Heat Transfer Process Research Articles

Mathematical analysis for flow of hybrid nanofluid over a vertical stretchable surface: Assisting and opposing flows

Research Problem: The importance of improving the temperature properties of commonly used fluids in industrial processes is being addressed in this research. Nanofluids, which are composed of extremely small particles dispersed in common liquids such as water or petrol, are the main subject of this area of study. Using a vertically stretchable surface subjected to thermal radiation, the study examines the heat transfer behavior and efficiency of nanofluids. Methodology: Nanofluids that convey heat are studied by applying the fundamental rules of fluid physics to the variables that control their motion. To measure the amount of energy transferred, a nanofluid model is used. Similarity transformations are used to convert the system’s differential equations into ordinary differential equations (ODEs). The subsequent set of nonlinear ODEs is solved using numerical methods. Utilizing graphical analysis, patterns of velocity and temperature may be seen, and their responses to changes in other parameters can be investigated. Implications: This research has important implications for our knowledge of how nanofluids act in heat transfer applications, especially when exposed to thermal radiation and working with vertically stretchy surfaces. The effects of flow direction and thermal conductivity on distributions of velocity and temperature were elucidated, among other important results. More effective heating and cooling systems may be possible as a result of these findings, which have consequences for improving heat transfer processes in industrial environments. Future Work: To better understand how nanofluids behave in heat transfer applications, future studies might investigate more complicated situations and boundary circumstances. It may be possible to optimize nanofluid formulations by studying the impact of various nanoparticle kinds and concentrations on heat transfer efficiency. Research could be more applicable to real-world industrial processes if the numerical results were experimentally validated.

Magnetohydrodynamic Analysis and Fast Calculation for Fractional Maxwell Fluid with Adjusted Dynamic Viscosity

From the perspective of magnetohydrodynamics (MHD), the heat transfer properties of Maxwell fluids under MHD conditions with modified dynamic viscosity present complex challenges in numerical simulations. In this paper, we develop a time-fractional coupled model to characterize the heat transfer and MHD flow of Maxwell fluid with consideration of the Hall effect and Joule heating effect and incorporating a modified dynamic viscosity. The fractional coupled model is numerically solved based on the L1-algorithm and the spectral collocation method. We introduce a novel approach that integrates advanced algorithms with a fully discrete scheme, focusing particularly on the computational cost. Leveraging this approach, we aim to significantly enhance computational efficiency while ensuring accurate representation of the underlying physics. Through comprehensive numerical experiments, we explain the thermodynamic behavior in the MHD flow process and extensively examine the impact of various critical parameters on both MHD flow and heat transfer. We establish an analytical framework for the MHD flow and heat transfer processes, further investigate the influence of magnetic fields on heat transfer processes, and elucidate the mechanical behavior of fractional Maxwell fluids.

Configuration optimization of a biomass chemical looping gasification (CLG) system combined with CO2 absorption

Biomass chemical looping gasification (CLG) combined with CO2 absorption in a dual circulating fluidized bed (DCFB) has emerged as an advanced technology for clean and efficient biomass utilization, yet the reactor design for achieving higher gasification performance and the in-depth understanding of physical-thermal-chemical characteristics is still lacking. This study presents an optimized design aimed at enhancing hydrogen production and carbon reduction in the biomass CLG process with a DCFB reactor by employing the multiphase particle-in-cell (MP-PIC) method integrated with thermochemical sub-models. The proposed reactor is comprehensively compared with the original reactor from the experimental setup in terms of particle mixing, heat transfer, and gasification behaviors. The results indicate that compared to the original setups, the proposed CLG system demonstrates: (i) an improved gas-solid mixing, as evidenced by the particle mixing index rising from 0.23 to 0.34; (ii) an enhanced particle heat transfer coefficient, which boosts heat and mass transfer process; (iii) a 10.11 % increase in H2 concentration alongside a 23.71 % decrease in CO2 concentration; (iv) a particle distribution characterized by higher concentration at the bottom and lower concentration at the top, along with intensified particle back-mixing. The pressure drop inside the combustor is higher than that in the gasifier. A smaller absorbent mean particle diameter and lower-positioned biomass feeding port contribute to the improvement of the CLG performance.

