Nusselt Number Research Articles

Thermo-mechanical analysis of free convection in an octagonal cavity with adjustable active walls and flexible separator

This study investigates free convective within an octagonal cavity, which is partitioned into two compartments by a flexible separator. One of the left walls is maintained at a high temperature, while a lower temperature is applied to one of the right walls. The position of these active walls is adjustable, and the separator can be oriented vertically or inclined with either a positive or negative slope. The deformation of the flexible separator is modeled using the Arbitrary Lagrangian–Eulerian method. The outcomes indicate that locating the hotter wall near the top and moving the colder wall downwards hinders free convection and reduces the stress in the separator. Moreover, upward movement of both active walls leads to a decrease in the average temperature. An inclined separator with a positive slope enhances the heat transfer rate and experiences the lowest stress levels compared to vertical and negatively sloped separators. Raising Rayleigh number enhances the flow intensity and the stress in the flexible separator. Furthermore, it is found that a decrease in the elasticity modules of the separator from 1014 to 5 × 1011 results in a 5% increase in the average Nusselt number.

Artificial neural network analysis of Jeffrey hybrid nanofluid with gyrotactic microorganisms for optimizing solar thermal collector efficiency

This article investigates solar energy storage due to the Jeffrey hybrid nanofluid flow containing gyrotactic microorganisms through a porous medium for parabolic trough solar collectors. The mechanism of thermophoresis and Brownian motion for the graphene and silver nanoparticles are also encountered in the suspension of water-based heat transfer fluid. The gyrotactic microorganisms have the ability to move in an upward direction in the nanofluid mixture, which enhances the nanoparticle stability and fluid mixing in the suspension. Mathematical modeling of the governing equations uses the conservation principles of mass, momentum, energy, concentration, and microorganism concentration. The non-similar variables are introduced to the dimensional governing equations to get the non-dimensional ordinary differential equations. The Cash and Carp method is implemented to solve the non-dimensional equations. The artificial neural network is also developed for the non-dimensional governing equations using the Levenberg Marquardt algorithm. Numerical findings corresponding to the diverse parameters influencing the nanofluid flow and heat transfer are presented in the graphs. The thermal profiles are observed to be enhanced with the escalation in the Darcy and Forchheimer parameters. And the Nusselt number enhances with the escalation in the Deborah number and retardation time parameter. Entropy generation reduces with an enhancement in Deborah number and retardation time parameter. Solar energy is the best renewable energy source. It can fulfill the energy requirements for the growth of industries and engineering applications.

An Analytic Study on the Enhancement of Heat Transfer with Nanofluid

The article studies the problem of boundary layer fluid flow for two dimensional steady and incompressible hybrid nanofluids over the nonlinear stretching surface. The problem is analysed for the distribution of velocity, temperature, and concentration profile influenced by the parameters taken for study. The pertinent parameters analysed in the boundary value problem are magnetic, non-linear stretching parameter, Prandtl number, radiation, Brownian, thermophoresis. The governing sets of PDE’s are converted to a set of ODES using the similarity transformations. The numerical results are obtained by RK algorithm techniques. The study portrays the results for skin friction and Nusselt number for varying the parametric values. The interpretation of results is done graphically and in tabular format. The detailed parametric study is explored for the enhancement of heat transfer, the influence of the parameters on velocity, temperature, and volume fraction of the nanofluid, skin friction coefficient, and Nusselt number. The wide applications of the problem taken for the study where the control of complex parametric influence in heat transfer is applied in the field of energy recovery, biomedical, and industrial systems in the present global scenario.

Investigation of temperature jump, first and second-order velocity slip effects on blood-based ternary nanofluid flow in convergent/divergent channels

Purpose High surface area-to-volume ratios make nanoparticles ideal for cancer heat therapy and targeted medication delivery. Moreover, ternary nanofluids (TNFs) may possess superior thermophysical properties compared to mono- and hybrid nanofluids due to their synergistic effects. In light of this information, the objective of this article is to examine the blood-based TNF flow within convergent/divergent channels under velocity slip and temperature jump. Design/methodology/approach Leading partial differential equations corresponding to the problem are transformed into a system of nonlinear ordinary differential equations by using similarity variables. The bvp4c code that uses the finite difference method is used to obtain a numerical solution. Findings The effect of nanoparticles may change depending on the characteristics of flow near the wall. The properties and proportions of the used nanoparticles become important to control the flow. When TNF was used, an increase in the Nusselt number between 4.75% and 6.10% was observed at low Reynolds numbers. At high Reynolds numbers, nanoparticles reduce the Nusselt number and skin friction coefficient values under some special flow conditions. Importantly, the effects of second-order slip on engineering parameters were also investigated. Furthermore, the Nusselt number increases with increasing shape factor. Research limitations/implications Obtained results of the study can be beneficial in both nature and engineering, especially blood flow in veins. Originality/value The main innovations of this study are the usage of blood-based TNF and the examination of the effect of shape factor in convergent/divergent channels with second-order velocity slip.

