Velocity Graphs Research Articles

Theoretical Aspects of Soil Layer Turnover Within the Boundaries of Its Own Furrow

The paper highlights that soil layer turnover remains the most widely used method of primary tillage. Among the existing techniques, smooth plowing without producing back ridges or furrows, which is achieved using reversible plows, best meets the high standards of modern agricultural practices. (Research purpose) The study aims to substantiate the kinematics of soil layer turnover within the boundaries of its own furrow without lateral displacement. (Materials and methods) In analyzing the kinematics, the soil layer is assumed to behave as a cohesive elastic substance undergoing deformation during turnover within its own furrow, without disintegration. This assumption is quite reasonable, as it is well-established that a sodded and moist layer can be extracted as a continuous, intact strip that retains its geometric dimensions when turned 180°. The trajectory of the layer is derived using classical methods of theoretical mechanics. (Results and discussions) The equations governing the motion of the soil layer points during turnover within its own furrow are analyzed. During this process, all points in the cross-section of the layer undergo spatial displacement. Changes in displacement, velocity, and acceleration of the i-th point of the hypothetical layer exhibit smooth dependencies described by trigonometric functions. However, at a rotation angle of ωt = π/2, an abrupt change occurs in the trajectories of displacement, velocity and acceleration graphs, indicating sharply variable loads acting on the soil layer at this point. The abrupt change is attributed to a shift in the support rib which serves as the axis for the rotation of the soil layer's crosssection. The center of gravity of the cross-section moves with variable velocity and acceleration, which indicates the presence of inertial forces. Overcoming these forces requires a certain amount of energy. (Conclusions) The energy required largely depends on the geometric parameters of the layer a, b and its rotation modes (ω). When the layer cross-section rotates by an angle When the layer cross-section rotates by an angle ωt = π/2 – γ, the vertical acceleration of the central point (О) reaches its maximum value. Under certain conditions, the soil layer may detach from the furrow bottom in this position. The kinematics analysis of a soil layer turnover within the boundaries of its own furrow reveals new phenomena occurring during its motion to identifies the patterns of influence that the soil layer's geometric parameters exert on its dynamic characteristics.

Inertial aftermaths on peristaltic drive of MHD micropolar fluid in a two-dimensional asymmetric inclined porous soaked channel independent of wavelength: Galerkin finite element simulation

This manuscript presents a detailed investigation of the peristaltic propulsion of a micropolar fluid in an inclined asymmetric channel, which is also subjected to a magnetic field applied in the normal direction. The medium is considered to be a porous, saturated environment. Unlike traditional lubrication theory, which often assumes long wavelengths and negligible Reynolds numbers, our analysis does not adhere to these constraints. This approach introduces nonlinearity into the modeled equations and allows for significant Reynolds numbers, thereby enhancing our understanding of the peristaltic phenomenon. Numerical solution of coupled partial differential equations is gained by employing a novel Galerkin built finite element method and is presented through graphs of velocity and pressure distributions in accordance with variation in several flow parameters. Streamlines’ gyration, microrotation, and vorticity for different configurations that emerged with varying phase transitions are displayed in this regard as well. It is confessed that peristaltic mixing diminishes for all values of phase differences as the permeability parameter increases, while a rising Hartmann number significantly exacerbates this effect. In addition, the microrotation of micropolar particles is observed to become increasingly distorted with higher Reynolds numbers. Furthermore, the pressure rise throughout both pumping and co-pumping regions is enhanced when the inclined channel is subjected to a greater angle of inclination.

Computational heat transfer analysis of ternary hybrid nanofluid flow over a rotating disk using the Cattaneo-Christov model: Application of the Lobatto-III formula

This work investigated the impact of ternary nanoparticles on the flow dynamics across a revolving disk. This study examines the nanoparticles of magnesium oxide (MgO), titanium dioxide (TiO2), and CoFe2O4 that were dispersed in different liquids -water and ethylene glycol (EG). This study examines the joint impacts of a varying inclined magnetic field and CattaneoChristov heat and mass flux on the flow of two ternary nanofluids across a spinning disk. Problems of this nature predominantly arise in symmetrical phenomena through the use of similarity transformations and are relevant to engineering, physics, and applied mathematics. The phenomena were expressed as partial differential equations, which were subsequently transformed into an ordinary differential equation within the existing system. Subsequently, this work is computed with the bvp4c scheme in MATLAB. Graphical results are employed to evaluate the examination of mass and heat transfer. The velocities increase with the inclined magnetic impression for both ternary nanofluids. The temperature increases and concentration declines with the increasing volume fraction of TiO2 and CoFe2O4 for both ternary nanofluid flows. The Nusselt number declines for I-ternary nanofluid flow and increases for II-ternary nanofluid flow with the thermal and solutal relaxation parameter along with the increasing volume fraction of TiO2 and MgO. In addition, the alterations in concentration, temperature, and velocity graphs for different dimensionless parameters are briefly examined through related diagrams. The Nusselt number declines with the I-ternary group and increases with the II-ternary group for the nanoparticle MgO concentration.