ANALYSING THE EFFICIENCY OF USING POROUS METALS IN HEAT EXCHANGERS

This study focuses on analysing the effectiveness of porous metals in heat exchangers, focusing on their effect on improving heat transfer processes. Porous metals, due to their unique structure, have high thermal conductivity and increased contact surface area, which contributes to more efficient heat transfer. As part of the study, experiments and theoretical analyses were carried out to evaluate the effect of porosity coefficient on heat exchange performance. The plotted dependence of Freon mass flow rate and heat quantity on porosity coefficient demonstrate the linear nature of these dependencies. Mathematical processing of the data showed that an increase in the porosity coefficient leads to an increase in both the amount of heat transferred by Freon and Freon mass flow rate, indicating an increase in heat exchange efficiency. The results confirmed that porous metals can significantly improve the performance of heat exchangers and energy saving. Based on the study, further investigation and implementation of porous metals in heat exchangers is recommended to optimise their performance and improve the overall system efficiency. These results open new perspectives for the application of porous metals in various industries including power and mechanical engineering.

Non-steady flow decomposition behaviors of heat and mass transfer on intrinsic kinetics for methane hydrate particles transported in pipelines

The differential equations governing the decomposition rate and activation energy, convective mass transfer, methane diffusion and fugacity, as well as heat conduction and enthalpy change were derived by integrating thermal convection, heat conduction, mass transfer and intrinsic kinetics. Mathematical models for decomposition kinetics and thermodynamics in a non-steady field were solved using a radial logarithmic grid for node division and discretization of the equations. The study elucidated the heat and mass transfer processes as well as decomposition kinetics in pipelines by analyzing the impacts of particle size, temperature, pressure, flow rate and activation energy on decomposition rate. The results indicated that compared with the isothermal decomposition of the intrinsic kinetic model and static experimental decomposition, the complex non-steady multiphase flow model offers a more accurately simulation of hydrate decomposition as well as associated heat and mass transfer processes. Hydrate decomposition is characterized as a non-isothermal dynamic ablation process with heat transfer rate and intrinsic kinetics dominating during the preliminary stage and the stable stage, respectively. An increasing in the slurry temperature, temperature fluctuation and flow rate accelerated the heat transfer rate capacity, enhanced convective heat transfer capacity and facilitated hydrate decomposition, with the mass transfer rate exhibiting lesser influence. The particle surface area and slurry temperature exhibited the most significant influence on hydrate decomposition, which was followed by flow rate. Upon increasing particle size from 1 mm to 5 mm and the temperature from 293 K to 313 K, the decomposition rate increased by 20.7 times and 13.5 times, respectively. Furthermore, enhancing temperature and flow rate while decreasing particle size and pressure decreased both the decomposition time and the duration required for the decomposition rate to reach its peak. Additionally, the decomposition rate and its constant vary with the activation energy.

Optimization of the annular fin arrangement in phase change heat storage units based on response surface methodology

Latent heat thermal energy storage (LHTES) technology is of increasing industrial interest due to its advantages such as high heat storage density and near-constant temperature during the phase change process. However, the latent heat storage technology is impacted by the low thermal conductivity of the phase change material (PCM), leading to delays and heat loss in the heat transfer process within LHTES. This limitation reduces the efficiency of heat transfer and diminishes the performance of the heat storage unit. To address this issue, this paper employs numerical simulation and response surface methodology to investigate different types of annular fin phase change heat storage units, aiming to derive the optimal configuration for enhancing unit performance. Therefore, the effect of fin type and number on the melting and solidification process is analyzed in detail. The research results indicate that among the five different types of fins studied, the total time required for the unit to complete melting and solidification is the least with type “e” fins, only 51.78 h, demonstrating that type “e” fins have the best effect on improving unit performance. For type “e” fins, when the number of fins n is 15, it can most effectively shorten the melting and solidification time of the phase change heat storage unit, reducing it to only 47.81 h. In addition, the response surface methodology was utilized to derive the optimal fitting formulas for different types of annular fins and to validate these formulas, and the error between the validation analysis and the numerical simulations was within 5%, which confirms the reliability of the fitting formulas developed in this study. This approach facilitates the selection of various annular fin models for subsequent experimental and simulation studies, thereby reducing the time and cost associated with model selection.

