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The presence and progression of stenosis disturb the normal circulation of blood through an artery and cause serious consequences. The proposed investigation is aimed to assess non-Newtonian characteristics of blood in an elliptical artery having stenosis. The blood is taken as Sutterby fluid flowing via a multi-stenosed elliptical cross-section artery.

The analytical solution of a mathematical model representing the considered problem is extracted in a non-dimensional form by utilizing the perturbation technique under the mild stenosis assumptions.

The graphical nature of these results is examined and discussed comprehensively for different physical parameters. The height and shape of stenosis are noted to have prominent effects on flow velocity. The wall shear stress and flow velocity attained high values in the stenotic portion of the artery. The non-uniform stenosis is observed to create higher resistance to the flow than the uniform stenosis. Further, a high disorder is noticed in the constricted region of the artery by streamlines analysis.

The manuscript completely comprehends the blood’s non-Newtonian flow in the arteries of elliptical shape having multiple stenoses. The present study is about the properties of non-Newtonian blood flow through an elliptical artery with many stenoses. The Sutterby fluid model is used to describe the blood’s non-Newtonian nature. By utilizing presumptions of mild stenosis, the mathematical model’s non-linearity is decreased, and the perturbation method is applied to generate the resulting equations.

The presence of stenosis can significantly impact the circulation of blood flow. When an artery becomes narrowed, it can create a constriction or obstruction in the flow path of blood, which can lead to several important fluid dynamics phenomena, i.e. increased velocity, shear stress, pressure drop, etc. The presence of stenosis can cause various damages and complications in the affected blood arteries and surrounding tissues, resulting in heart attacks or diseases like atherosclerosis.

The work presented in the manuscript was not published earlier in any form.

The purpose of this paper is to scrutinize the marketing orientation and market-oriented cultural elements of integrated Islamic schools. These integrated schools teach modern science curriculum alongside comprehensive religious instruction in an Islamic environment.

This is an inductive, exploratory research from an interpretivist study. Narrative inquiry was undertaken to understand the perceptions, attitudes and actions of school senior management and teachers. Content analysis of the school websites and social media pages was carried out. In total, 7 schools and 16 respondents became part of the purposive sample.

The presence of several integrated Islamic schools, experienced Islamic education leadership and Islamic education consultants are evidence of a growing sector. The schools are technologically enabled, strongly customer-oriented and adept at inter-functional coordination. The need-gap found in this sector is in competitor orientation, curriculum development and recruitment of specific criteria-based staff.

With the mushrooming of integrated Islamic schools in Pakistan, the level of competition has also risen. The schools have made a considerable investment and strives to maintain and increase the enrollment rate of the institute. This research can enlighten integrated Islamic educators about effective education marketing practices and the prevalence of marketing orientation in such schools.

In Pakistan, private primary schools strive to differentiate themselves and competitively position their value proposition. The marketization of education has begun to affect perceptions of school staff, teachers, students and academic work itself. Yet, there is scarce exploratory research on marketing done by integrated Islamic primary schools. This study will contribute foundational work for the development of a holistic marketing model tailored to the requirements of integrated Islamic schools.

The boundary layer flow of immiscible fluids plays a crucial role across various industries, influencing advancements in industrial processes, environmental systems, healthcare and more. This study explores the thermally radiative boundary layer flow of a shear-driven Ree–Eyring fluid over a nanofluid. The investigation offers valuable insights into the intricate dynamics and heat transfer behavior that arise when a nanofluid, affected by thermal radiation, interacts with a non-Newtonian Ree–Eyring fluid. This analysis contributes to a deeper understanding of the complex interactions governing such systems, which is essential for enhancing efficiency and innovation in multiple applications.

The simulation investigates the convergence of boundary layers under varying shear strengths. A comparative analysis is conducted using γAl2O3 and Al₂O₃ nanoparticles, with water as the base fluid. The model’s numerical outcomes are derived using the bvp4c method through the application of appropriate similarity transformations. The resulting numerical data are then used to produce graphical representations, offering valuable insights into the influence of key parameters on flow behavior and patterns.

The temperature of the Al₂O₃ nanoparticles is always higher than the γAl2O3 nanoparticles, and hence, Al₂O₃ nanoparticles become more significant in the cooling process then γAl2O3 nanoparticles. It is also observed that the fluid velocity for both regions is enhanced by increasing values of the Ree–Eyring fluid parameter.

The results stated are original and new with the thermal radiative boundary layer flow of two immiscible Ree–Eyring fluid and Al₂O₃/γAl2O3 nanofluid.

The purpose of this paper is to examine the impact of owner family involvement in business on sustainable survival of family small-to-medium enterprises (SMEs) and to empirically validate the intervening role of corporate social responsibility (CSR).

The authors analyze data from 489 owner and nonowner executives of 150 family SMEs using PLS-SEM (Partial Least Square–Structural Equation Modeling).

The authors found evidence that family involvement in business positively impacts the sustainable survival of family SMEs while corporate social responsibility partially mediates this relationship. Apart from effective family involvement in business, active involvement in social causes enhances a firm's ability to survive longer.

This study was conducted in a geographic context and data were collected from family-managed and controlled firms. Further research is needed to generalize the findings to all types of family firms in the global context. In an Islamic society, family firms need to invest in social causes, human development, and environmental sustainability through zakat, sadaqat, and donations.

The findings imply that family firms require stakeholder-centric competitive strategies and socially responsible behavior along with effective family control, commitment, enrichment, and successful succession since the path to sustainable survival goes through CSR.

Survival is the biggest challenge facing family SMEs forcing them to achieve the ability to sustain longer. Rooted in transaction cost economics (TCE) theory of the family firm and stakeholder theory, this paper validates an integrative model for family SMEs' sustainable survival.

This paper aims to explore dual solutions for the flow of a hybrid nanofluid over a permeable melting stretching/shrinking sheet with nanoparticle shape factor, second-order velocity slip conditions and viscous dissipation. The hybrid nanofluid is formulated by dispersing alumina (Al₂O₃) and copper (Cu) nanoparticles into water (H₂O).

The governing partial differential equations (PDEs) are first reduced to a system of ordinary differential equations (ODEs) using a mathematical method of similarity transformation technique. These ODEs are then numerically solved through MATLAB’s bvp4c solver.

Key parameters such as slip parameter, melting parameter, suction parameter, shrinking parameter and Eckert number are examined. The results reveal the existence of two distinct solutions (upper and lower branches) for the transformed ODEs when considering the shrinking parameter. Increasing value of Cu-volume fraction and the second-order velocity slip enhances boundary layer thicknesses, whereas the heat transfer rate diminishes with rising melting and suction parameters. These numerical results are illustrated through various figures and tables. Additionally, a stability analysis is performed and confirms the upper branch is stable and practical, while the lower branch is unstable.

The analysis of hybrid nanofluid flow over a shrinking surface has practical significance with applications in processes such as solar thermal management systems, automotive cooling systems, sedimentation, microelectronic cooling or centrifugal separation of particles. Both steady and unsteady hybrid nanofluid flows are relevant in these contexts.

While the study of hybrid nanofluid flow is well-documented, research focusing on the shrinking flow case with specific parameters in our study is still relatively scarce. This paper contributes to obtaining dual solutions specifically for the shrinking case, which has been less frequently addressed.