Similarity Transformation Research Articles

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.

Interplay of Structural Properties and Redox Behavior in CeO2 Nanoparticles: Impact on Reactivity and Bioavailability.

The environmental redox transformation of CeO2 is crucial for evaluating its ecological risk and understanding the geochemical cycling of cerium (Ce). In this study, we examined the effects of crystallinity on CeO2 dissolution and monitored the structural evolution during redox transformations. The reductive dissolution and reoxidation behavior of CeO2 (100 mg/L) was examined in the presence of 200 μM citrate. Our findings indicate that ligand-induced dissolution is more pronounced in CeO2 with lower crystallinity under both dark and light conditions. This dependence is related to the intensive ligand complexation at oxygen vacancy sites, resulting in a higher complexation of Ce(III) and more efficient photoelectron generation for Ce(IV) reduction. During cyclic dissolution-reprecipitation, CeO2 notably transformed into an amorphous phase, progressively decreasing the crystallinity of the nanoparticles. Consequently, the dissolution fraction of well-crystallized CeO2 increased significantly from 1.2% in the first cycle to 11.4% in the third cycle, suggesting a transition to structures with higher interfacial reactivity. Similar transformation and dissolution behavior was observed in redox oscillations in a soil environment. Additionally, hydroponic exposure experiments with Arabidopsis thaliana, treated with 100 mg/L CeO2 for 7 days, demonstrated increased Ce uptake by roots post-transformation, with a higher proportion of CePO4 detected within the plants. This comprehensive study not only provides vital mechanistic insights into the transformation processes of CeO2 but also aids in assessing the ecological risks associated with engineered CeO2 nanomaterials.

Regression analysis for multiple shape effects on magnetized power law nanofluid flow along a thin needle: An application in targeted drug delivery system

Nowadays, therapeutics mainly depend on drug delivery and magnetic nanofragments in the human body’s circulatory system. The drug particles are infused into the bloodstream with magnetic effects during this treatment, which is normally applied and aids in releasing the medications to the proper organs under magnetic intensity. Numerous medical procedures employ this approach, such as targeted drug delivery, cancer treatments, reduction of excessive bleeding during surgery, the healing process of wounds, and magnetic attraction of blood. However, the nanoparticle’s shape factor causes faster/slower drug release before/after reaching its targeted region. This study strives to investigate the effects of nanoparticle shape on the magnetized power law fluid flow along a thin needle. Additionally, viscous dissipation, suction, and ohmic heating are also considered. The governing equations are transformed with the help of appropriate similarity transformation into a dimensionless form and solved using the Bvp4c technique. The findings reveal that the magnetic field and needle thickness reduce fluid velocity. Further, regression analysis is incorporated to provide further insight into engineering quantities. The platelet-shaped nanoparticle averagely transmits thermal energy an average of [Formula: see text] more than brick, [Formula: see text] more than the blade and [Formula: see text] more than cylinder-shaped nanoparticles.

Theoretical Analysis of Nonlinear Partial Differential Equations with Mixed Boundary Conditions

The solution of author’s mathematical model of Magnetohydrodynamics (MHD) flow of a Casson fluid is discussed. The given nonlinear partial differential equations are converted into nonlinear ordinary differential equations using similarity transformations. The simple and closed form analytical expression for concentration profiles is provided. The compatibility of analytical results with simulation results can be observed from the graphs and table presented.

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.

The Influence of Uncertainty, Communication and Employee Passion on Readiness to Change at PT XYZ

Organizational change often brings uncertainty among employees, which can affect their readiness to adapt to the change. In this context, effective communication and employee passion are key factors in reducing uncertainty and increasing readiness to change. PT XYZ, a large manufacturing company in Indonesia, is undergoing a digital transformation through the implementation of a new ERP system aimed at improving work efficiency and effectiveness. This study aims to explore the influence of uncertainty, communication, and passion on employee readiness to change at PT XYZ. The objective of this study is to examine the influence of uncertainty, communication, and employee passion on readiness to change at PT XYZ. This study also aims to identify the most significant factors affecting employee readiness to adapt to the ongoing changes. Thus, it is expected that this research will provide valuable insights for PT XYZ's management in managing change and minimizing employee resistance. Using a quantitative approach, data were collected from 266 employees across various departments and analyzed with the Partial Least Squares (PLS) method. The findings reveal that uncertainty negatively affects readiness to change, while effective communication and employee passion significantly enhance it. Notably, communication effectiveness and employees’ enthusiasm for change emerged as key drivers of organizational adaptability. The study highlights the need for PT XYZ’s management to minimize uncertainty through transparent communication strategies and foster a positive work culture to enhance employee readiness. These insights provide valuable guidance for organizations undergoing similar transformations, emphasizing the critical role of communication and employee engagement in change management success.