Numerical Assessment of MHD Tri-Hybrid Nanoparticles by Tangent Hyperbolic Model with Chemical Reaction: Thermodynamic Analysis

This paper investigates the influence of magneto-tangent hyperbolic nanofluid on the flow of a tri-hybrid nanoliquid consisting of [Formula: see text], and [Formula: see text] particles suspended in [Formula: see text]. The entropy production is encountered in this analysis. The fluid flows over a stretch sheet is considered. In addition, the energy equation also assumes the existence of a uniform heat source or sink and thermal radiation. Furthermore, the concentration equation emphasizes the chemical reaction. The current proposed model yields a set of nonlinear governing equations. The modeled formulation is transformed into a dimensionless system through the application of a suitable alteration. The complex nonlinear equation system was solved using the bvp4c through numerical methods. The main motive of this exploration is to emphasize the rate of heat and mass transfer in a flow of [Formula: see text], and [Formula: see text]-based hybrid nanofluid across a stretch sheet. The graphical study illustrates that Weissenberg number and magnetic field enhancement result in decreasing the velocity. But thermal layer, entropy production, and Bejan number are enhanced with larger values of Weissenberg number and magnetic field. This study focuses on different profiles with various flow parameters. Furthermore, we have compared the tri-hybrid nanofluid with the hybrid and mono nanofluid in all the figures and tabular format. Additionally, we have compared tri-hybrid, hybrid, and mono nanofluid using graphs for velocity, temperature, concentration, entropy production, and Bejan number.

Brownian motion in a magneto Thermo-diffusion fluid flow over a semi-circular stretching surface

The current study explores the mass and heat transport analysis of a Casson liquid stream past a curved surface. The current model considers the effect of magnetic strength brought on by the strength of the applied uniform magnetic field. The significance of thermophoresis and Brownian motion are also taken into account using the Buongiorno nano-liquid model. The study of liquid flow over stretching sheets frequently addresses practical issues that have garnered significant attention from researchers due to their importance in various domains, including microfluidics, fibreglass production, manufacturing, transportation, metal extrusion, thermal insulation, glass production, paper manufacturing, and acoustic blasting. The governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) using the similarity variables. These equations are numerically solved using the finite difference method (FDM). The concentration, temperature, and velocity graphs were produced by varying the different physical parameters. The upsurge in the magnetic parameter reduces the velocity profile. As the magnetic parameter increases, thermal and concentration profiles upsurge. The decrease in velocity profile can be seen as the Casson parameter rises. The intensification in values of thermophoretic parameter enhances the thermal and concentration profiles. The concentration and thermal profiles reduce as the curvature parameter upsurges.

Automobile response to road safety barriers upon collision

During a collision between an automobile and a road safety barrier, the vehicle will go through many behavior transition phases. This research will focus on determining the behavior of two car models including a sedan car and a pickup truck in collision with two safety road barriers using numerical simulation. This paper will also present images, total force graphs, and velocity graphs throughout the process to evaluate the vehicle's behavior at different impact speeds and angles. It is recognized that at similar impact speeds, collision angles, and barrier types, the pickup truck suffers more damage than the sedan. In addition, the pickup truck colliding with a concrete barrier exhibits the highest force, while the sedan colliding with a W-Beam barrier records the lowest force among the four collision types. Regarding the road safety barrier, the concrete barrier has a shorter force increase/decrease duration than the W-Beam barrier.

