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This paper aims to present a comprehensive analysis of conjugate heat transfer phenomena occurring within the developing region of square ducts under both isothermal and isoflux boundary conditions. The study involves a rigorous numerical investigation, using advanced computational methods to simulate the complex heat exchange interactions between solid structures and surrounding fluid flows. The results of this analysis provide valuable insights into the heat transfer characteristics of such systems and contribute to a deeper understanding of fluid–thermal interactions in duct flows.

The manuscript outlines a detailed numerical methodology, combining computational fluid dynamics and finite element analysis, to accurately model the conjugate heat transfer process. This approach ensures both the thermal behaviour of the solid walls and the fluid flow dynamics are well captured.

The results presented in the manuscript reveal significant variations in heat transfer characteristics for isothermal and isoflux boundary conditions. These findings have implications for optimizing heat exchangers and enhancing thermal performance in various engineering applications.

The insights gained from this study have the potential to influence the design and optimization of heat exchange systems, contributing to advancements in energy efficiency and engineering practices.

The research introduces a novel approach to study conjugate heat transfer in square ducts, particularly focusing on the developing region. This unique perspective offers fresh insights into heat transfer mechanisms that were previously not thoroughly explored.

The investigation concentrated on studying a distinct category of tubular heat exchanger that uses swirling airflow over tube bundle maintained at constant heat flux. Swirl flow is achieved using a novel perforated baffle plate with rectangular openings and multiple adjustable opposite-oriented saw-tooth flow deflectors. These deflectors were strategically placed at the inlet of the heat exchanger to create a swirling flow downstream.

The custom-built axial flow heat exchanger consists of three baffle plates arranged longitudinally supporting tube bundle maintained at constant heat flux. The baffle plate equipped with saw-tooth flow deflector of various geometry represented by space height ratio(e/h). Next, ambient air was then directed over the tube bundle at varying Reynolds number and the effect of baffle spacing (PR), Space height ratio (e/h) and inclination angle(a) of deflectors on performance of heat exchanger was experimentally analyzed.

The heat transfer augmentation of heat exchanger for given operating condition is strongly dependent on geometry, inclination angle of deflector and baffle spacing.

An average improvement of 1.42 times in thermal enhancement factor was observed with inclination angle of 30°, space height ratio of 0.4 and a pitch ratio of 1.2 when compared to a heat exchanger without a baffle plate under similar operating conditions.

The present numerical investigation examines the magnetohydrodynamic (MHD) double diffusion natural convection of power-law non-Newtonian nano-encapsulated phase change materials (NEPCMs) in a trapezoidal cavity.

The governing Navier-Stokes, energy and concentration equations based on the Cartesian curvilinear coordinates are solved using the collocated grid arrangement’s finite volume method. The in-house FORTRAN code is validated with the different benchmark problems. The NEPCM nanoparticles consist of a core-shell structure with Phase Change Material (PCM) at the core. The enclosure, shaped as a trapezoidal hollow, features a warmed (T_h) left wall and a cold (T_c) right wall. Various parameters are considered, including the power law index (0.6 ≤ n ≤ 1.4), Hartmann number (0 ≤ Ha ≤ 30), Rayleigh number (10⁴ ≤ Ra ≤ 10⁵) and fixed variables such as buoyancy ratio (Br = 0.8), Prandtl number (Pr = 6.2), Lewis number (Le = 5), fusion temperature (Θ_f = 0.5) and volume fraction (ϕ = 0.04).

The findings indicate a decrease in local Nusselt (Nu) and Sherwood (Sh) numbers with increasing Hartmann numbers (Ha). Additionally, for a shear-thinning fluid (n = 0.6) results in the maximum local Nu and Sh values. As the Rayleigh number (Ra) increases from 10⁴ to 10⁵, the structured vortex in the streamline pattern is disturbed. Furthermore, for different Ra values, an increase in n from 0.6 to 1.4 leads to a 67.43% to 76.88% decrease in average Nu and a 70% to 77% decrease in average Sh.