Studying the influence of coolant speed on the processes of heat and mass transfer in technological equipment for processing disperse materials

Studying the influence of coolant speed on the processes of heat and mass transfer in technological equipment for processing disperse materials

Analysis of electroviscous effects in electrolyte liquid flow through a heterogeneously charged uniform microfluidic device

Charge-heterogeneity (i.e., surface charge variation in the axial direction of the device) introduces non-uniformity in flow characteristics in the microfluidic device. Thus, it can be used for controlling practical microfluidic applications, such as mixing, mass, and heat transfer processes. This study has numerically investigated the charge-heterogeneity effects in the electroviscous (EV) flow of symmetric (1:1) electrolyte liquid through a uniform slit microfluidic device. The Poisson’s, Nernst-Planck (N-P), and Navier–Stokes (N-S) equations are numerically solved using the finite element method (FEM) to obtain the flow fields, such as total electrical potential (U), excess charge (n *), induced electric field strength (E x), and pressure (P) fields for following ranges of governing parameters: inverse Debye length (2 ≤ K ≤ 20), surface charge density (4 ≤ S 1 ≤ 16), and surface charge-heterogeneity ratio (0 ≤ S rh ≤ 2). Results have shown that the total potential (∣ΔU∣) and pressure (∣ΔP∣) drop maximally increase by 99.09% (from 0.1413 to 0.2812) (at K = 20, S 1 = 4) and 12.77% (from 5.4132 to 6.1045) (at K = 2, S 1 = 8), respectively with overall charge-heterogeneity (0 ≤ S rh ≤ 2). Electroviscous correction factor (Y, i.e., ratio of effective to physical viscosity) maximally enhances by 12.77% (from 1.2040 to 1.3577) (at K = 2, S 1 = 8), 40.98% (from 1.0026 to 1.4135) (at S 1 = 16, S rh = 1.50), and 41.35% (from 1 to 1.4135) (at K = 2, S rh = 1.50), with the variation of S rh (from 0 to 2), K (from 20 to 2), and S 1 (from 0 to 16), respectively. Further, a simple pseudo-analytical model is developed to estimate the pressure drop in EV flow, accounting for the influence of charge-heterogeneity based on the Poiseuille flow in a uniform channel. This model predicts the pressure drop ± 2%–4% within the numerical results. The robustness and simplicity of this model enable the present numerical results for engineering and design aspects of microfluidic applications.

Thermal Energy Resource Potentials of the Kara-Bogaz-Gol Gulf as a “Solar Pond”

Introduction. The use of environmentally-friendly engineering systems including solar energy technologies makes it possible to reduce energy costs and therefore to lower production costs and anthropogenic stress on the environment.Aim of the Study. The authors used innovative techniques to assess the thermal resource potential of solar radiation, to analyze the salt deposits of the Kara-Bogaz-Gol Gulf as thermal accumulators for the development, introduction and use of solar thermal technologies and to justify the technical and economic feasibility of their use in engineering systems in the Kara-Bogaz-Gol Gulf (Caspian region).Meterials and Methods. The study design is based on systematic theoretical calculations of the gross, technical, economic and ecological potentials of solar radiation taking into account environmental conditions. For calculating there were used the methods of mathematical modeling of heat and mass transfer processes in active solar energy systems when converting solar energy into thermal energy in the salty reservoir of the Kara-Bogaz-Gol Gulf as a “solar pond”.Results. There have been assessed the solar energy characteristics for the introduction of various engineering storage systems and technologies. There have been determined the results of energy storage on the reservoir salt surface during the day: in winter – 1 009.0 W/m2 per day, in summer – 1 574.7 W/m2 per day. It has been proven that the potential of solar energy conversion into thermal energy varies from 40 to 70% depending on the season. Aaccording to theoretical calculations, the solar pond efficiency in winter is 11.4% and in summer – 14.6%. In summer, there was measured the average temperature on the salt surface of the reservoir bottom, it ranges from 55.04 to 79.8 ºC, in winter from 20.0 to 25.6 ºC.Discussion and Conclusion. The results obtained can be used for strengthening energy security, developing energy systems and producing autonomous thermal power devices based on solar energy that will reduce the energy consumption of fossil fuels and improve the environmental situation in the region. The materials of the article can be used in preparing design estimates and feasibility study for developing various solar energy systems and technologies in the Caspian region.