Thermal conductivity impact on MHD convective heat transfer over moving wedge with surface heat flux and high magnetic Prandtl number

The present evaluation focused on heat transfer and magnetic flux along the moving non-conducting wedge shape with thermal conductivity and surface heat flux effects. A suitable and well-known similarity transformation for integration is used for the coupled non-linear partial differential equations with stream formulations. The Keller Box technique is utilized to integrate the final non-similar equations numerically. The discretized algebraic equations are displayed graphically and numerically using the MATLAB software. The physical characteristics like temperature, magnetic field, velocity profiles, skin friction, heat transfer and magnetic intensity are investigated with various factors. The influence of relevant characteristics like thermal conductivity ξ, Prandtl number Pr, wedge parameter β, variable viscosity ε, and Biot number Bi is interpreted graphically and numerically. It is noted that velocity graph effects are declined at lower value of Biot number and enhanced value is obtained at the higher value of Biot number. The fluid temperature with highest thermal slip effects is displayed with minimum value of thermal conductivity but minimum value is obtained at large value of thermal conductivity. The maximum heat flux value is obtained at large value of moving parameter.

Numerical Investigation of Nucleotides’ Interaction Considering Changes Caused by Liquid Influences

This work is devoted to the interaction of nucleotides. The goal of this study is to learn or try to learn how the interaction between nucleotides with exposure to a liquid takes place. Will the interacting forces of the nucleotides be sufficient to approach the incision? A numerical imitation of the interaction is conducted using the discrete element method and a Gears predictor–corrector as part of the integrated scheme. In this work, the results reflect the dynamics of nucleotides: velocity, displacement, and force graphs are presented with and without the effect of the liquid. During changes caused by the influence of a liquid, the nucleotide interaction transforms and passes three stages: a full stop, one similar to viscous damping, and one similar to non-dissipative behaviors. The main contribution of this work is a better understanding of the behavior of infinitely small objects that would be difficult to observe in vivo. The changing influence of a liquid can transform into certain effects. As a result, a model is provided, which can be based on the results of well-known physical experiments (DNA unzipping) for modeling nucleotide interactions.

Numerical Solution Analysis of Planetary Motion Models Using the Runge-Kutta Method

Purpose of the study: This study aims to solve the planetary motion model numerically using the fourth-order Runge-Kutta method and analyze the planetary motion profile through the resulting numerical solutions. Methodology: The process is carried out by solving the planetary motion model numerically using the fourth-order Runge-Kutta method, creating a program from the numerical solution, and simulating the program with variations in the parameters of the stability of the trajectory and the distance of the planet to the sun. The simulation results are in the form of estimates of the speed of the planet's motion in the x and y directions against time, and the influence of these parameters on the trajectory and velocity graphs are analyzed. Main Findings: Simulations show that the trajectory stability parameter and the planet's distance to the sun affect the planet's trajectory and velocity graphs. On the trajectory graph, the planet's distance to the sun affects the aphelion, minor axis, and major axis values ​​of the orbit. The closer the planet is to the sun, the smaller its orbit, and vice versa. Novelty/Originality of this study: The novelty of this research lies in the application of the fourth-order Runge-Kutta method to solve the planetary motion model numerically, without requiring function derivatives. This research also connects the numerical results with Newton's law of gravity to understand the relationship between the distance of a planet to the sun and its orbital pattern.

Unveiling thermal and hemodynamic effects of aneurysm on abdominal aorta using power law model and finite element analysis

The objective of this study is to find causes of aortic diseases and investigating the ways for better treatment. The governing system of equations has been demonstrated to account for characteristics of blood. The governing system of equation has been solved using the finite element method with appropriate boundary conditions. We analyzed into the relationship between flow characteristics via the aneurysmal abdominal aorta and the aneurysm height, aneurysm length, and non-Newtonian behavior. It investigates how thermal and hemodynamics effects change across the abdominal aortic aneurysm. The velocity, pressure, and temperature surface plots of the results are displayed. There have also been graphic displays of line graphs of axial velocity, radial velocity, axial pressure, radial pressure, axial temperature and radial temperature across the aneurysm. The blood flow simulations obtained results show that increasing blood temperature, pressure and intake velocity all contribute to an increase in viscosity. The results indicate that while the temperature varies little to not at all, the blood flow pressure decrease and velocity significantly vary.

