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The purpose of this paper is to present a modeling approach for aggregate and disaggregate level models for cluster‐based diffusion of a new technology. The aggregate approach refers to the diffusion modeling of a product at the overall population level, while the disaggregate approach refers to the diffusion process at the individual entity level.

The pattern of diffusion of a new technology in a representative two‐cluster situation is studied. In the aggregate level modeling, a diffusion model is developed in which potential adopters of both clusters learn about the new technology from each other. This is done by a Lotka‐Volterra type of dynamical system of equations. Then, to focus on relatively micro‐level phenomena, such as different propensities of imitation and innovation of firms within a cluster, an agent‐based disaggregate model for cluster‐based diffusion of technology is proposed. In these disaggregate models, the effects of heterogeneity and the inter‐cluster and intra‐cluster distances between the agents are captured.

The results highlight two major points: first, both aggregate and disaggregate models are in agreement with each other, and second, both of the models exhibit a form similar to the Bass model. Thus, consistent with the general theme of why the Bass model fits without decision variables, it is found that the Bass model, when extended appropriately, can be expected to work well also in the cluster‐based technology diffusion situation.

This modeling approach can be applied to the modeling of those situations in which heterogeneous industrial units are present in geographical clusters. It can also be applied in the related contexts such as diffusion of practices (e.g. quality certifications) within a multi‐divisional organization or across various networked clusters.

For a homogenous population, the Bass model has been used extensively to predict the sales of newly introduced consumer durables. In comparison, little attention has been given to the modeling of the technology adoption by the industrial units present in disparate groups, called clusters. The major contribution of this paper is to propose a framework for cluster‐based diffusion of technological products, and then to present an analysis of that framework using two different methodologies.

This study aims to investigate the impact of different heater geometries (flat, rectangular, semi-elliptical and triangular) on hybrid nanofluidic (Cu–Al₂O₃–H₂O) convection in novel umbrella-shaped porous thermal systems. The system is top-cooled, and the identical heater surfaces are provided centrally at the bottom to identify the most enhanced configuration.

The thermal-fluid flow analysis is performed using a finite volume-based indigenous code, solving the nonlinear coupled transport equations with the Darcy number (10^–5 ≤ Da ≤ 10^–1), modified Rayleigh number (10 ≤ Ra_m ≤ 10⁴) and Hartmann number (0 ≤ Ha ≤ 70) as the dimensionless operating parameters. The semi-implicit method for pressure linked equations algorithm is used to solve the discretized transport equations over staggered nonuniform meshes.

The study demonstrates that altering the heater surface geometry improves heat transfer by up to 224% compared with a flat surface configuration. The triangular-shaped heating surface is the most effective in enhancing both heat transfer and flow strength. In general, flow strength and heat transfer increase with rising Ra_m and decrease with increasing Da and Ha. The study also proposes a mathematical correlation to predict thermal characteristics by integrating all geometric and flow control variables.

The present concept can be extended to further explore thermal performance with different curvature effects, orientations, boundary conditions, etc., numerically or experimentally.

The present geometry configurations can be applied in various engineering applications such as heat exchangers, crystallization, micro-electronic devices, energy storage systems, mixing processes, food processing and different biomedical systems (blood flow control, cancer treatment, medical equipment, targeted drug delivery, etc.).

This investigation contributes by exploring the effect of various geometric shapes of the heated bottom on the hydromagnetic convection of Cu–Al₂O₃–H₂O hybrid nanofluid flow in a complex umbrella-shaped porous thermal system involving curved surfaces and multiphysical conditions.