Steady-state Conduction Research Articles

Thermoelastic flexural behaviour of sandwich plates stacked with porous FGM layer under the 3D state heat conduction

This work intends to analyze numerically the thermoelastic bending behaviour of sandwich plates stacked with FGM (functionally graded material) layer containing porosities. For this purpose, a quasi-3D (three-dimensional) shear deformable theory based IGA (isogeometric analysis) method is established, and the 3D steady-state conduction of heat is considered as the thermal environment to reflect the real circumstance. An equation to dictate the nonlinear temperature distribution induced by the 3D state heat conduction of the porous functionally graded sandwich plate is presented accordingly. Two kinds of the porous sandwich plates having various lamination schemes are taken into consideration. Benchmark problems on the thermoelastic bending responses of the sandwich plates with FGM layer have been solved, and the results are compared to the reference solutions to demonstrate the performance capability of the proposed IGA method. Further parametric examinations illustrate the impacts of the composition pattern, material gradient, porosity degree, plate geometric parameter as well as the stacking sequence, i.e., the location of the FGM lamina on the 3D heat conduction induced thermoelastic flexural response behaviour of the porous sandwich plates. The achieved new outcomes for the thermoelastic bending response behaviour of the sandwich plates having porous FGM core or skins are regarded to be used as the future reference.

Yielding onset in FGM thick-walled spherical shells under thermo-mechanical loading

Based on von Mises yield criterion, a thermoelasto-plastic analysis of a thick-walled spherical shell composed of functionally graded material (FGM) subjected to internal pressure and thermal gradient is conducted in order to accurately predict the onset radius of yielding within the vessel wall. The modulus of elasticity, thermal conductivity and thermal expansion coefficients, and yield stress of FGM are assumed to follow power-law functions in radius according to Erdogan’s model. The equilibrium differential equation of the shell under thermo-mechanical loading in steady-state conduction heat transfer are derived analytically and then solved to determine through-thickness variations of the radial and circumferential stresses and radial displacement in elastic and perfectly plastic zones in the vessel wall. The presented approach leads to the definition of new formulation to predict the onset radius of yielding. Moreover, a neural network (NN) solution to reliable quantify the influence of all uncertain input parameters with respect to uncertain output parameter is utilized. The numerical results showed that for various FGM parameters and specific thermal gradient, the plastic zone can commence from inside radius, outside radius, simultaneously in both radii, or may be launched in the intermediate radius of the spherical shell wall.

Numerical search for the effective thermal conductivity of cracked media

Spacecraft parts accumulate damage during operation and defects that are invariably present even in new designs may grow. This leads to changes in the behavior of individual parts of the space vehicle and, consequently, to the risk of fracture. A more accurate assessment of spacecraft safety requires internal defects to be included in the material models under consideration. One of the main hazardous effects on space objects is multiple temperature heating and cooling due to periodic action of solar rays. This paper presents a study of thermal conduction of media containing cracks. It is carried out with the help of a technique developed by the authors to determine the effective thermal conductivity of materials and based on approximate numerical solution of the steady-state thermal conduction problem for a three-dimensional medium with cracks by the boundary element method. This technique allows to obtain the distribution of the temperature field and heat flux density at any point of the body under consideration, as well as to calculate the effective parameters of materials with high accuracy at relatively low calculation time using ordinary personal computers of average power. The basis of the numerical method presented in this paper is the decomposition of the desired solution into a series of some pre-calculated analytical solutions of the heat conduction equations. The dependence of the effective thermal conductivity on the density of thermally insulated cracks was considered. The formula of this dependence is proposed. Verification of the proposed methodology was carried out by comparing the numerical results of a number of problems with the results of other authors.

Stability analysis for viscoelastic fluid with thermorheological effects: Linear and nonlinear approaches

This study investigates the stability analysis of Rayleigh-Bénard configuration for a viscoelastic fluid subject to thermorheological effects, using the D2-Chebyshev-τ method. The fluid is modeled as a third-order viscoelastic fluid. This study accentuates how salting the fluid layer affects the thresholds for the onset of instability in a fluid of third order encompassing physically realistic rigid boundaries. The dynamic model incorporates advection-diffusion of temperature and solute concentration and a modified Navier–Stokes equation. We determine instability thresholds for the complex non-Newtonian fluid by analyzing the linear stability of the steady-state conduction solution. Our analysis proves the strong form of the principle of exchange of stabilities, demonstrating that convective motions can only occur through stationary motion. Additionally, a nonlinear stability analysis using the energy method is performed, deriving an unconditional nonlinear stability criterion. The results provide a comprehensive understanding of how variable viscosity and viscoelasticity impact system stability. Both the viscosity parameter and the third-grade fluid parameter exhibit stabilizing effects. Notably, we observe a discrepancy between the linear and global nonlinear stability results, indicating the presence of a subcritical instability region. This study contributes to the understanding of complex fluid dynamics in non-linear mechanical systems, with potential applications in various industrial and natural processes.