Flow analysis of MHD ternary hybrid nanofluid over a permeable wedge with variable surface temperature and slip effect

A comparative flow analysis of a water based- ternary hybrid nanofluid has been studied in this article over a moving permeable wedge in the presence of variable wedge surface temperature. The model has been developed keeping in mind magnetic, velocity slip, buoyancy, and suction effects. The primary nanoparticle was Nimonic 80A, Fe 3 O 4 being the secondary nanoparticle and Graphene Oxide ( GO ) ternary nanoparticle. The velocity, temperature, heat transfer rate, and shear drag profiles for various parametric values of the magnetic parameter ( M ), velocity ratio parameter ( R ) , velocity slip parameter ( h ) , buoyancy parameter ( γ ) and suction parameter ( S ) was investigated. MATLAB bvp4c code was utilized for obtaining the numerical results by solving the nondimensional differential equations obtained using similarity transformations. All the results and graphs were formulated after a positive outcome of our results with that available in existing literature. An increase in the velocity slip parameter ( h ) and velocity ratio parameter ( R ) resulted in an increase in velocity profiles and local Nusselt number graphs while a reverse trend was observed for temperature and skin friction profiles. Also, the velocity graphs faced an increase by 0.09% with an increment in M = 0.4 to M = 0.8 . The present study finds its extensive applications in medical industries, water heaters, and forging of hot exhaust valve heads.

Comparative examine of fluid pressure within microchannel through integrated cantilevers for microfluidic applications

This paper aims to explore the concept of a microfluidic pressure sensing mechanism across a microchannel, integrated with different structures of microcantilevers. Various structures of microcantilevers are integrated into a microchannel where laminar fluid flows and the microcantilever senses the fluid velocity and pressure. The different structures of the microcantilever include rectangular, T-shaped, and Pi-shaped designs, which are placed at the centre of the microchannel. The 2D microchannel has a length of 4000 μm and a height of 840 μm, while the microcantilever is positioned at a distance of 2000 μm from the inlet of the microchannel. The analysis of the fluid sensor is observed by plotting graphs of velocity, pressure, displacement of the microcantilever, Reynolds number, and friction factor with respect to the time domain. An inlet velocity of 8.33 µm/s is applied at the microchannel, and the fluidic sensor shows a significant change in the fluid characteristics, comparing them across all types of microcantilevers. The simulation results show that the T-microcantilever has a maximum displacement of 4.97 µm compared to other microcantilevers, with a maximum pressure of 1.58 Pa for the Pi-cantilever. The integrated device is suitable for healthcare applications, measuring fluid pressure in syringes, where the T-microcantilever proves to be more compatible than the other two microcantilevers (R-cantilever and Pi-cantilever). The design and simulation of the microfluidic pressure sensing process are conducted using the FEM tool COMSOL Multiphysics.

MHD Stagnation Point Radiative Flow of Hybrid Casson Nanofluid across a Stretching Surface

This paper aims to investigate the hybrid stagnancy point in casson nanofluid on a transient elongation plane in accordance with impact of thermal heat. Resistive heating effect also considered in this study. Nano particles of assumed Cu and Al are utilized. Hence derived partial differential equations are broken down into nonlinear differential equations using suitable Transformations. Then succeeding results are worked out by employing Bvp4c Method. The obtained values for the analysis are indicated by indicating velocity and temperature graphs for distinct constants like radiation constant (Rd), Casson constant (β), magnetic variable (M), Prandtl constant (Pr), unsteady parameter (s). As well, the confined parameter, coefficient of skin friction is analysed. For continuing estimates of Casson parameter speed of liquid flow will be lessen. On intensifying Prandtl number of liquid shrink gradually. It is observed that for rapidly rised values of both Nano molecules velocity of the liquid lessens whereas reverse tendency is identified for temperature profile. Utilisation of hybrid nanoflows has a benifit of heat convertion improvement. The outcomes of current investigation are liquid is better within the congruence with comparision of subsist work.

Analyzing Physics Experiment using Sensor Smartphone in Traveling Carnival

Smartphone integration for high school students has significant potential in physics learning. This research aims to analyze smartphone sensor data in the context of physics experiments carried out at traveling carnivals. This research uses experimental methods to compare smartphone sensor data collected via the Phyphox application with video analysis data obtained using Tracker software. The research results show the effectiveness of smartphone sensors in several carnival games, including simple leg swings, bicycle spins, kora-kora vehicles, and merry-go-rounds. Smartphone sensors can show graphs of simple harmonic motion, angular velocity, and centripetal acceleration on the game vehicle. However, limitations arise in the case of Ferris wheels and mini Ferris wheels, where smartphone sensors show reduced effectiveness caused by the instability of passenger seats during the ride. This research suggests avenues for further exploration by computing physical quantity values derived from smartphone sensor data, offering insights into potential improvements and applications in dynamic environments such as theme parks.

Use of interactive mathematical simulations in Fundamentals of Biochemistry, a LibreText online educational resource, to promote understanding of dynamic reactions.