Unsteady MHD flow of tangent hyperbolic ternary hybrid nanofluid in a darcy-forchheimer porous medium over a permeable stretching sheet with variable thermal conductivity

Background This research investigates the unsteady magnetohydrodynamic (MHD) flow, heat, and mass transfer of tangent hyperbolic ternary hybrid nanofluids over a permeable stretching sheet. The study considers three types of nanoparticles—aluminum oxide (Al₂O₃), copper (Cu), and titanium oxide (TiO₂)—dispersed in a base fluid of ethylene glycol (C₂H₆O₂). This ternary hybrid nanofluid (Al₂O₃–Cu–TiO₂/C₂H₆O₂) has potential applications in cooling systems, biomedical uses for targeted drug delivery and hyperthermia treatments, heat exchangers, and polymer processing techniques like extrusion and casting. Methods The study examines the effects of various parameters, including the Weissenberg number, power law index, nanoparticle volume fraction, viscous dissipation, magnetic field, heat generation, nonlinear thermal radiation, temperature ratio, Joule heating, Brownian motion, thermophoresis, porous permeability, variable thermal conductivity, Eckert number, Prandtl number, Schmidt number, chemical reaction, velocity ratio, Forchheimer number, and unsteady parameters. The governing equations are transformed into similarity equations using appropriate transformations and solved numerically with the MATLAB BVP5C package. The results are validated against data from published articles to ensure reproducibility. Results The findings reveal that an increase in the Weissenberg and Forchheimer numbers reduces the velocity profile, while the temperature distribution increases. The variable thermal conductivity parameter (Γ) leads to a higher temperature profile, indicating improved heat transfer. Higher nanoparticle concentrations in the nanofluids and hybrid nanofluids result in enhanced skin friction, Nusselt number, and Sherwood number. Ternary hybrid nanofluids show the most significant improvement in heat transfer and thermal conductivity. Conclusions Ternary hybrid nanofluids significantly enhance heat and mass transfer, showing potential for applications in cooling systems, drug delivery, and polymer processing. The numerical results are consistent with previous research, confirming the reliability and reproducibility of the findings

Unsteady Magneto-radiative Flow of Copper-water Nanofluid Over an Exponentially Stretching Surface

Understanding the complex behavior of fluid flows under various physical influences is crucial for advancing engineering and industrial applications. This paper presents the investigation of the unsteady, incompressible, single-phase magneto-radiative flow of a copper-water nanofluid over an exponentially stretching surface, considering the effects of viscous dissipation and temperature-dependent heat sources. This model, proposed in the present analysis, is based on fundamentals of the continuity and Navier–Stokesequations with mass conservation. Further, use of a similarity transformation will reduce the equations to dimensionless form and provide a numerical solution using the Runge–Kutta–Fehlberg method. In physics, engineering, and industrial applications, the most interesting parameters are the velocity, temperature, skin friction, and the Nusselt number (Nu). The results of this study are compared with previous works, showing significant agreement with findings under similar conditions. The analysis reveals that both temperature and velocity boundary layer increase when all very specific effects of radiation (R), heat source (Q), copper nanoparticle volume fraction, and magnetic field strength parameter are present. On the other hand, it is found that skin friction increases when considering both copper nanoparticle volume fraction and magnetic field strength parameter, but the Nu decreases if R, Q, copper nanoparticle volume fraction, and magnetic field strength parameter are the factors responsible for that. These outcomes will be further delineated through graphics and be elaborated in engineering and industrial context.