Modeling of Filtration and Heat and Mass Transfer Processes in Groundwater

Purpose. The method of mathematical modeling is an important tool for solving complex problems involving the analysis of groundwater dynamics and heat and mass transfer processes in them when studying their contamination from various anthropogenic sources in the event of accidental spills of chemically hazardous substances, etc. The main purpose of the article is to develop a set of mathematical models for calculating the process of filtration of non-pressure groundwater, mass transfer of impurities and the process of heat transfer in groundwater. Methodology. The two-dimensional Boussinesq equation of filtration was used to predict the dynamics of groundwater. The two-dimensional equation of convective-diffusive transport of impurities was used to model the processes of mass transfer in groundwater. The process of freezing of individual sections of the groundwater flow is modeled using the Laplace equation for the velocity potential (calculation of the flow velocity field in a time-varying geometry) and the two-dimensional equation of heat transfer in groundwater. Finite difference schemes were used to solve the modeling equations of groundwater dynamics and heat and mass transfer. Findings. A set of mathematical models has been developed to calculate the process of filtration of non-pressure groundwater and its chemical contamination. The experiment has confirmed the adequacy of the constructed numerical model of filtration of a non-pressure groundwater flow. An effective mathematical model was developed that allows determining the temperature fields in groundwater during the operation of a well used to freeze certain sections of the flow. The results of computer modeling indicate the effectiveness of the developed mathematical models. Originality. Effective mathematical models for predicting the level of chemical contamination of groundwater, its dynamics and thermal regime are proposed. The constructed mathematical models make it possible to determine the dynamics of changes in the temperature regime of groundwater during the operation of wells through which refrigerant is supplied to freeze individual areas. A computer program has been developed that allows for a comprehensive assessment of groundwater conditions. Practical value. A set of computer programs has been developed to conduct a computational experiment to study the processes of filtration, chemical contamination of groundwater and heat transfer processes in them. This set of programs can be used for the scientific substantiation of engineering solutions aimed at protecting groundwater.

Study on Oxygen-Enriched Combustion Characteristics of Blast Furnace Gas Boiler

ABSTRACT To study the dynamic characteristics of OEC (oxygen-enriched combustion) in a BFG (blast furnace gas) boiler, the BFG boiler of an iron and steel enterprise is taken as the research object, and a thermal test bed for OEC of BFG is set up, and a thermodynamic simulation model of the BFG boiler is constructed based on the heat loss of chemical incomplete combustion obtained from thermal test, using MSP (Multi-Subject Simulation Platform). The effects of OC (oxygen concentration) and the position of oxygen entering the furnace chamber on the key parameters of the OEC process of the BFG boiler under different working conditions were analyzed. The results showed that the excess air coefficient of 1.2 and exhaust temperature of 120°C was kept constant during the thermal test. With a fuel volume of 2.4 Nm3/h, for example, after the OC was increased from 21% to 40%, the combustion flame temperature in the furnace was increased by about 34°C, the heat loss due to unburned gas was reduced by 0.21%, and the boiler efficiency was increased by 1.38%. In the dynamic model, at the instant when the OC is changed, the disturbance of the whole system is relatively large, and the FAT (furnace average temperature) outlet, the pressure of the steam ladle, and the MST (main steam temperature) will have a step change, and then gradually level off again. With the increase of OC, the combustion reaction is more and more intense, the steam side of the heat transfer process is strengthened, the boiler efficiency is improved, and the FAT chamber outlet, the steam ladle pressure and the MST after OEC in different ways of oxygen entry into the furnace chamber will be longer and longer to reach a stable value. The results of the study can provide a reference for the OEC operation of BFG boilers.