Alamethicin channel inactivation caused by voltage-driven flux of alamethicin

We show that voltage alone can inactivate alamethicin channels, which has been previously observed for monazomycin and suzukacillin channels. The voltage required to trigger inactivation is above the potential to form channels, and, like with channel activation, this threshold reduces with increasing peptide concentration and membrane fluidity. Since similar monazomycin channels inactivate via channel break up and translocation, we hypothesized that inactivation of alamethicin channels occurs via the same mechanism. Our data prove this hypothesis to be true through two experiments. First, we show that inactivation of channels at positive voltages when peptides are supplied to only the cis side correlates to new channel activity on the trans side at negative potentials. This result indicates translocation of alamethicin peptides occurs only during voltage-induced inactivation. Second, we measured the ratio of steady-state (with inactivation) to ideal (without inactivation) conductance versus voltage for membranes with equal amounts of alamethicin on both sides and used these values to quantify alamethicin flux. Plotting flux versus steady-state conductance across multiple alamethicin concentrations shows a single linear dependence, signifying that translocated peptides originate from active channels that break up under prolonged voltage. Given the frequent use of alamethicin as model ion channels, these results add important understanding of their kinetic responses when subjected to prolonged, high voltages.

Finite element solution of heat conduction in complex 3D geometries

This paper presents the use of the finite element method (FEM) to solve heat conduction problems in complex 3-dimensional geometries not amenable to analytical solutions. Heat conduction is important across engineering domains, but closed-form solutions only exist for basic shapes. For intricate real-world component geometries, numerical techniques like FEM must be applied. The paper outlines the mathematical formulation of FEM, starting from the heat conduction governing equations. The domain is discretized into a mesh of interconnected finite elements. Element equations are derived and assembled into a global matrix system relating nodal temperatures. Boundary conditions are imposed and the matrix equations solved to find the temperature distribution. An example problem analyzes steady state conduction in an L-shaped block with 90-degree corners and surface convection. Results show FEM can capture localized gradients and discontinuities difficult to model otherwise. Detailed temperature contours provide insight. FEM enables robust thermal simulation of complex 3D geometries with localized effects, expanding analysis capabilities beyond basic analytical shapes. Proper application of FEM is critical for accurate results.

Method for determining the Schottky injection barrier at the interface of a metal electrode with insulating oil or pressboard

The Schottky injection barrier plays a crucial role in determining the charge movement and migration process, yet its electric field and temperature properties remain unclear. The precise determination of the Schottky injection barrier value is essential for understanding the charge migration dynamics at the interface between the metal electrode and the oil-pressboard insulating medium. This study introduces a computational approach to determine the Schottky injection barrier, derived from classical Schottky emission theory. The methodology employed in this research aligns with previous studies, utilizing the Schottky emission current mechanism to describe steady-state conduction current. Results indicate that the Schottky injection barrier increases with temperature, with a 17.09% rise for oil-electrode and an 8.3% increase for pressboard-electrode in the temperature range of 299 K–353 K. These temperature-dependent variations are attributed to the negative temperature dependence of the Fermi energy levels of the metal electrodes. Furthermore, the impact of electric field strength on the Schottky injection barrier is found to be minimal. By developing a bipolar charge transport simulation model and validating the injection barrier for 0.5 mm oil-immersed pressboard, this study confirms the accuracy of the calculated Schottky injection barrier. The insights provided in this research could aid in simulating charge transport and analyzing charge characteristics in oil-paper/pressboard insulation systems.

