The entrance region flow of a Casson fluid in a tube has been investigated numerically without making prior assumptions on the form of velocity profile within the boundary layer region, which is determined by a cross sectional integration of the momentum differential equation for a given distance from the channel entrance. Using the macroscopic mass and momentum balance equations, the thickness of the core, the entrance length, and the pressure drop have been obtained at each cross section of the entrance region of the tube for specific values of Casson number.

The present paper reports the theoretical results on the thermal performance of proposed Integrated Hybrid Nanofluid Hemi-Spherical Fin Model assuming a combination of Fe₃O₄-Ni/C₆H₁₈OSi₂ hybrid nanofluid. The model leverages the concept of symmetrical geometries and optimized nanoparticle shapes to enhance the heat flux, with a focus on symmetrical design applications in thermal engineering. The simulations are carried out by assuming a silicone oil as a base fluid, due to its exceptional stability in hot and humid conditions, enriched with superparamagnetic Fe₃O₄ and Ni nanoparticles to enhance the heat transfer capabilities, with the aim of contributing to the field of nanotechnology, electronics and thermal engineering, The focus of this work is to optimize the heat dissipation in systems that require high thermal efficiency and stability such as automotive cooling systems, aerospace components and power electronics. In addition, the study explores the influence of key parameters such as heat transfer coefficients and thermal conductivity that play an important role in improving the thermal performance of cooling systems. The overall thermal performance of the model is evaluated based on its heat flux and thermal efficiency. The study also examines the impact of the shape optimized nanoparticles in silicone oil by incorporating shape-factor in its modelling equations and proposes optimization of parameters to enhance the overall thermal performance of the system. Darcy’s flow model is used to analyse the key parameters in the system and study the thermal behaviour of the hybrid nanofluid within the fin by incorporating natural convection, temperature-dependent internal heat generation, and radiation effects. By using the similarity approach, the governing equations were reduced to non-linear ordinary differential equations and numerical solutions were obtained by using four-stage Lobatto-IIIA numerical technique due to its robust stability and convergence properties. This enables a systematic investigation of various influential parameters, including thermal conductivity, emissivity and heat transfer coefficients. Additionally, it stimulates interest among researchers in applying mathematical techniques to complex heat transfer systems, thereby contributing towards the development of highly efficient cooling system. Our findings indicate that there is a significant enhancement in the heat flux as well as improvement in the thermal efficiency due to the mixture of silicone oil and shape optimized nanoparticles, that was visualized through comprehensive graphical analysis. Quantitatively, the proposed model displays a maximum thermal efficiency of 57.5% for lamina shaped nanoparticles at $N_c$ = 0.5, $N_r$ = 0.2, $N_g$ = 0.2 and ${\Theta }_a$ = 0.4. The maximum enhancement in the heat flux occurs when $N_c$ doubles from 5 to 10 for $m_2$ = 0.2 and $N_r$ = 0.1. Optimal thermal performance is found for $N_c$, $N_r$ and $m_2$ values in the range 5 to 10, 0.2 to 0.4 and 0.4 to 0.8 respectively.