Enhancing the Prediction of Flow Characteristics in an Inventive Plate Heat Exchanger Using Deep Learning Techniques

Abstract In modern energy research, minimizing fuel usage and harmful gas emissions are critical priorities. The application of advanced deep learning (DL) models to predict thermohydraulic characteristics of an innovative plate heat exchanger (IPHE) is investigated in this study. Building upon our prior work utilizing machine learning (ML) models, the focus is placed on predicting the Nusselt Number (Nu), friction factor (f), and performance (P) within a Reynolds number range of 500 to 5000. Advanced DL architectures—GRU, LSTM, and CNN—are utilized, resulting in substantial improvements in prediction accuracy and robustness. The LSTM model demonstrates superior performance, achieving R² scores of 0.9986, 0.9985, and 0.9968 for Nu, f, and P, respectively, significantly surpassing prior ML model results of 0.98, 0.979, and 0.9628. The findings highlight the capacity of DL models to capture complex, nonlinear relationships in thermohydraulic data, offering an enhanced approach to optimizing plate heat exchanger (PHE) performance. This work contributes to energy-efficient technological advancements, supporting global efforts to reduce environmental impacts while addressing rising energy demands.

The role of machine learning in analyzing magnetic field localization and vortex generation in tetra-hybrid nanofluid: A numerical study

This research distinguishes itself by integrating machine learning algorithms to assess the impact of confined magnetic fields on vortex dynamics in hybrid nanofluid flow, through the inclusion of both vertical and horizontal magnetic field strips. Specifically, the study focuses on a vertical cavity with an aspect ratio of 1:5, where a bottom lid moves horizontally from left to right to drive the flow. We have applied a limited magnetic field consisting of vertical, and horizontal strips. The authors have developed MATLAB codes to implement an algorithm for solving the governing equations of the nanofluid flow and heat transfer. The algorithm is based on the Stream-Vorticity formulation and uses a finite difference method. The algorithm can examine how several parameters, such as magnetic field strength (0–300), nanoparticle volume fraction (0–20%), and Reynolds number (Re) (1–50), impact the characteristics of nanofluids in terms of flow and thermal properties. The results demonstrate that magnetic fields influence the stress distribution of the flow pattern and the temperature distribution. Further, the presence of a magnetic field also affects stress distribution. Moreover, it has been determined that the Nusselt number (Nu) experiences a 60% increase due to the magnetic field, while there is a remarkable rise attributed to the Re. Similarly, significant changes are observed in skin friction under both parameters. These findings carry implications for designing and operating devices.

Unsteady MHD Free Convective Flow of a Micro‐Polar Fluids Over a Vertical Porous Plate in the Presence of Radiation and Chemical Reaction

ABSTRACTObjective of the paper is to investigate the motion of an unsteady free convective MHD flow of a micro‐polar fluid over semi‐infinite vertically moving porous plate in the presence of chemical reaction and thermal radiation. A transverse magnetic field is applied, assuming a low magnetic Reynolds number. We have discussed the effects of heat radiation due to a heat source and first order chemical reaction within the medium. The perturbation method is applied to solve the nonlinear coupled partial differential equations in their dimensionless form, converting them into a system of ordinary differential equations, which are then solved analytically. The effects of magnetic field, medium permeability, buoyancy force, heat source, concentration gradient, Prandtl number, thermal diffusion, heat radiation, and first order chemical reaction on velocity, temperature and concentration are discussed graphically. The graphical representations are generated using MATLAB software. For engineering interest, their effects on skin friction, heat and mass transfer in terms of Nusselt number and Sherwood number are discussed; numerical values are shown in tabular form. The results show that magnetic fields reduce fluid velocity, while thermal radiation decreases temperature, and chemical reactions lower concentration. Radiation increases skin friction and heat transfer, while chemical reactions reduce mass transfer. Findings have relevance in various problems and situations arising with micro‐polar fluidic devices, industrial like petroleum and lubrication, mixing etc.

Evaluating experimentally the viability of employing hybrid nanofluids as an operating fluid in a shell-and-tube heat exchanger.

The use of hybrid nanofluids (HNF) in heat transfer applications has become the subject of studies during recent periods. Its ability to transfer heat is superior to single nanofluids, and this has been proven in many research. Shell and tube heat exchanger is one of the most common types and are therefore always under research to improve their performance. This study is a practical study that examines the effectiveness of HNF in their use as operating fluids in shell-and-tube heat exchangers instead of traditional operating fluids. A laboratory heat exchanger was used to complete this study. A group of HNF (MWCNTs- Al2O3/water) was synthesized at different concentration rates ranging from 0.4 to 2%. Tests were conducted for Reynolds values in the range from 2500 to 12,560. By measuring the variables in the tests and calculating some factors the results showed that, in comparison between the use of HNF and distilled water, it was found that there is an increase in the value of the Nusselt number for the HNF over the distilled water in a range of 10- 28.5%. The effectiveness increased when using the HNF by up to 22.7% compared to distilled water. Through experiments, an equation was deduced to calculate the value of the Nusselt number. There is good agreement between the results of this research and previous literature.