A coupled local front reconstruction and immersed boundary method for simulating 3D multiphase flows with contact line dynamics in complex geometries

Multi-phase flows in the presence of complex solid geometries are encountered widely throughout industrial processes to intensify mass and heat transfer processes. The efficiency of these processes relies largely on the predominant fluid dynamics regime inside the reaction vessel (e.g. trickle bed, bubble column reactor). The prevailing flow structure is influenced by many factors including the nature of the fluid-solid interactions (i.e. wetting or non-wetting). Such flows are often studied using front-capturing techniques to capture the fluid-fluid interface in combination with an auxiliary model to account for fluid-solid interactions. However, these front-capturing methods have difficulties in accurately representing the interface. Therefore, we adopted a front-tracking method: the Local Front Reconstruction Method (LFRM). In this study, LFRM is coupled with the Immersed Boundary method to incorporate the no-slip boundary condition at the solid surface. The model performance is assessed using droplet spreading simulations, where the equilibrium droplet shape (i.e. radius, height, and outline), the interfacial pressure difference, and the surface tension force are compared to analytical solutions and literature data. The results show an excellent match with the analytical solutions, and additionally superior performance to state-of-the-art volume tracking models.

Convective diffusive thermal flow over an inclined surface with viscous dissipation and aligned magnetic field applications

This investigation incorporating the fluctuation in heat and mass transfer associated to the mixed convection magnetized flow of viscous fluid due to inclined surface with porous media. The contribution of Soret effects and viscous dissipation appliances is addressed. Furthermore, the heat transfer improvement is also assessed by thermal radiation, heat source and joule heating effects. The chemical reaction enrollment is also studied for concentration phenomenon. The convection of problem into non-dimensional framework is based on implication of new variables. The perturbation technique is followed to tracking the analytical outcomes. Physical visualization and interpretation of results under the influence of perturbed parameters have been studied. It is observed that heat and mass transfer enhances due to Soret number. Presence of chemical reaction leads to decrement of concentration profile. Claimed results presents applications in heat and mass transfer processes, chemical reaction, manufacturing systems, chemical engineering, extrusion processes etc.

Humic substances and inorganic ions synergistically precipitate at the gas–liquid interface in a simulation experiment of direct-contact heat and mass transfer processes

Direct-contact heat and mass transfer processes are widely employed in saline wastewater treatment. However, these processes are accompanied by serious ultrafine particle emission, a phenomenon associated with the solute’s transition across the gas–liquid interface. A thorough comprehension of the solute’s behavior at this gas–liquid interface is vital for clarifying the crossing process and guiding particle control strategies. Here, solutions containing saturated inorganic ions and humic substances were evaporated to analyze their behaviors at the gas–liquid interface in an experimental simulation of direct-contact heat and mass transfer processes. It was found that these substances co-precipitated at this interface. Humic substances can bind with inorganic ions via chemical bonds, monovalent ions through cation-π interactions, and divalent ions through electrostatic and chelation interactions. Moreover, humic substances can act as nucleation sites for precipitating inorganic crystals. These distinctive binding mechanisms caused a synergistic relationship between humic substances and inorganic ions during precipitation. Amidst precipitation, humic substances with high humification degrees and large molecular weights were predominantly enriched. Inorganic ions, comprising over 93% of the total precipitate mass, constituted the principal constituents. Among these, Na+, with an enrichment factor of 2.10, precipitated more readily at the gas–liquid interface compared to divalent ions. These conclusions concerning the binding mechanisms of humic substances and inorganic ions, along with their precipitation characteristics, were validated in the submerged combustion evaporation process of membrane-concentrated leachate.

