reynolds and Prandtl numbers, radiation parameter, velocity slip parameter, energy dissipation parameter and viscosity parameter on the velocity and temperature profile are displayed numerically and graphically.

By using simplification, nonlinear differential equations are converted into ordinary nonlinear equations. Modeling is done in the Cartesian coordinate system. The finite element method (FEM) and the Akbari-Ganji method (AGM) are used to solve the present problem. The finite element model determines each parameter’s effect on the fluid’s velocity and temperature.

The results show that if the viscosity parameter increases, the temperature of the fluid increases, but the velocity of the fluid decreases. As can be seen in the figures, by increasing the permeability parameter, a reduction in velocity and an enhancement in fluid temperature are observed. When the Reynolds number increases, an increase in fluid velocity and temperature is observed. If the speed slip parameter increases, the speed decreases, and as the energy dissipation parameter increases, the temperature also increases.

When considering factors like thermal conductivity and variable viscosity in this context, they can significantly impact velocity slippage conditions. The primary objective of the present study is to assess the influence of thermal conductivity parameters and variable viscosity within a porous medium on ferrofluid behavior. This particular flow configuration is chosen due to the essential role of ferrofluids and their extensive use in engineering, industry and medicine.

Scenario planning has significant applications in the field of strategic management and facilitating decision making under uncertainty, and hence this study aims to integrate scenario planning and the preference ranking organisation method for enrichment evaluations (PROMETHEE) method to propose a new methodology to design a portfolio.

The methodology has been designed in two stages, the first of which identifies the investment environment in Iran and defines possible scenarios for the future based upon the opinion of experts and uncertainties established in the identified environment. In the second stage, the views of experts are elicited on business area performance within each scenario. The business areas are subsequently ranked based on their final performance scores in each scenario area using the PROMETHEE method. Through use of a linear programming model, the percentage of investment in each business area is then determined according to the net flow of the area (i.e. the priority of a certain area relative to others).

The portfolio design in an Iranian investment company has been considered as a case study. The building industry and cement industry have been selected as preferable strategic business areas based on hypothetical scenarios for investment environment in Iran over five years (2008‐2012) and the strategies of the investment company.

The integration of scenario planning and multi‐criteria decision analysis (MCDA) holds great potential for strategic decision support due to the complementary nature of these two approaches. In this article, the authors provide a methodology to apply scenario planning alongside other MCDA methods to portfolio design, focusing on an innovative use of the PROMETHEE method with scenario planning.

The purpose of this paper is to provide some insights regarding the adoption of internet advertising by Iranian small and medium‐sized enterprises. The recent negative trends leading to a lack of competitive advantage in small businesses and the advantages of internet advertising makes it imperative to study various factors affecting this area of marketing.

This study reviewed 59 previous related studies, resulting in a comprehensive theoretical framework which explains the advantages of internet advertising for small to medium‐sized enterprises (SMEs). Via questionnaire, the paper compiles 346 Iranian experts’ opinions in order to test the validity and applicability of variables in Iran. A structural equation model and LISREL software were used to analyze the data.

A total of seven latent variables of internet advertising adoption were examined: advertising agencies, internet publishers, small and middle‐sized enterprises, government role, e‐commerce development and user types. The paper found that these constructs successfully explain internet advertising adoption by incorporating readiness and globalization stages. The small and medium‐sized enterprises were found to be the most significant for explaining internet advertising adoption.

The sample was restricted to Iranian experts.

This study offers one of the first attempts to build a comprehensive theoretical model explaining internet advertising adoption. Second, this study offers a new scale for internet advertising adoption with higher content validity.