Analytical irreversible thermodynamics in conduction-radiative heat transfer of neutral gases through a lens of thermal radiation fields

An analytical investigation has been conducted on the steady-state conduction and a diluted gas exposed to a thermal radiation field experiences radiative heat transfer. Analytical solutions have been derived for the transport Boltzmann BGK partial differential equations system. The investigation delves into the irreversible thermodynamic behavior of the system through the utilization of the Liu-Lees model, which employs two-stream Maxwellian distribution functions. The moment approach is utilized to predict the behavior of macroscopic gas parameters like temperature, concentration, and Fourier heat flux. This process entails substituting these parameters into the two-stream Maxwellian distribution functions to analyze the system's non-equilibrium thermodynamic characteristics, which encompass gas particles and the heated plate. Through this analysis, kinetic coefficients, entropy, entropy flux, entropy production, and thermodynamic forces are determined. The investigation assesses the validation of Onsager's reciprocity relation, the Boltzmann H-theorem, the Le Chatelier principle, and the second law of thermodynamics within the system. Furthermore, the Gibbs formula is employed to estimate the ratios between various contributions to internal energy changes, which are determined by the total derivatives of extensive parameters. The non-equilibrium velocity distribution function was calculated for the first time, and its behavior was compared with that of the equilibrium one using 3D graphics. The behavior of the computed variables is predicted through graphical analysis and discussion of the results.

Estimating Non-Linear Heat Flux in Continuous Billet Casting Process With Limited Sensors

In a continuous billet caster, the heat transfer from the pool of molten steel to the cooling water via the copper mold depends non-linearly upon several casting parameters. A reliable and accurate methodology based on the principle of inverse heat transfer technique has been proposed in this work to obtain the nonlinear heat flux of a continuous billet casting mold. Differential evolution optimization technique has been used, in conjunction with the 2-D and 3-D steady state conduction heat transfer equations to develop the complete algorithm. It has been observed that both the 2-D and 3-D models are able to accurately predict the heat flux for different numbers and locations of temperature sensors. While the 2-D model estimates the 1-D heat flux profile varying along casting direction within a very short time period, the 3-D model offers the advantage of estimating a more accurate 2-D heat flux profile varying along both the mold length and width. The 2-D model has also been used to estimate the heat flux for an industrial continuous casting mold using measured plant data. It is observed that the present methodology accurately estimates the boundary heat flux in the continuous billet caster mold.

Monte Carlo functional estimation of the radiative source term in a semi-transparent medium: A faster coupled conductive–radiative model resolution

The estimation of thermo-physical properties of materials at high temperatures requires the development of robust and fast-enough direct models that takes into account the strong coupling between conduction and radiation. The interest in using the Monte Carlo method to obtain a conduction–radiation model in a semi-transparent material solved in a reduced computational time is addressed in this study. An academic configuration that consists of an absorbing/emitting and non-scattering gray medium with steady-state conduction is investigated since this study is meant to be a proof of concept. It is demonstrated that the radiative source term of the heat equation may be estimated as a function of the temperature field to the fourth power, using a Finite Differences algorithm and a single Monte Carlo simulation of radiation. The results of the numerical study show that, on the one hand, they are in good agreement with those found in the literature and, on the other, that the coupled model can be resolved in a significantly shorter amount of computational time than with traditional methods thanks to the functional estimation of the radiative source term. In fact, in each of the fifteen analyzed cases, the coefficients of the function were determined in approximately 6 s using the Monte Carlo method using a laptop with standard computational resources. The computation of the function and its application revealed that, depending on the studied configuration, a resolution with the finite differences–functional Monte Carlo algorithm can be around twenty to one thousand times faster than a classic Finite Differences–Monte Carlo algorithm. Due to these characteristics, as well as the fact that the functional estimation is insensitive to geometry complexity and can be extended to configurations with heterogeneous radiative properties, it becomes possible to utilize this method in inversion procedures, since the direct model must be evaluated numerous times.

Influence of Ag Doping on Thermal Conductivity and Magnetic Levitation of Single Grain YBCO Superconductors for High-Temperature Superconducting Maglev

Ag doping in (RE)Ba2Cu3O7−δ [(RE)BCO] bulk high-temperature superconductors has been recognized as an effective way to improve the mechanical and superconducting properties of REBCO bulk superconductors for practical applications such as high-temperature superconducting (HTS) Maglev. Ag2O nanoparticles doped YBCO samples with different doping amounts (x, x varies from 0∼0.5 wt%) were fabricated by Top-Seeded Melt-Growth method (TSMG). The samples’ steady-state thermal conductivity (λ) and the magnetic levitation force (FL) were measured by a testing platform under a similar condition to the HTS Maglev system. The effects of Ag2O doping on the λ and FL of single domain YBCO bulks have been systematically studied. The λ of the c-axis and the ab-plane were calculated through the steady-state heat flow method. We observed that λ increases distinctly when x ≥0.3 wt%. The doping amount of 0.3 wt% has been evidenced to be the optimal value, of which the λ of the c-axis and ab-plane are approximately 52% and 48% higher than the undoped one respectively. According to the results of the FL measurement, we found FL will increase while the relaxation rate of the FL will decrease by adding trace amounts of Ag2O nanoparticles in comparison to the undoped sample. This observation suggests that Ag-doping is an effective way to enhance thermal conductivity as well as the superconducting properties of YBCO superconductors for practical applications.