Mechanical behaviour of dual-phase SS301 under cryogenic conditions

The present work is the first comprehensive investigation of the cryogenic behaviour of dual-phase SS301 stainless steel over an extensive temperature range, including 20 K, 30 K, 40 K, 77 K, 120 K, 150 K, 170 K, and 300 K. The range of temperature involved in this study renders critical insights on the temperature sensitivity of the mechanical properties of SS301, such as yield strength, and ultimate tensile strength. This work notably unravels that the ductility and toughness of dual-phase SS301 remain largely unchanged between cryogenic and room temperatures owing to the similar level strain-induced transformation of martensite, and the resulting comparable phase-fractions. Furthermore, in addition to the two-stage serrations which are generally observed in discontinuous plastic-deformation, the present investigation reveals that the yield at 40 K accommodates four-stage serrations. However, interestingly, the four-stage of the serrations at 40 K progressively transition into two-stages as the deformation proceeds. Ultimately, the current work elucidates the mechanical behavior of dual-phase SS301 at cryogenic temperatures, in contrast to the more commonly analyzed austenitic stainless steels.

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.

Ferrohydrodynamic on Heat Transfer in Hybrid Ferrofluid over an Elongation Sheet

Advancing hybrid ferrofluids enhances biomedical engineering and leads to better treatments for cancer and other diseases. Due to their distinctive composition, they exhibit enhanced thermal conductivity, rendering them exceptionally efficient for hyperthermia therapies, which include eliminating the growth of cancer cells at increased temperatures. This study investigates the influence of magnetism on a hybrid ferrofluid flowing past an elongation sheet. The combination of magnetite ferrite-cobalt ferrite nanoparticles (Fe_3 O_4/CoFe_2 O_4) dispersed in a water-ethylene glycol mixture, in the presence of a magnetic dipole, is analysed. The governing equations of the hybrid ferrofluid are derived using Tiwari and Das's model. Subsequently, the similarity transformation approach is applied to simplify the partial governing equations and the Keller box method is employed to solve them. The numerical results of velocity and temperature distributions for pertinent parameters, such as ferrohydrodynamics (FHD) effect and concentrations of the nanoparticles, are graphically presented. The results indicate that the FHD impact diminishes the velocity profile, but enhances the temperature field of the hybrid ferrofluid flow. The shear stress is enhanced by 90.79% and the heat transfer rate is reduced by 12.12%. The presence of hybrid nanoparticles in the fluid not only enhances the temperature distribution but also suppresses the movement of the particles. These outcomes provide insights into the interplay between magnetic fields and heat transfer, relevant to magnetic hyperthermia cancer treatment.

Analytical simulation of mixed convective Williamson nanofluid flow above a stretched Riga plate considering viscous dissipation effects

This work examines, accounting for viscous dissipation, an analytical simulation of mixed convection heat transfers in a Williamson blood base nanofluid flow on a stretched Riga plate (RP). The Lorentz force, which influences fluid dynamics, is produced by the alternating magnetic fields that comprise the RP. The flow characteristics are further complicated by the blood base Williamson nanofluid’s (WN) non-Newtonian behavior. The governing partial differential equations (PDEs) for momentum and energy are transformed into a set of nonlinear ordinary differential equations (NODEs) by similarity transformations. We solve these equations analytically using the homotopy analysis method (HAM). We investigate in detail how the temperature and velocity profiles (VPs) are affected by significant parameters as the Williamson parameter (WP), viscous dissipation, volume friction of nanoparticles, modified Hartmann number (MHN), heat generation parameter and Biot number (BN). The findings show that the thermal conductivity (TC) of nanoparticles is increased, improving the efficiency of heat transfer. Moreover, a Lorentz force generated by the RP considerably alters the temperature and flow fields. With regard to the design and optimization of thermal systems utilizing complex boundary conditions (BCs) and non-Newtonian nanofluids, this work offers significant new insights.

