This article comprehensively investigates the thermal performance of a ternary hybrid nanofluid flowing in a permeable inclined cylinder/plate system. The study focuses on the effects of key constraints such as the inclined geometry, permeable medium, and heat source/sink on the thermal distribution features of the ternary nanofluid. The present work is motivated by the growing demand for energy-efficient cooling systems in various industrial and energy-related applications. A mathematical model is developed to describe the system’s fluid flow and heat-transfer processes. The PDEs (partial differential equations) are transformed into ODEs (ordinary differential equations) with the aid of suitable similarity constraints and solved numerically using a combination of the RKF45 method and shooting technique. The study’s findings give useful insights into the behavior of ternary nanofluids in permeable inclined cylinder/plate systems. Further, important engineering coefficients such as skin friction and Nusselt numbers are discussed. The results show that porous constraint will improve thermal distribution but declines velocity. The heat-source sink will improve the temperature profile. Plate geometry shows a dominant performance over cylinder geometry in the presence of solid volume fraction. The rate of heat distribution in the cylinder will increase from 2.08% to 2.32%, whereas in the plate it is about 5.19% to 10.83% as the porous medium rises from 0.1 to 0.5.

The utilization of Maxwell fluid with nanoparticle suspension exhibits promising prospects in enhancing the efficacy of energy conversion and storage mechanisms. They have the potential to be utilized in sophisticated cooling systems for power generation facilities, thereby augmenting the overall energy efficacy. Keeping this in mind, the current research examines the Maxwell nanofluid flow over a rotating disk with the impact of a heat source/sink. The present study centers on the examination of flow characteristics in the existence of a uniform magnetic field. The conversion of governing equations into ordinary differential equations is achieved using appropriate similarity variables. To derive the Nusselt number (Nu) and skin friction (SF) model related to the flow and temperature parameters, the suggested back-propagation artificial neural networking (ANN) technique is used. The Runge-Kutta-Fehlberg fourth-fifth order (RKF-45) method is used to solve the reduced equations and produce the necessary data to create the Nu and SF model. Both the Nu and SF models require 1000 data for training the network, respectively. Graphs are utilized to communicate numerical outcomes. The results concluded that the upsurge in magnetic parameter drops the velocity profile but advances the heat transport. Rise in the thermal conductivity parameter, increases the heat transport.

The current study explores a three-dimensional swirling flow of titania–ethylene glycol-based nanofluid over a stretchable cylinder with torsional motion. The heat transfer process is explored subject to heat source/sink. Here, titania–ethylene glycol–water-based nanofluid is used. The Maxwell–Bruggeman models for thermal conductivity and modified Krieger–Dougherty models for viscosity are employed to scrutinize the impact of nanoparticle aggregation. A mathematical model based on partial differential equations (PDEs) is developed to solve the flow problem. Following that, a similarity transformation is performed to reduce the equations to ordinary differential equations (ODEs), which are then solved using the finite element method. It has been proven that nanoparticle aggregation significantly increases the temperature field. The results reveal that the rise in Reynolds number improves the heat transport rate, whereas an increase in the heat source/sink parameter value declines the heat transport rate. Swirling flows are commonly found in many industrial processes such as combustion, mixing, and fluidized bed reactors. Studying the behavior of nanofluids in these flows can lead to the development of more efficient and effective industrial processes.

The time-dependent Maxwell nanofluid flow with thermophoretic particle deposition is examined in this study by considering the solid–liquid interfacial layer and nanoparticle diameter. The governing partial differential equations are reduced to ordinary differential equations using suitable similarity transformations. Later, these reduced equations are solved using Runge–Kutta–Fehlberg’s fourth and fifth-order method via a shooting approach. An artificial neural network serves as a surrogate model, making quick and precise predictions about the behaviour of nanofluid flow for various input parameters. The impact of dimensionless parameters on flow, heat, and mass transport is determined via graphs. The results reveal that the velocity profile drops with an upsurge in unsteadiness parameter values and Deborah number values. The rise in space and temperature-dependent heat source/sink parameters value increases the temperature. The concentration profile decreases as the thermophoretic parameter upsurges. Finally, the method’s correctness and stability are confirmed by the fact that the maximum number of values is near the zero-line error. The zero error is attained near the values $2.68\times {10}^{-6}$, $2.14\times {10}^{-9}$, and $8.5\times {10}^{-7}$ for the velocity, thermal, and concentration profiles, respectively.

The temperature distribution in a conductive-radiative rectangular profiled annular fin with internal heat generation is scrutinized in the present investigation. The nonlinear variation of thermal conductivity and heat transfer coefficient governed by the power law is considered. The analytical approximation for the non-dimensional temperature profile is obtained using the differential transform method (DTM)-Pade approximant. The nondimensionalization of the governing energy equation using dimensionless terms yields a nonlinear ordinary differential equation (ODE) with corresponding boundary conditions. The resulting ODE is analytically solved with the assistance of the DTM-Pade approximant procedure. Furthermore, the impact of thermal parameters on the temperature field and thermal stress is elaborated with graphs. The important results of the report divulge that temperature distribution greatly enhances with an augmentation of the heat generation parameter, but it gradually reduces with an increment in the magnitude of the thermogeometric and radiative-conductive parameter.