Design and Optimization of Precision Fertilization Control System Based on Hybrid Optimized Fractional-Order PID Algorithm

In order to mitigate time-varying, lag, and nonlinearity impacts on fertilization systems and achieve precise control of liquid conductivity, we propose a novel hybrid-optimized fractional-order proportional-integral-derivative (PID) algorithm. This algorithm utilizes a fuzzy algorithm to tune the five parameters of the fractional-order PID algorithm, employs the Smith predictor for structural optimization, and utilizes Wild Horse Optimizer, improved by genetic algorithms, to optimize fuzzy rules. We conducted MATLAB simulations, precision experiments, and stability tests on this controller. MATLAB simulation results, along with precision experiment results, indicate that compared to PID controllers, Smith predictor-optimized PID controllers, and fuzzy-tuned fractional-order PID controllers, the proposed controller has the narrowest steady-state conductivity range, the shortest settling time, and the lowest overshoot, showcasing excellent overall dynamic performance. Stability test results demonstrate that the controller maintains stable operation under different pressure conditions. Therefore, this control system from our study achieves superior control effectiveness, providing a viable approach for the control of nonlinear time-delay systems.

Heat transport with a twist.

Despite the desirability of polymers for use in many products due to their flexibility, light weight, and durability, their status as thermal insulators has precluded their use in applications where thermal conductors are required. However, recent results suggest that the thermal conductance of polymers can be enhanced and that their heat transport behaviors may be highly sensitive to nanoscale control. Here we use non-equilibrium molecular dynamics simulations to study the effect of mechanical twist on the steady-state thermal conductance across multi-stranded polyethylene wires. We find that a highly twisted double-helical polyethylene wire can display a thermal conductance up to three times that of its untwisted form, an effect which can be attributed to a structural transition in the strands of the double helix. We also find that in thicker wires composed of many parallel strands, adding just one twist can increase its thermal conductance by over 30%. However, we find that unlike stretching a polymer wire, which causes a monotonic increase in thermal conductance, the effect of twist is highly non-monotonic, and certain amounts of twist can actually decrease the thermal conductance. Finally, we apply the Continuous Chirality Measure (CCM) in an attempt to explore the correlation between heat conductance and chirality. The CCM is found to correlate with twist as expected, but we attribute the observed heat transport behaviors to structural factors other than chirality.

Frictional strength, electrical conductivity, and microstructure of calcite–graphite mixtures sheared at a subseismic slip rate

Calcite is a common mineral found in carbonate-bearing fault zones. Crystalline graphite (Gr) can be generated within calcite-bearing fault zones, which may contribute to their low strength and high electrical conductivity. To investigate the mixed effects of Gr on calcite gouges, a dedicated assembly was employed in a rotary-shear friction experiment, which enabled simultaneous measurement of friction and electrical conductivity. The experiments were conducted on synthetic dry calcite–Gr mixtures with 0–50 wt% Gr under a fixed normal stress of approximately 2 MPa at approximately 20 °C. A constant equivalent slip rate of 1 mm/s was imposed, with displacements ranging from 0.8 to 4.6 m. To resolve the microstructure evolution, four additional displacement-controlled experiments were performed on the 6 wt% Gr-bearing specimens under the same conditions. Following high peak friction, all Gr-bearing mixtures experienced dramatic slip weakening. The steady-state electrical conductivity of the specimens increased by over eight orders of magnitude when the Gr content exceeded 6 wt%. Microstructures indicated that the calcite particles initially formed a strong framework with distributed Gr, followed by the gradual development of conductive strain-localization zones (SLZs) and Gr-lubricated slip surfaces with increasing displacement. Even the mixtures with low-Gr content (< 2.4 vol%) developed smooth slip surfaces, sustaining low-level electrical conductivities throughout the experiments. For specimens with high electrical conductivities (Gr > 5.3 vol%), abundant Gr flakes were present in the SLZs, forming an interconnected structure. Combined with our companion study on quartz-Gr mixtures, we propose that the conductivity and frictional strength trends with displacement for Gr-bearing mixtures are not always consistent. Mineral crystal properties (e.g., hardness and crystal structure) may influence the frictional properties of these mixtures significantly, while the level of electrical conductivity of a fault zone cannot be used to infer its frictional strength.