This study numerically investigates and optimizes the thermal performance of Al $$_2$$ 2 O $$_3$$ 3 , CuO and MWCNT T-HNF embedded semispherical fin model in various base fluids. The present work focuses on identifying the most suitable base fluid and optimizing the governing parameters values to improve the heat transfer capability of the proposed configuration. A mathematical model describing the heat transfer behavior of the proposed fin system is developed by formulating the governing energy equation under appropriate physical assumptions. The resulting nonlinear ordinary differential equation is reformulated into non-dimensional terms using similarity transformation and solved numerically to capture the heat transfer characteristics of the model. The heat transfer performance of the proposed configuration is assessed by examining its heat flux and thermal efficiency, under various operating conditions. A simulation based comparative analysis was carried out to examine the impact of various base fluids on the heat transfer characteristics of porous fin. Among the base fluids considered, water-based T-HNF demonstrated the highest heat transfer rate, achieving a heat transfer rate enhancement of 3.60% to 20.98% over rest of the base fluids across all the governing parameters. Conversely, methanol-based T-HNF exhibited maximum thermal efficiency, with an enhancement in the range 5.27%−7.90% over water based T-HNF across $$\hat{N}_R$$ N ^ R and $$\hat{\theta }_{a}$$ θ ^ a governing parameters. Further, the RSM framework is employed to optimize the governing parameters values that yield enhanced thermal performance in terms of heat transfer rate. The results provide valuable insights into the combined effects of nanofluid composition, base fluid selection and parameter optimization, offering ideas to improve the design and efficiency of materials used in advanced thermal management systems, including heat exchangers, electronic cooling devices, energy systems and cooling of porous structures in high-temperature environments these findings contribute to optimization of sustainable energy nanofluid based thermal management systems, pointing towards potential directions for developing next generation energy efficient cooling systems.

This study presents a novel analysis of the coupling effects of magnetic field and nanoparticle aggregation on heat flux and entropy generation in porous radial fin embedded in a water-based MWCNT nanofluid. Unlike conventional analysis, the proposed model explicitly accounts for aggregated and non-aggregated nanoparticle states to capture their effect on thermophysical properties. The governing nonlinear energy model, incorporating the effects of nanoparticle aggregation, magnetic field, thermal conductivity, and viscous dissipation, is transformed into a dimensionless framework, and the resulting boundary value problem is solved numerically using high-accuracy Lobatto-IIIA technique. A comprehensive parametric analysis reveals that heat flux and entropy generation varies significantly across various governing parameters and operating conditions. The non-aggregated nanofluid model consistently outperforms the aggregated case, exhibiting a heat flux enhancement ranging from 14 to 63%, along with a maximum reduction in entropy generation of 48.45%. An average increase in heat flux of 38.23% and 49.5% is observed with increasing Nc and G parameters, while an enhancement of 20.2%, 50.36%, 23.06%, and 25.33% are obtained with decreasing Nr, $$\theta _\textrm{a}$$ θ a , $$m_2$$ m 2 , and H , highlighting the strong sensitivity of the model to thermal and magnetic parameters. Similarly, a notable reduction in entropy generation, ranging from 2.12 to 48.45%, is observed for non-aggregated model with decreasing $$\theta _\textrm{a}$$ θ a , $$m_2$$ m 2 , and H , while a reduction in the range of 20.15–39.64% is achieved with increasing Nc and G parameters. The observed enhancement in the thermal performance arises from improved nanoparticle dispersion and increased thermal conductivity induced by magnetic field. These findings emphasize that ensuring stable and uniform nanoparticle dispersion along with proper tuning of governing parameters are critical for reducing entropy generation and achieving superior heat transfer performance in fin-based thermal systems. It also offers valuable insights into the design and optimization of thermal management systems.

The objective of the paper is to investigate the variation of core thickness of a non-Newtonian fluid in an annular cylinder at the entrance region. It is derived numerically, with no prior assumptions on the form of the Velocity profile. The thickness of the core is examined at each cross section of annuli for various values of Bingham number and aspect ratio by applying mass balance equation. The effect of various parameters on the flow rate are obtained graphically. The examination incorporates Bingham plastic fluids, Casson and Herschel-Bulkley fluid. The administering equations are solved using an iterative procedure by converting non-linear algebraic equation, expressing the variation in pressure in terms of core thickness obtained using the mass balance equation and plug core velocities along the boundary layers. The core thickness is obtained numerically by solving this equation using an iterative procedure. MATLAB programming tool has been employed to get the graphical variation of core thickness for different values of aspect ratio. The comparisons have been made between the obtained results and the results of Casson and Herschel-Bulkley fluids. Also, we find excellent agreement between our numerical results and the results available in literature.