This research is for two-dimensioal laminar flow only.

PCMs represent a class of practical substances that behave as a function of temperature and have the innate ability to absorb, release and store heated energy in the form of hidden fusion enthalpy, or heat. They are valuable in these systems as they can store significant energy at a relatively constant temperature through their latent heat phase change.

As per the literature review and the authors’ understanding, an examination has never been conducted on MHD double diffusion natural convection of power-law non-Newtonian NEPCMs within a trapezoidal enclosure. The current work is innovative since it combines NEPCMs with the effect of magnetic field Double diffusion Natural Convection of power-law non-Newtonian NEPCMs in a Trapezoidal enclosure. This outcome can be used to improve thermal management in energy storage systems, increasing safety and effectiveness.

This study aims to examine the cilia-driven flow of magnetohydrodynamics (MHD) non-Newtonian fluid through a porous medium. The Jeffrey fluid model is taken into account. The fluid motion in a two-dimensional symmetric channel emphasizes the dominance of viscous properties over inertial properties in the context of long wavelength and low Reynolds number approximations.

An integrated numerical and analytic results are obtained by hybrid approach. A statistical method analysis of variance along with response surface methodology is used. Sensitivity analysis is used to validate the accuracy of nondimensional numbers.

The impact of various flow parameters is presented graphically and in numerical tables. It is noted that the velocity slip parameter is the most sensitive flow parameter in velocity and relaxation to retardation time ratio in temperature.

A model on cilia-generated flow of MHD non-Newtonian Jeffrey fluid is proposed.

The boundary integral method (BIM) is very attractive to practicing engineers as it reduces the dimensionality of the problem by one, thereby making the procedure computationally inexpensive compared to its peers. The principal feature of this technique is the limitation of all its computations to only the boundaries of the domain. Although the procedure is well developed for the Laplace equation, the Poisson equation offers some computational challenges. Nevertheless, the literature provides a couple of solution methods. This paper revisits an alternate approach that has not gained much traction within the community. The purpose of this paper is to address the main bottleneck of that approach in an effort to popularize it and critically evaluate the errors introduced into the solution by that method.

The primary intent in the paper is to work on the particular solution of the Poisson equation by representing the source term through a Fourier series. The evaluation of the Fourier coefficients requires a rectangular domain even though the original domain can be of any arbitrary shape. The boundary conditions for the homogeneous solution gets modified by the projection of the particular solution on the original boundaries. The paper also develops a new Gauss quadrature procedure to compute the integrals appearing in the Fourier coefficients in case they cannot be analytically evaluated.

The current endeavor has developed two different representations of the source terms. A comprehensive set of benchmark exercises has successfully demonstrated the effectiveness of both the methods, especially the second one. A subsequent detailed analysis has identified the errors emanating from an inadequate number of boundary nodes and Fourier modes, a high difference in sizes between the particular solution and the original domains and the used Gauss quadrature integration procedures. Adequate mitigation procedures were successful in suppressing each of the above errors and in improving the solution accuracy to any desired level. A comparative study with the finite difference method revealed that the BIM was as accurate as the FDM but was computationally more efficient for problems of real-life scale. A later exercise minutely analyzed the heat transfer physics for a fin after validating the simulation results with the analytical solution that was separately derived. The final set of simulations demonstrated the applicability of the method to complicated geometries.

First, the newly developed Gauss quadrature integration procedure can efficiently compute the integrals during evaluation of the Fourier coefficients; the current literature lacks such a tool, thereby deterring researchers to adopt this category of methods. Second, to the best of the author’s knowledge, such a comprehensive error analysis of the solution method within the BIM framework for the Poisson equation does not currently exist in the literature. This particular exercise should go a long way in increasing the confidence of the research community to venture into this category of methods for the solution of the Poisson equation.

This study aims to focus on understanding how different jet angles and Reynolds numbers influence the phase change materials’ (PCMs) melting process and their capacity to store energy. This approach is intended to offer novel insights into enhancing thermal energy storage systems, particularly for applications where heat transfer efficiency and energy storage are critical.