Closed-loop control of BLDC motor using Hall effect sensors

Due to its key advantages of top performance, strong torque, and simple volume, brushless direct current (BLDC) motors are now extensively employed in a variety of industrial sectors, including the automotive industry, robotics, and electrical vehicles. Yet, in some circumstances, it can be challenging to use speed control techniques for specific devices. The major goal of this work is to use a proportional integral derivative (PID) converter to regulate the speed characteristics of BLDC. PID converter is preferred over all other converters because of its straightforward design and straightforward implementation. Using MATLAB simulation results are verified at different reference speed changing conditions, the motor input current and back electromotive force (EMF) values are verified. The speed and torque characteristics are verified during steady and transient state conduction.

Evaluation of physicochemical characteristics and centerline temperatures of Sr ceramic waste form

When disposing of spent fuel, nuclides such as Cs-137 and Sr-90, which generate short-term decay heat, must be removed from the spent nuclear fuel for efficient storage facility utilization. The Korea Atomic Energy Research Institute (KAERI) has been developing a nuclide management process that can enhance disposal efficiency by sorting and collecting primary nuclides and a technology for separating Sr nuclides from the spent nuclear fuels using precipitation and distillation. In this study, we prepared Sr ceramic waste form, SrTiO3, using the solid-state reaction method to immobilize the Sr nuclides, and its physicochemical properties were evaluated. Moreover, the radiological and thermal characteristics of the Sr waste form were evaluated by estimating the composition of Sr nuclides considering the spent nuclear fuel history such as burn-up and cooling period. The waste form was found to be stable with good mechanical strength and leaching properties in addition to a low coefficient of thermal expansion, which would be advantageous for intermediate storage. Based on the experimental and radiological results, the centerline temperature of the waste form caused by Sr-90 nuclide was estimated using the steady-state conduction equation. The centerline temperature increased with increasing diameter of the waste form. When generating the SrTiO3 waste form using the Sr nuclide recovered after a cooling period of 10 years, the centerline temperature was estimated to exceed the melting point of SrTiO3 at a diameter of 0.275 m, under all burn-up conditions. These results provide fundamental data for the management and intermediate storage of Sr waste.

Diagnostics of Transmission Bearing Units Based on Thermal Load Study

Abstract. The operating temperature of the transmission unit is noted to affect its reliability and can serve as a diagnostic criterion. It is proposed to diagnose the transmission unit technical condition by the temperature in the friction zone in order to take into account the influence of air temperature, solar radiation heating and adjacent heat-producing objects. (Research purpose) To ensure the bearing unit controllability based on the thermal load study. (Materials and methods) The study uses the results of calculating the nominal and operational load of the rear power take-off shaft of the Belarus-82.1 tractor. The study uses the three-dimensional modeling and finite element analysis of the temperature distribution under steady-state thermal conductivity conditions. To establish the functional relationship between the temperature in the friction zone and the diagnostic temperature, the method of finite element analysis is used under steady-state thermal conductivity conditions. (Results and discussion) The maximum load modes and temperatures in the friction zone were determined for the 60310A bearing of the power take-off shaft gearbox during aggregation with different agricultural machines such as 4300 Newtons and 2.4 degrees Celsius for FS-2.0U garden cutter (540 revolutions per minute); 4126 Newtons and 40.7 degrees Celsius for Rovatti T3K80/90/2 (540 revolutions per minute) irrigation pump; 956 Newtons and 13.0 degrees Celsius for ROU-6 (1000) manure spreader; 2615 Newtons and 36.6 degrees Celsius for KPRN-3.0A (1000) mower-conditioner. The maximum temperatures as a diagnostic criterion are established in the friction zone, which equal to 41.7 degrees Celsius at 540 revolutions per minute engine speed and 31 degrees Celsius at 1000 revolutions per minute. (Conclusions) Since the direct measurement of the temperature in the friction zone is hardly possible without changing the bearings design, it is proposed to measure the diagnostic temperature on the unit used for mounting the temperature sensor. The coefficient of proportionality k=0.53 of the finite element model is determined. In order to implement diagnostics in an automatic mode, an algorithm is developed for a digital transmission malfunction recorder. Its design is based on the ATmega328 programmable microcontroller and TMP36 temperature sensors. It is found that the digital transmission malfunction recorder provides automatic control of up to seven different transmission units simultaneously, taking into account the ambient temperature.