Biology is perhaps the most complex of the sciences, given the incredible variety of chemical species that are interconnected in spatial and temporal pathways that are daunting to understand. Their interconnections lead to emergent properties such as memory, consciousness, and recognition of self and non-self. To understand how these interconnected reactions lead to cellular life characterized by activation, inhibition, regulation, homeostasis, and adaptation, computational analyses and simulations are essential, a fact recognized by the biological communities. At the same time, students struggle to understand and apply binding and kinetic analyses for the simplest reactions such as the irreversible first-order conversion of a single reactant to a product. This likely results from cognitive difficulties in combining structural, chemical, mathematical, and textual descriptions of binding and catalytic reactions. To help students better understand dynamic reactions and their analyses, we have introduced two kinds of interactive graphs and simulations into the online educational resource, Fundamentals of Biochemistry, a LibreText biochemistry book. One is available for simple binding and kinetic reactions. The other displays progress curves (concentrations vs. time) for simple reactions and complex metabolic and signal transduction pathways. Users can move sliders to change dissociation and kinetic constants as well as initial concentrations and see instantaneous changes in the graphs. They can also export data into a spreadsheet for further processing, such as producing derivative Lineweaver-Burk and traditional Michaelis-Menten graphs of initial velocity (v0) versus substrate concentration.

CFD Analysis for Valve-Holding Camber Permanent Inhaler Spacer (AerospaAcer) with Different Valves

During the COVID-19 pandemic, data statistics showed that patients with respiratory problems become infected. One of the therapy techniques for the respiratory condition was the use of a metered-dose inhaler and spacer. The objective of this paper is to determine the flow parameters of three types of valves which is duckbill valve, cross slit valve and umbrella valve in inhaler spacer to compare fluid flow between valve Previous researchers chose the duckbill valve to control fluid flow in inhaler spacer. The flow characteristics are unaffected by the materials used in the new disposable inhaler spacers, such as paper and polylactic acid (PLA). Several design valves reduced the skewness below 0.94 by suppressing the fillet and chamfer. ANSYS Workbench Fluent 19.2 is used to calculate flow parameters such as turbulence kinetic energy (TKE), turbulence eddy dissipation (TED), velocity, particle velocity magnitude, streamline, and vector velocity. The setup input data is based on the previous researcher's specified parameters such as viscosity model, drug characteristics (salbutamol and propellant), discrete phase model (DPM) equal to 80, boundary condition model, and SIMPLE technique. For the three types of valves, the nozzle injection used a 0.50-millimetre dimension. The simulation work is cross-checked against the results of prior simulations. Within each iteration, the transient flow employed a time step size of 0.01 for 200 steps. The results show that computational analysis can distinguish between models of varying complexity. The TED, TKE, and velocity graphs showed the approximate value between the model geometries. Overall, the study was successful in achieving the desired velocity magnitude in terms of visual and graph representations of the various valve.

Comparing the Velocity Spectrum Caused by the Presence of Circular Urban Subway Tunnels With Free‐Field Conditions

For structures in the near field, the velocity spectrum is significant. The aim of this study is to examine, taking into account the soil–structure interaction (SSI), how metropolitan subway tunnels with a circular cross section in alluvial soils affect the ground surface velocity spectrum. The frequency of the soil–tunnel systems was altered by varying the parameters of the soil and the geometrical features of the tunnel, such as the radius, the lining’s thickness, and the depth of burial. The maximum velocity was determined at several sites on the ground surface as well as the tunnel crown. Based on the soil–tunnel system’s period, the spectrum velocity graph was produced by averaging and squaring the standard deviation of the highest velocity for every frequency. Ansys finite element software and Plaxis2D were used in this study. The findings demonstrate that the tunnel’s presence reduces spectral velocity (SV) relative to free‐field (FF) circumstances during the examined period at the position that corresponds to the ground‐based image of the tunnel crown. The tunnel’s existence lowers the ground‐level velocity range by 14.5 percent. By moving away from the image of the tunnel crown on the ground surface, the presence of the tunnel amplifies the SV at more points by 5.5% at long periods. In addition, the tunnel crown velocity spectrum was developed. The findings indicate that the velocity spectrum diagram’s envelope for the tunnel crown is a nonlinear function of the soil–tunnel system’s period.