Geometric optimization of Kenics-type static mixers: numerical analysis of thermal and dynamic performance

Static mixers play an important role in industry by facilitating mixing and heat transfer processes. This study investigates the effect of geometry on the thermal and dynamic performance of a Kenics-type static mixer by examining four different configurations. Numerical simulations using Fluent.20 software were used to analyze parameters such as Reynolds number (ranging from 0.1 to 80), pressure drop, shear rate, fluid temperature, and Nusselt number. The results highlight the critical importance of geometry in fluid dynamics, which affects thermal performance. Among the configurations studied, the third case, characterized by three cavities occupying the entire length of the helix, proved to be the most efficient. This research thus provides valuable insights into the dynamic and thermal characteristics of kinetic static mixers, underscoring the critical importance of geometry in optimizing overall performance. What's more, this performance improvement can be observed at different Reynolds numbers, resulting in improved mixing efficiency and reduced pressure losses. This study shows that the third geometric configuration outperforms the other proposed mixers, with a performance improvement of 99%.

Predicting the Consequences of an Emergency at a Railway Station

Purpose. The paper considers the problem of determining the size of the damage zones in the event of an emergency at a railway station due to a tanker fire. The task of forecasting is to determine the zones of thermal pollution, as well as chemical and mechanical pollution. The main objective of the study is to create numerical models for calculating the zones of mechanical and thermal pollution in the event of a fire at a railway station. Methodology. To analyze the size and intensity of zones of thermal, chemical, and mechanical environmental pollution in the event of an extreme situation at a railway station, we used the equations of heat and mass transfer and Newton's second law for modeling mechanical environmental pollution. To solve the equations, numerical methods such as Euler's method and finite difference schemes were used. On the basis of the developed numerical models, a computer code was created to conduct a computational experiment. Findings. Modern computer models for assessing the zones of chemical, thermal, and mechanical pollution in the event of an extreme situation have been developed. The results of computer modeling are presented. Originality. A set of numerical models for computer simulation of heat and mass transfer processes and dynamics of point motion has been created, which allows conducting a computational experiment to determine the contamination zones during a fire at a railway station. Practical value. A computer code was developed on the basis of the created mathematical models. This code is a tool for solving important problems in the field of environmental safety and civil protection. The computer code makes it possible to quickly determine the intensity and size of environmental pollution zones in the event of an extreme situation.

Nusselt and Reynolds numbers correlation for oscillatory flow of thermoacoustics over heated tube banks

The back-and-forth motion characteristic of the oscillatory flow brings complexity in predicting the heat transfer nature for thermoacoustic wave conditions. Investigating this is crucial as the flow forms the backbone for the thermodynamic cycles of its operation. Often, the steady approximation in calculating heat transfer leads to ambiguity in designing the system. This concern is addressed in this paper via an in-depth analysis of the fluid dynamic behavior and heat transfer characteristics of oscillatory flow within a thermoacoustic framework, spanning experimental works for Reynolds numbers ranging from 300 to 24,000. The investigation focused on a tube bank heat exchanger composed of nine tubes arranged in inline and staggered configurations. Experiments were conducted at constant tube surface temperatures treated at 40 °C and 80 °C, respectively. The distinguishing difference in heat transfer behaviors for oscillatory flow is visualized by the Computational Fluid Dynamics (CFD) models, employing the Reynolds-Averaged Navier Stokes equation with the k-omega turbulence shear stress transport model. The flow never leaves the system, and it cyclically crosses the tubes back and forth with a travel distance that depends on the drive ratio of the flow. The unique nature of the flow forms the foundation for the experimental findings that show a linear relationship between the Nusselt and Reynolds numbers regardless of the configuration of tube banks and tube bank temperature. The Pearson ruler regression analysis was conducted using Matlab R2022b and a Nusselt correlation, Nu = 0.000853RePr⅓, is proposed with a confidence level of 95 %. Notably, the correlation aligns with the constant value known as the Colburn-j factor, with a value of 0.00083. The small Colburn-j value is shown to be the influence of the log-mean temperature difference characteristic of oscillatory flow. It shows a consistent heat transfer process between the heated tubes and surrounding fluid, which is important to sustain the thermoacoustic effect in the system. For future thermoacoustic design, the use of steady heat transfer correlation should be avoided or at least used with caution as the comparative analysis with published works concluded that the Nusselt and Reynolds correlation for steady flow tends to overpredict the heat transfer by two to threefold.