Analysis of heat transfer of second-grade hybrid nanofluid and optimization using response surface methodology for thermal enhancement

The fluid flow and heat transfer applications in coaxial double-revolving disks are extensive and encompass multiple engineering and scientific disciplines. This study presents a comprehensive heat transfer analysis in a second-grade hybrid nanofluid. The fluid, influenced by variable thermal conductivity, is confined between two rotating disks in a magnetohydrodynamic Darcy-Forchheimer flow. The hybrid nanofluid combines titanium dioxide (TiO2) and cobalt ferrite (CoFe2O4) nanoparticles with engine oil. These issues have not been addressed in previous research. Similarity transformations make flow equations dimensionless. The resulting equations are solved using a semi-analytical approach called the homotopy analysis method (HAM). This approach provides flexibility in selecting the base function and an initial estimate. The temperature profile improved with higher values of the variable thermal conductivity parameter. Furthermore, the heat transfer rate was enhanced by increasing the variable thermal conductivity, the volume fraction concentration of TiO2, and the Reynolds number.The sensitivity analysis is performed using response surface methodology (RSM). Both the R-squared and adjusted R-squared values attain 100%. The heat transfer rate is found to have a maximum sensitivity of 0.50243 towards varying thermal conductivity parameters and a minimum sensitivity of -0.00666 towards magnetic field parameters. The research utilizes RSM to elucidate methods for improving heat transfer. This work offers practical solutions for developing more efficient thermal management systems. This research provides practical strategies for improving thermal management systems. These solutions are especially useful in rotating machinery-intensive industries. Designing biochemical and pharmaceutical microfluidic pumps and mixers requires understanding hybrid nanofluid flows between spinning disks.

Six Decades of Rural Landscape Transformation in Five Lebanese Villages

During the last six decades, Lebanon’s landscapes have undergone significant regime shifts whose causes are under-investigated. Using land cover maps from 1962 and satellite imagery from 2014 and 2023 in five randomly selected villages across Lebanon’s major agroecological zones (AEZs), we identified salient trends in the urbanization-driven transformation of land use and land cover (LULC). Household socio-economic characteristics and environmental pressures were analyzed as independent variables influencing land use decisions. Logistic regression (LR) was employed to assess the significance of these variables in shaping farmers’ choices to transition toward “perennialization”—namely fruit tree monocropping or protected agriculture. The LR results indicate that education reduced the likelihood of “perennialization” by 45% (p < 0.001). Farm size positively influenced “perennialization” (p < 0.01), suggesting that land availability encourages this agricultural practice. In contrast, water availability negatively affects “perennialization” (p < 0.01), though farmers may still opt to irrigate by purchasing water during shortages. Our findings underline the complex interplay of socio-economic and environmental dynamics and historical events in shaping Lebanon’s rural landscapes and they offer insights into similar transformations across the Middle East and North Africa (MENA) region.

Numerical Analysis of Heat Transfer and Flow Characteristics of Jeffrey Nanofluid Over Stretched Surfaces With MHD and Slip Effects

ABSTRACTThis study employs the Jeffrey fluid model to investigate stress relaxation in non‐Newtonian fluids, offering a more precise representation than conventional viscous models. It explores the influence of multiple slip conditions and magnetohydrodynamics (MHD) on Jeffrey fluid flow and heat transfer across irregular surfaces. Additionally, the impact of thermal radiation and internal heat sources on heat transfer is examined, essential for a comprehensive understanding of the system's thermal dynamics. Using the Buongiorno model, the diffusion and thermophoresis of nanoparticles within the flow are analyzed. Nonlinear coupled governing equations covering flow dynamics, heat transfer, and nanoparticle transport are transformed into ordinary differential equations (ODEs) through similarity transformations and solved numerically using the Runge–Kutta fourth‐order (RK4) method combined with shooting techniques. Results indicate significant effects of physical parameters on temperature, velocity, and mass profiles: a 20% decrease in temperature profiles with an increase in the dimensionless thermal slip coefficient from 0.1 to 0.5 and a 15% reduction in velocity profiles from a 0.1 unit increase in the magnetic parameter . The study also quantifies mass and heat transfer rates to elucidate their impacts. These findings have profound implications for engineering applications involving non‐Newtonian and nanofluids in complex geometrical configurations.