LAND CONSERVATION FOR REHABILITATION OF CRITICAL WATERSHEDS: CASE IN WAY CENGKAAN, WAY BESAI SUB-WATERSHEDS, LAMPUNG, INDONESIA

Land and water conservation are the keys to success in controlling the rate of sedimentation. The sediment runoff rate represents the catchment area that increases erosion. This study was conducted to analyze the sedimentation rate in the upstream part of the Way Cengkaan, Way Campang tributary rivers located in Pekon Karang Agung, Way Tenong District, West Lampung Regency. It was carried out from January to December 2020. The research equipment included: a current meter, a stopwatch, a rollmeter, a rainfall recorder, an automatic water level recorder (AWLR), a peiscal, sediment bottles, scales, ovens, and cups. While the materials used are sediment samples, discharge measurement results, and water level. The calculation of flow was carried out at two observation points, upstream and downstream of the Cengkaan River before entering the Way Campang River. Calculation of flow rate using the velocity-area methods using the current meter and the float method. During the observation period from January to July 2020, the sediment velocity increased in line with the trend of the sediment velocity map. The sediment velocity curve for upstream stations is steeper than for downstream stations. The sediment volume decreased relatively in December 2020, and the slope of the sediment velocity graph at the downstream observation point is larger than that at the upstream observation point. This finding reflected that in the one-year observation period from January to December 2020, the evaluation resulted from a decreasing trend of sedimentation in the Way Cengkaan River. Based on these conditions, the implementation of a land conservation program carried out in collaboration between farmer groups and beneficiary stakeholders has a positive impact and effectively contributes to improving the quality of the watershed by reducing the sedimentation rate.

Influence of complete slip conditions on peristaltic transport of third-grade fluid with suction and injection

This study is important for the fields of pharmaceutical nano-drug suspension, biomedical engineering, pressure surges and food processing systems. The slip condition is necessary for polishing internal cavities and artificial heart valves in a variety of manufactured objects, micro- or nano-channels, and applications. Low Reynolds number (Re[Formula: see text] and long wavelength ([Formula: see text]) considerations are used in the formulation of the mathematical model at low non-Newtonian parameter values, nonlinear boundary conditions and the governing nonlinear equation are analytically solved using the perturbation method. The graphs of frictional force, pressure rise, velocity, pressure gradient, and streamline graphs are done using Wolfram MATHEMATICA software. In this paper, we compared the results of the total slip condition with those of the first-order slip condition and the absence of any slip effects. It has been noticed that increasing the suction and injection parameters leads to a decrease the pressure rate with complete slip effects, partial slip effects and no slip effects. We show that an increase in the third grade fluid parameter [Formula: see text] increases the magnitude of axial velocity. From a physical perspective, it shows the shear thinning characteristic, which causes a decrease in viscosity and an increase in fluid velocity. Frictional force behaves differently when compared to pressure rate. In other words, the pressure gradient acts as an obstacle to the peristalsis-driven flow. The objective of the study is to find the impact of the peristaltic flow phenomena and the impact of peristaltic on third-grade non-Newtonian fluid where the suction and injection are prevailing which is similar to the thing in biomechanical devices, like blood vessels, etc. there is a change of oxygen and carbon dioxide from the tissue layer to the fluid within the blood vessel.

Optimization of Non-Newtonian Flow through a Coat-Hanger Die Using the Adjoint Method

The use of coat-hanger dies is prevalent in the plastic film and sheet extrusion industry. The product quality and the power of the extrusion machine depend on the uniformities of the fluid velocity at the exit and the pressure drop. Die manufacturers face the challenge of producing coat-hanger dies that can extrude materials uniformly and with a minimal pressure drop. Previous studies have analyzed the die outlet’s flow homogeneity and pressure drop using various numerical simulations. However, the combination of the scheme programming language together with the Adjoint Method of Optimization has yet to be attempted. The adjoint optimization method has been demonstrated to be beneficial in addressing issues related to shape optimization problems and it may also be beneficial in optimizing the design of dies used in polymer melt extrusion. In this study, the proposed innovations involve incorporating both the Scheme programming language and Adjoint solver to examine and optimize the coat hanger’s flow homogeneity and pressure drop. Before optimization, the outlet velocity was almost 10 times higher at the die center than at the edges but after optimization, it became more uniform. The proposed optimized coat-hanger die geometry results in more uniform melt flow as demonstrated by the velocity contour plot and the outlet velocity graph in the die slit area, reducing the deviation value from 0.097 to 0.015. Additionally, the mass flux variance across the die outlet decreased by 71.6% from 0.015069 kg m−2 s−1 to 0.004281 kg m−2 s−1. Therefore, using this method reduces the amount of time wasted on trial and error or other optimization techniques that may be limited by design constraints.