Modeling and simulation of entropy optimization in Darcy–Forchheimer flow of magneto-Ree–Eyring nanofluid with suction/injection and motile microorganisms

Recent studies indicate that nanofluids are crucial for solar heat exchange operations and solar energy collectors. Furthermore, the importance of energy and mass transfer in entropy creation is significantly increased in a number of industrial and engineering processes, such as mechanical power collectors, air conditioning, food processing, refrigeration, and heat exchangers. As a result of this advancement, this research is aimed to explore the comparative study on bioconvective Darcy–Forchheimer flow of an incompressible hydromagnetic Ree–Eyring nanofluid over a chemically activated expanding sheet in suction and injection cases while including the consequences of radiation, energy generation, and convective boundary conditions. Boundary layer approximation is utilized to represent this investigation’s primary partial differential equations (PDE). Then, using the appropriate transformation, the models are rebuilt into nonlinear ordinary differential equations (ODE). Utilizing the BVP5C inbuilt MATLAB package, the numerical solutions for this examination are established. Further, the graphical and tabular representations allow us to analyze the impacts of several relevant features on the microorganism’s density, concentration, entropy creation, velocity, temperature, friction factor, Sherwood, and Nusselt number distribution. The outcomes reveal that the velocity field of the liquid movement is declined by applying positive amounts of the Darcy–Forchheimer and magnetic parameters, respectively. Boosting values of the radiation, thermal ratio parameter, and temperature Biot number assist an increase in the thermal field. It reveals the augmented entropy generation with the rising values of bioconvection Lewis number and Brinkman number. Furthermore, the mass transfer rate increases with larger values of the Brownian parameter and chemical reaction parameter.

Numerical investigation of hydrothermal performance of double pipe heat exchangers with corrugation configuration

Numerical investigation of hydrothermal performance of double pipe heat exchangers with corrugation configuration

Study on the thermal control performance of lightweight minimal surface lattice structures for aerospace applications

Study on the thermal control performance of lightweight minimal surface lattice structures for aerospace applications

Soret-driven thermosolutal convection in bidispersive porous medium with vertical throughflow

This article investigates thermosolutal convection in bidispersive porous medium with Soret effect and vertical throughflow. The Oberbeck–Boussinesq approximation assumed and fluid flow obeys Darcy's law. Local thermal equilibrium is considered between solid and fluid phases. We analyze the system stability through linear instability, nonlinear stability (energy method), and weak nonlinear analysis. The expression for Ra is derived analytically, using the Galerkin orthogonalization technique. The Ginzburg–Landau equation is derived to get deep insight into convective amplitudes, also we explore the heat and mass transfer in the system by defining Nusselt and Sherwood numbers. The research delves into the influence of various physical parameters on the system's stability. The solutal Rayleigh number and Soret number have destabilizing property, whereas the Lewis number, momentum transfer coefficient, and permeability ratio have the stabilizing nature. The sub-critical region decreases as the Soret number increases. The strong buoyancy force delays the heat transfer and mass transfer by disrupting existing mass transfer. The critical Rayleigh number maintains symmetry over the upward and downward throughflow. The less area under the curve for average Nusselt and Sherwood number over permeability ratio implies total heat and mass transfer alleviating.

Combined natural and forced convection in vertical concentric annuli at high Prandtl numbers

The combined natural and forced convection in vertical concentric annuli at high Prandtl numbers is a common problem in engineering. The hydrodynamical and thermal flow state in annuli depends on the Grashof number. In this paper, first, mathematical models of the combined natural and forced convection in vertical concentric annuli at high Prandtl numbers are established. For diverse Grashof number ranges, integral and analytical methods are introduced to solve annuli's velocity and temperature profiles. Subsequently, a computational fluid dynamic simulation based on the finite volume method is carried out to verify the accuracy of the integral and analytical methods. Under various physical configurations, annuli's heat and mass transfer characteristics are accurately predicted. The relative error of the average fluid velocity is less than 4.4745%, and the relative error of the maximum temperature is less than 2.3719%. The integral and analytical methods perform much better in computation speed, increasing by 180 and 3000 times, respectively. Finally, based on the faster numerical computation scheme developed, local Nusselt number correlations suitable for different Grashof number ranges are proposed, considering different thermal and pressure boundary conditions.

