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The particle distribution in a fluid is mostly not homogeneous. The inhomogeneous dispersion of solid particles affects the velocity profile as well as the heat transfer of fluid. This study aims to highlight the effects of varying density of particles in a fluid. The fluid flows through a wavy curved passage under an applied magnetic field. Heat transfer is discussed with variable thermal conductivity.

The mathematical model of the problem consists of coupled differential equations, simplified using stream functions. The results of the time flow rate for fluid and solid granules have been derived numerically.

The fluid and dust particle velocity profiles are being presented graphically to analyze the effects of density of solid particles, magnetohydrodynamics, curvature and slip parameters. Heat transfer analysis is also performed for magnetic parameter, density of dust particles, variable thermal conductivity, slip parameter and curvature. As the number of particles in the fluid increases, heat conduction becomes slow through the fluid. Increase in temperature distribution is noticed as variable thermal conductivity parameter grows. The discussion of variable thermal conductivity is of great concern as many biological treatments and optimization of thermal energy storage system’s performance require precise measurement of a heat transfer fluid’s thermal conductivity.

This study of heat transfer with inhomogeneous distribution of the particles in a fluid has not yet been reported.

This study aims to investigate the comparative importance of factors influencing the customer shift behavior from conventional to Islamic banking for consumer finance in Pakistan.

First, a comprehensive analysis of the existing literature was conducted to identify a broad range of factors related to customer shift behavior. Through an expert sampling, 14 essential factors were chosen for further investigation. Second, a questionnaire was developed using the analytical hierarchy process (AHP). This questionnaire was then distributed among customers who had previously been using conventional banking services but had made a shift toward Islamic banking. The purpose of this questionnaire was to gather data and insights regarding their motivations and decision-making process behind the shift, and a sample 215 customers are taken in the study.

The results of AHP depicts that the religiosity is a most important factor influencing customers to shift from conventional to Islamic banking, and the second most important factor is pricing. The other subsequent important factors are reputation of the bank, marketing and promotion, service quality, behavior of banks staff, Shariah compliance, management, convenience, fastness and charges/fees. Whereas documentation, ambiance and recommendation are found least important factors to patronize Islamic banking.

The study recommends Islamic banks to create awareness, concentrating on religious factor to have a greater impact on growth of Islamic banking and shrinking of conventional banking. Further, it suggests Islamic banks to apply Shariah-recommended approach of doing business, to help community in best possible way and to launch differentiated marketing techniques to attract customers. It also proposes regulatory authorities to provide facilitation to Islamic banking business by providing level playing field similar to conventional banking, tax equality and conversion of public financing from conventional banking to Islamic banking.

The originality of this study lies in its comprehensive analysis of factors influencing consumer shift behavior from conventional to Islamic banking in the context of consumer finance in Pakistan. By using the AHP, the study provides a structured approach to understanding the relative importance of these factors. This is the uniqueness of the paper that it applies the AHP for the analysis. Furthermore, the study offers practical implications for Islamic banks and regulatory authorities to effectively address and capitalize on this consumer shift trend.

In recent times, there has been a growing interest in buoyancy-induced heat transfer within confined enclosures due to its frequent occurrence in heat transfer processes across diverse engineering disciplines, including electronic cooling, solar technologies, nuclear reactor systems, heat exchangers and energy storage systems. Moreover, the reduction of entropy generation holds significant importance in engineering applications, as it contributes to enhancing thermal system performance. This study, a numerical investigation, aims to analyze entropy generation and natural convection flow in an inclined square enclosure filled with Ag–MgO/water and Ag–TiO2/water hybrid nanofluids under the influence of a magnetic field. The enclosure features heated slits along its bottom and left walls. Following the Boussinesq approximation, the convective flow arises from a horizontal temperature difference between the partially heated walls and the cold right wall.

The governing equations for laminar unsteady natural convection flow in a Newtonian, incompressible mixture is solved using a Marker-and-Cell-based finite difference method within a customized MATLAB code. The hybrid nanofluid’s effective thermal conductivity and viscosity are determined using spherical nanoparticle correlations.

The numerical investigations cover various parameters, including nanoparticle volume concentration, Hartmann number, Rayleigh number, heat source/sink effects and inclination angle. As the Hartmann and Rayleigh numbers increase, there is a significant enhancement in entropy generation. The average Nusselt number experiences a substantial increase at extremely high values of the Rayleigh number and inclination.

This numerical investigation explores advanced applications involving various combinations of influential parameters, different nanoparticles, enclosure inclinations and improved designs. The goal is to control fluid flow and enhance heat transfer rates to meet the demands of the Fourth Industrial Revolution.

In a 90° tilted enclosure, the addition of 5% hybrid nanoparticles to the base fluid resulted in a 17.139% increase in the heat transfer rate for Ag–MgO nanoparticles and a 16.4185% increase for Ag–TiO2 nanoparticles compared to the base fluid. It is observed that a 5% nanoparticle volume fraction results in an increased heat transfer rate, influenced by variations in both the Darcy and Rayleigh numbers. The study demonstrates that the Ag–MgO hybrid nanofluid exhibits superior heat transfer and fluid transport performance compared to the Ag–TiO2 hybrid nanofluid. The simulations pertain to the use of hybrid magnetic nanofluids in fuel cells, solar cavity receivers and the processing of electromagnetic nanomaterials in enclosed environments.