Rural Transformation in the Philippines and the Role of Institutions, Policies, and Investments

This paper examines the status and rural transformation trends in the Philippines. Using secondary data covering 1988 to 2023, the levels of rural transformation across the country’s sixteen regions were analyzed based on three key indicators: the share of gross value added in high-value agriculture to the total GDP of agriculture, forestry and fishery, share of off-farm employment to the total rural labor force, and agricultural labor productivity. Through a panel regression analysis, this study also determined how selected institutional reforms, policies, and investments (IPIs) influenced the rural transformation that happened in the regions. The findings reveal that rural transformation in the Philippines has been generally slow because of the uneven progress across its local regions, with only three out of the sixteen regions reaching a high level of rural transformation from 1988 to 2023 and two regions remaining at low level of transformation, while the rest are still moving from a slow to moderate level of transformation. This study highlights the critical role of IPIs in driving rural transformation, demonstrating that their effects vary depending on the transformation stage of each region. These results underscore the need to properly identify, logically sequence, and efficiently integrate IPI interventions to address the transformation challenges effectively. Beyond its Philippine context, this study provides insights applicable to other developing countries facing similar rural transformation challenges, offering a replicable methodology for analyzing the transformation and guiding context-specific strategies.

Thermal Analysis of Eyring-Powell Hybrid Nanofluid: A Case of Combined Convective Transport and Radiative Heat Flux along Inclined Stretching/Shrinking Sheet

Hybrid nanofluids are designed to improve conventional nanofluids' stability and other thermal properties. The present work investigates the flow of combined convective transport and the influence of radiation on the studied flow. A hybrid nanofluid ( Cu Al O  2 3 /water) flows through a vertically inclined stretching/shrinking sheet. To simplify the governing equations, the deterministic two-variable differential equations (PDEs) are systematically transformed into a system of one-variable differential equations by using appropriate similarity transformations. The bvp4c function of the MATLAB program is also used to solve the simplified mathematical model. The present study investigates and presents in tabular and graphical form the effects of stretching/shrinking surfaces, suction, and volume fraction of the nanoparticles on the velocity and temperature profiles as well as on the engineering quantities. The present results are first validated and confirmed as acceptable before the full calculations are performed. Overall, the results of this study show that the investigated parameters influence the flow characteristics, which can serve as a controlling factor for heat transfer.

Mathematical modelling of MHD hybrid nanofluid flow in a convergent and divergent channel under variable thermal conductivity effect

Abstract The aim of this research is to analyse the combined effect of variable thermal conductivity and nonlinear thermal radiation on magnetohydrodynamic (MHD) hybrid nanofluid flow in convergent-divergent channels. The effects of two nanoparticles (i.e. ZrO 2 {\text{ZrO}}_{\text{2}} and SiO 2 {\text{SiO}}_{\text{2}} ) in base fluid (i.e. H 2 O {\text{H}}_{\text{2}}\text{O} ) are considered in this work. The partial differential equations modelling the problem are reduced to ordinary differential equations following the application of the similarity transformations. The system has been solved analytically with the differential transform method and numerically with the Runge–Kutta–Fehlberg 4th–5th order method with the assistance of the shooting technique. Comprehensive analysis and discussion have been conducted regarding the impact of multiple governing parameters on the dimensionless velocity and temperature distributions. These parameters include variable thermal conductivity, nonlinear thermal radiation, Hartman number, and hybrid nanoparticle volume fraction. Finally, this method will provide some insights into the usefulness of MHD hybrid nanofluid flow in convergent-divergent channels, and the results produced by the analytical data have also been strengthened and verified by the use of numerical data as well as data from the literature.

Darcy-Forchheimer Flow of Hybrid Carbon Nanotube over a Permeable Stretching/Shrinking Curved Surface

The Darcy-Forchheimer flow of hybrid carbon nanotube over a permeable curved stretching/shrinking surface is investigated in this work. The Darcy-Forchheimer phrase is used to describe porous spaces with different porosity and permeability. The current problem is modelled using curvilinear coordinates due to the curved form of the geometry. A similarity transformation will be applied to the partial differential equations (PDEs) of the fluid flow to convert them to ordinary differential equations (ODEs). The numerical solutions of the equations of continuity, momentum, and energy are obtained using the bvp4c solver in MATLAB. To examine the impact of various physical parameters, including nanoparticle volume fraction, suction, inertia coefficient, and porosity, on temperature and velocity profiles, as well as the local Nusselt number and skin friction, a comprehensive graphical analysis is conducted. By carefully modifying these parameters and scrutinizing their effects on the flow and heat transfer properties, a dual solution was observed on the graphs. The results suggest that increasing the single-wall carbon nanotube (SWCNT) nanoparticle and inertia coefficient parameters narrow the range of solutions. When the SWCNT of a shrinking curved sheet is raised, the skin friction increases. Meanwhile, the inertia coefficient showed the opposite pattern. The increased SWCNT and inertia coefficient parameters decrease the local Nusselt number. Moreover, the findings are compared and rigorously confirmed with previous reported findings in the literature.