Terrestrial heat flow measurement and numerical simulation of lithospheric thermal structure in western Sichuan, China

The western Sichuan in the eastern Qinghai-Tibet plateau has significant geothermal potential. Heat flow is one of the most important parameters in geothermic, its measurement can help obtain a better understanding of the regional lithospheric thermal structure. In this study, we reported 4 heat flow data based on the continuous steady-state temperature logging and rock thermal conductivity test, including two class-A and two class-D data. Furthermore, we calculated the lithospheric thermal structure by a 2D steady-state thermal conduction equation in COMSOL, analyzing the lateral differences of lithospheric thermal structure in the eastern Qinghai-Tibet plateau. Our study has determined that the heat flow values in the western Sichuan range from 94.7 to 116.2 mW/m2, with a corresponding geothermal gradient of 32.1–37.3 °C/km. Moreover, numerical simulation results indicate significant differences in lithospheric thermal structure between western Sichuan and Sichuan Basin, where the Longmen Shan fault zone is a crucial regional tectonic boundary and a significant temperature gradient zone. Specifically, the Moho temperature in the western Sichuan region ranges from 1000 to 1200 °C with an average temperature of 1060 °C, while the Sichuan Basin ranges from 600 to 700 °C. Besides, the thermal lithosphere thickness in the western Sichuan and the Sichuan Basin is 88–97 km and 105–110 km, respectively. These observations suggest that the western Sichuan region is characterized by high thermal anomaly and provide theoretical evidence for the geodynamic and geothermal development in this area. Finally, we suggest that the high thermal anomaly in western Sichuan is the result of a combination of factors, such as thickened crust, high radioactive heat production, and shear frictional heating from deep fault and so on.

Using LAMMPS to shed light on Haven’s ratio: Calculation of Haven’s ratio in alkali silicate glasses using molecular dynamics

Haven and Verkerk studied the diffusion of ions in ionic conductive glasses with and without an external electric field to better understand the mechanisms behind ionic conductivity. In their work, they introduced the concept now known as Haven’s ratio (HR), which is defined as the ratio of the tracer diffusion coefficient (Dself) of ions to the diffusion coefficient from steady-state ionic conductivity (Dσ), calculated by the Nernst–Einstein equation. Dσ can be challenging to obtain experimentally because the number of charge carriers has to be implied, a subject still under discussion in the literature. Molecular dynamics (MD) allows for direct measurement of the mean squared displacement (r2) of diffusing cations, which can be used to calculate D, avoiding the definition of a charge carrier. Using MD, the authors have calculated the r2 of three alkali ions (Li, Na, and K) at different temperatures and concentrations in silicate glass, with and without the influence of an electric field. Results found for HR generally fell close to 0.6 at lower concentrations (x = 0.1) and close to 0.3 at higher concentrations (x = 0.2 and 0.3), comparable to the literature, implying that the electric field introduces new mechanisms for the diffusion of ions and that MD can be a powerful tool to study ionic diffusion in glasses under external electric fields.

Vascular Responses to Passive and Active Movement in Premenopausal Females: Comparisons across Sex and Menstrual Cycle Phase.

Adequate, robust vascular responses to passive and active movement represent two distinct components linked to normal, healthy cardiovascular function. Currently, limited research exists determining if these vascular responses are altered in premenopausal females (PMF) when compared across sex or menstrual cycle phase. Vascular responses to passive leg movement (PLM) and handgrip (HG) exercise were assessed in PMF ( n = 21) and age-matched men ( n = 21). A subset of PMF subjects ( n = 11) completed both assessments during the early and late follicular phase of their menstrual cycle. Microvascular function was assessed during PLM via changes in leg blood flow, and during HG exercise, via steady-state arm vascular conductance. Macrovascular (brachial artery [BA]) function was assessed during HG exercise via BA dilation responses as well as BA shear rate-dilation slopes. Leg microvascular function, determined by PLM, was not different between sexes or across menstrual cycle phase. However, arm microvascular function, demonstrated by arm vascular conductance, was lower in PMF compared with men at rest and during HG exercise. Macrovascular function was not different between sexes or across menstrual cycle phase. This study identified similar vascular function across sex and menstrual cycle phase seen in microvasculature of the leg and macrovascular (BA) of the arm. Although arm microvascular function was unaltered by menstrual cycle phase in PMF, it was revealed to be significantly lower when compared with age-matched men highlighting a sex difference in vascular/blood flow regulation during small muscle mass exercise.