Entropy generation and thermal behavior analysis of tube fitted with multi-perforation vortex generators

Entropy generation and thermal behavior analysis of tube fitted with multi-perforation vortex generators

Optimized heat transfer and drag reduction through corner modifications in square cylinders immersed in power-law fluids

This study numerically investigates fluid flow and heat transfer around a square cylinder with modified corner geometries, varying the corner radius ratio (CRR = r/d) from sharp (r/d = 0) to fully rounded corners (r/d = 0.5). Using computational fluid dynamics based on the finite volume method, the analysis is conducted for incompressible power-law non-Newtonian fluids with power-law indices (n = 0.6 to 1.4) and Reynolds numbers (Re = 5 to 40). The study focuses on how CRR influences heat transfer performance and flow behavior. Results show that increasing CRR significantly enhances heat transfer, as reflected in higher local and average Nusselt numbers (Nu). At Re = 40, the average Nusselt number (Nuavg) increases by 20%–26% when CRR changes from 0 to 0.5, demonstrating the thermal advantages of rounded geometries. Modified corners reduce recirculation lengths and delay flow separation, shifting the separation angle downstream and increasing the separation Reynolds number. These changes improve thermal mixing within the flow. Additionally, drag coefficients decrease by 7%–11% with increasing CRR, illustrating the dual benefits of drag reduction and heat transfer enhancement. Streamline, isotherms and vorticity contour plots provide detailed visualizations of boundary layer development and wake dynamics, revealing the role of CRR in disrupting flow structures and enhancing heat transport. This study highlights the potential of rounded geometries to optimize heat transfer and flow efficiency in systems using power-law non-Newtonian fluids, offering valuable insights for engineering applications.

A numerical and statistical analysis of the unsteady ternary hybrid nanofluid flow and heat transfer over a generalized stretching/shrinking wall

AbstractThis study analyzes unsteady ternary hybrid nanofluid flow and heat transfer over a generalized stretching/shrinking wall using both analytical and numerical methods. By applying similarity transformations, the governing nonlinear partial differential equations are reduced to a system of ordinary differential equations, which are numerically solved using the MATLAB bvp4c function. We find that the system exhibits two solution branches—an upper and a lower—within certain parameter ranges. A detailed stability analysis is conducted to determine the stability of these solutions. Additionally, the study presents analytical solutions for specific cases, which are relevant to heat exchangers in low‐velocity environments. Next, MINITAB software is used to statistically model the interactions of the parameters and assess their impact on the heat transfer performance (measured through the local Nusselt number), identifying low, medium, or strong effects through regression analysis. Finally, a sensitivity analysis is performed on the regression function obtained in MINITAB, focusing on key input parameters. To the best of our knowledge, this study is novel, as no previous work has explored this problem, making both the analytical and numerical results original.

Experimental study of enhanced convection in mini-tube with jet chamber insert using infrared thermometry

Experimental study of enhanced convection in mini-tube with jet chamber insert using infrared thermometry

Melting Heat Transfer Effects on MHD Chemically Thermally Radiative Micropolar Fluid Flow towards Stretching Exponentially Sheet with Heat Sink/Source

The effective use of non-Newtonian fluids is vital for situations involving heat and mass transfer. For instance, we employ thermal paste, a non-Newtonian fluid, to cool the CPU. By means of a computational approach, the behaviour of non-Newtonian on the surface of a two-dimensional steady MHD boundary layer flow and melting heat and mass transfer over a micropolar fluid is presented here, in conjunction with a partially slipper sheet at the surface providing heat generation/absorption. Further, heat radiation as well as chemical reactions are considered. Using similarity parameters, the governing nonlinear partial differential equations for heat, mass and flow are converted into a series of coupled nonlinear ordinary differential equations, then solved using the Runge–Kutta fourth order integration scheme and the shooting method. For various parameters defining the flow within the boundary layer, the new findings for velocity, microrotation, temperature and concentration are graphed. Graphic representations of local skin friction, Nusselt number and Sherwood number are provided. Boosting the melting parameter decreases fluid velocity, microrotation and temperature significantly. An intensification in slip near the boundary decreases both fluid velocity and microrotation, but opposite effects are observed on temperature.