Punctuated versus gradual shifts in the multivariate evolutionary process: a test with paired radiations of scincid lizards.

As lineages become separated in time, they are expected to accumulate mutational (or developmental-genetic) differences that influence the macroevolutionary trajectories of those lineages even under similar environmental conditions. Here, we compare the dynamics of phenotypic evolution in radiations of scincid lizards from Australia and Madagascar that are separated by more than 100 million years of independent evolution and show rampant phenotypic parallelism. We collected linear measurements of the skull, limbs, and limb girdles from micro-CT scans of 94 Australian and 29 Malagasy species. Using multivariate comparative methods, we tested whether the underlying evolutionary covariance structure for this superficial parallelism was conserved and whether these patterns were consistent across distinct functional modules. Malagasy and most Australian skinks have similar covariance matrices for skull evolution. Results are ambiguous for limbs and limb girdles, as some trait subsets support different evolutionary processes and for other subsets, a shared covariance matrix could not be rejected. However, across most trait sets, the extremely speciose Australian genus Ctenotus exhibits a radically different covariance structure from all other lizards in these groups, including several closely related genera. The shift in Ctenotus demonstrates that the architecture of trait correlations can change at relatively shallow timescales and may explain the unique position of this clade in morphospace relative to other scincid lizards from both geographic regions. More generally, our results demonstrate that the multivariate evolutionary process can change dramatically in a relatively short period of time.

Stability of Tollmien-Schlichting modes in magnetohydrodynamic boundary layer flow in porous medium: energy budget analysis

Abstract Linear temporal and spatial stability analyses of the magnetohydrodynamic boundary layer flow over a wedge embedded in a porous medium have been carried out to analyze the effects of pressure gradient, Hartmann and Darcy numbers. Firstly, we determine the base state velocity profiles by imposing suitable similarity transformations on governing boundary layer equations and then find linear perturbed equations involving Reynolds number and disturbance wavenumber using Fourier modes. The Chebyshev spectral collocation method which provides insight into the complete structure of the eigenspectrum is used. The effect of Hartmann and Darcy numbers on the boundary layer is to stabilize the flow for all adverse pressure gradient parameters while only unstable modes are noticed in the absence of these effects. The noticed unstable modes are always part of the wall mode for which the phase speeds are found to approach zero. The eigenspectrum for all involved parameters has a balloon-like structure with the appearance of wall mode instability. The critical Reynolds number is found to be increasing for increasing pressure gradient, Hartmann and Darcy numbers. For an adverse pressure gradient, the energy budget shows that the energy production due to Reynolds stress dominates the viscous dissipation which results in destabilization of the flow, while the kinetic energy due to magnetic field and porous medium plays a role in stabilizing the flow. The physical dynamics behind these interesting modes are discussed.

Numerical Study of Williamson Fluid Flow over a Stretching Sheet with Newtonian Heating Embedded in a Porous Medium in Presence of Thermal Radiation and Heat Source/Sink

Williamson fluid has been utilized to explore the aligned magnetic field in the presence of thermal radiation and heat source/sink utilizing Newtonian heating on a stretched sheet soaked in porous medium. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying similarity transformations. These equations are then solved using MATLAB and the Runge-Kutta fourth-order technique with a shooting technique. Graphs were used to investigate the effects of different factors on dimensionless velocity and temperature. A decrease in the velocity field and an improvement in the distribution of temperature are caused by an enhancement in the Non-Newtonian Williamson fluid parameter and permeability restriction K, whereas the opposite effect is evident when the Aligned angle parameter is increased. When the conjugate factor for Newtonian heating parameter is increased, temperature rises, even as the reverse effect is seen in Prandtl number The coefficient of skin friction is an decreasing function and the Nusselt number is increasing function of Non-Newtonian Williamson fluid parameter and permeability restriction K. while the reverse effect is seen in Aligned angle parameter . The Nusselt number is increased function of heat source/sink parameter , and Newtonian heating parameter . While the reverse effect is seen in Prandtl number .