The research involved an experimental and numerical analysis of PCM with a melting temperature range of 22 °C–26°C under various conditions. Three different jet angles (45°, 90° and 135°) and two container angles (45° and 90°) were tested. Additionally, two different Reynolds numbers (2,235 and 4,470) were used to explore the effects of jet outlet velocities on PCM melting behaviour. The study used a circular container and analysed the melting process using the hot air inclined jet impingement (HAIJI) method.

The obtained results showed that the average temperature for the last time step at Ф = 90° and Re = 4,470 is 6.26% higher for Ф = 135° and 14.23% higher for Ф = 90° compared with the 45° jet angle. It is also observed that the jet angle, especially for Ф = 90°, is a much more important factor in energy storage than the Reynolds number. In other words, the jet angle can be used as a passive control parameter for energy storage.

This study offers a novel perspective on the effective storage of waste heat transferred with air, such as exhaust gases. It provides valuable insights into the role of jet inclination angles and Reynolds numbers in optimizing the melting and energy storage performance of PCMs, which can be crucial for enhancing the efficiency of thermal energy storage systems.

This study aims to explore entropy evaluation in the bi-directional flow of Casson hybrid nanofluids within a stagnated domain, a topic of significant importance for optimizing thermal systems. The aim is to investigate the behavior of unsteady, magnetized and laminar flow using a parametric model based on the thermo-physical properties of alumina and copper nanoparticles.

The research uses boundary layer approximations and the Keller-box method to solve the derived ordinary differential equations, ensuring numerical accuracy through convergence and stability analysis. A comparison benchmark has been used to authenticate the accuracy of the numerical outcomes.

Results indicate that increasing the Casson fluid parameter (ranging from 0.1 to 1.0) reduces velocity, the Bejan number decreases with higher bidirectional flow parameter (ranging from 0.1 to 0.9) and the Nusselt number increases with higher nanoparticle concentrations (ranging from 1% to 4%).

This study has limitations, including the assumption of laminar flow and the neglect of possible turbulent effects, which could be significant in practical applications.

The findings offer insights for optimizing thermal management systems, particularly in industries where precise control of heat transfer is crucial. The Keller-box simulation method proves to be effective in accurately predicting the behavior of such complex systems, and the entropy evaluation aids in assessing thermodynamic irreversibilities, which can enhance the efficiency of engineering designs.

These findings provide valuable insights into the thermal management of hybrid nanofluid systems, marking a novel contribution to the field.

This study aims to analyze the two-dimensional ferrofluid flow in porous media. The effects of changes in parameters such as permeability parameter, buoyancy parameter, Reynolds and Prandtl numbers, radiation parameter, velocity slip parameter, energy dissipation parameter and viscosity parameter on the velocity and temperature profile are displayed numerically and graphically.

By using simplification, nonlinear differential equations are converted into ordinary nonlinear equations. Modeling is done in the Cartesian coordinate system. The finite element method (FEM) and the Akbari-Ganji method (AGM) are used to solve the present problem. The finite element model determines each parameter’s effect on the fluid’s velocity and temperature.

The results show that if the viscosity parameter increases, the temperature of the fluid increases, but the velocity of the fluid decreases. As can be seen in the figures, by increasing the permeability parameter, a reduction in velocity and an enhancement in fluid temperature are observed. When the Reynolds number increases, an increase in fluid velocity and temperature is observed. If the speed slip parameter increases, the speed decreases, and as the energy dissipation parameter increases, the temperature also increases.

When considering factors like thermal conductivity and variable viscosity in this context, they can significantly impact velocity slippage conditions. The primary objective of the present study is to assess the influence of thermal conductivity parameters and variable viscosity within a porous medium on ferrofluid behavior. This particular flow configuration is chosen due to the essential role of ferrofluids and their extensive use in engineering, industry and medicine.