Enhanced framework for solving general energy equations based on metropolis-hasting Markov chain Monte Carlo

Due to the widespread presence of heat and mass transfer phenomena in industrial applications, numerous studies have been devoted to the accurate solution of energy equations, providing a foundation for the analysis of heat and mass transfer processes in practical applications. In this study, a Green's Function Markov Superposition Monte Carlo (GMSMC) for solving general energy equations has been developed based on probability and statistical principles owing to its advantageous features of insensitivity towards dimension and geometric complexity as well as the capability to handle multiple integrals in complex domains. The energy equation is first decomposed, and corresponding probability models are established for each component, considering their interrelationships. Subsequently, a solution framework for solving the general energy equation is constructed by integrating these probability models based on a Markov chain structure. The mathematical principles and formulae of the proposed method are derived in detail. The performance of the proposed method is validated by several heat transfer systems with different combinations of boundary conditions and features, which mainly include the distribution of the internal heat source and whether the convection or transient term is included. Results of the validation show that the temperatures obtained by the proposed method are in good agreement with the FEM based on a fine grid, no matter whether the calculation is for a single point or a distribution.

Interfacial property determination from dynamic pendant-drop characterizations.

The properties of the interface between materials have practical implications in various fields, encompassing capillary action, foam and emulsion stability, adhesion properties of materials and mass and heat transfer processes. Studying the dynamics of interfaces is also fundamental for understanding intermolecular interactions, change of molecular conformations and molecular aggregations. Pendant-drop tensiometry and its extension, the oscillating drop method, are simple, versatile methods used to measure surface tension, interfacial tension and interfacial rheological properties. These methods can, however, generate unreliable results because of inadequate material preparation, an incorrect calibration method, inappropriate selection of data for analysis, neglect of optical influences or operating the system outside the linear viscoelastic regime. In addition, many studies fail to report accurate uncertainties. This protocol addresses all these critical points and provides detailed descriptions of some operation tips relating to purifying methods for different kinds of material, the time frame for analyzing measurement data, the correction method for optical effects, implementation of the oscillating method with a common programmable pump and remedies for some common problems encountered during the measurement. Examples of interfacial tension measurements for two- and three-phase systems, as well as interfacial dilational modulus measurements for N2 and surfactant solutions, are provided to illustrate procedural details and results. A single measurement takes minutes to hours to complete, while the entire protocol, including the leak test, cleaning, repeated measurements and data analysis, may take several days.

Numerical Study of the 3D MHD Radiative Flow of Williamson Nanofluid with Variable Characteristics Over a Double Stretching Sheet

The current study investigates the influence of variable thermal conductivity and mass conductivity on 3D MHD. The significance of this study lies in mass diffusion on a three-dimensional Williamson nanofluid fluid flow over a double stretched sheet. When thermal radiation and Hall current is present, the heat transfer process is explored to see how chemical reactions affect heat and mass transmission. Additional phenomena, such as momentum slip and convective boundary conditions, contribute to the model's uniqueness. The problem formulation becomes ordinary differential equations with application of the Von Karman similarity variable. Use of the bvp4c function in yields a numerical solution for the system of differential equations. Using MATLAB’s bvp4c function, a numerical solution to the differential equation system is obtained. A graphic is used to discuss the overall result of several metrics compared to the involved profiles. It is believed that as temperature-dependent thermal conductivity and viscosity increase, so does the temperature field. When the Williamson fluid and magnetic parameters rise, the velocity field decays in the x- and y-axis directions. To support the identified issue, a comparison between the current inquiry and a previously published work is also included.