Exponential Flux Research Articles

A comparative study of prescribed thermal analysis of a non-Newtonian fluid between exponential and linear porous surfaces

The present study communicates with the thermal analysis of an incompressible micropolar fluid by considering two different prescribed conditions corresponding to two different surfaces. On the porous surface of two different stretchable sheets, the unsteady flow problem of a micropolar fluid is explored by taking the variable impacts of the magnetic field. For both considered sheets, the prescribed thermal analysis is carried out with the contribution of joule heating, viscous dissipation, and radiation. Two prescribed cases of surface temperature and heat flux are discussed for linear stretched surface. Similarly, prescribed cases of exponential surface temperature and exponential heat flux are investigated for the case of an exponential stretchable surface. An effective technique of bvp4c in MATLAB is utilized to numerically tackle the governing equations of the problem. Both the distributions of temperature and velocity and the field of microrotation are graphically scrutinized relative to different geometries and several pertinent parameters. This study of thermal analysis with prescribed conditions elucidates that for an exponential surface, three distributions of flow phenomenon (temperature, microrotation, velocity) manifest more prominent results in comparison to the stretchable surface with linear velocity.

Heat Transfer Augmentation for Impingement of Steady Air Jet under Exponential Heat Flux Boundary Condition

Heat Transfer Augmentation for Impingement of Steady Air Jet under Exponential Heat Flux Boundary Condition

Uncertainty analysis and interval prediction of LEDs lifetimes

Lifetime analyses are crucial for ensuring the durability of new Light-emitting Diodes (LEDs) and uncertainty quantification (UQ) is necessary to quantify a lack of usable failure and degradation data. This work presents a new framework for predicting the lifetime of LEDs in terms of lumen maintenance, effectively quantifying the natural variability of lifetimes (aleatory) as well as the reducible uncertainty resulting from data scarcity (epistemic). Non-parametric survival models are employed for UQ of low-magnitude failures, while a new parametric interval prediction model (IPM) is introduced to characterize the uncertainty in high-magnitude lumen depreciation events and long-term extrapolated lifetimes. The width of interval-valued predictions reflects the inherent variability in degradation paths whilst the epistemic uncertainty, arising from data scarcity, is quantified by a statistical bound on the probability of the prediction errors for future degradation trajectories. A modified exponential flux decay model combined with the Arrhenius equation equips the IPM with physical information on the physics of LED luminous flux degradation. The framework is tested and validated on a novel database of LED degradation trajectories and in comparison to well-established probabilistic predictors. The results of this study support the validity of the proposed approach and the usefulness of the additional UQ capabilities.

Characteristic Length for Pinning Force Density in Nb3Sn.

The pinning force density, Fp, is one of the main parameters that characterize the resilience of a superconductor to carrying a dissipative-free transport current in an applied magnetic field. Kramer (1973) and Dew-Hughes (1974) proposed a widely used scaling law for this quantity, where one of the parameters is the pinning force density maximum, Fp,max, which represents the maximal performance of a given superconductor in an applied magnetic field at a given temperature. Since the late 1970s to the present, several research groups have reported experimental data on the dependence of Fp,max on the average grain size, d, in Nb3Sn-based conductors. Fp,maxd datasets were analyzed and a scaling law for the dependence Fp,maxd=A×ln1/d+B was proposed. Despite the fact that this scaling law is widely accepted, it has several problems; for instance, according to this law, at T=4.2 K and d≥650 nm, Nb3Sn should lose its superconductivity, which is in striking contrast to experiments. Here, we reanalyzed the full inventory of publicly available Fp,maxd data for Nb3Sn conductors and found that the dependence can be described by the exponential law, in which the characteristic length, δ, varies within a remarkably narrow range of δ=175±13 nm for samples fabricated using different technologies. The interpretation of this result is based on the idea that the in-field supercurrent flows within a thin surface layer (thickness of δ) near grain boundary surfaces (similar to London's law, where the self-field supercurrent flows within a thin surface layer with a thickness of the London penetration depth, λ, and the surface is a superconductor-vacuum surface). An alternative interpretation is that δ represents the characteristic length of the exponential decay flux pinning potential from the dominant defects in Nb3Sn superconductors, which are grain boundaries.

The Sensitivity of Convective Cloud Ensemble Statistics to Horizontal Grid Spacing in Idealized RCE Simulations

Abstract In this work, cloud ensemble statistics are extracted from idealized radiative–convective equilibrium simulations performed at horizontal grid spacings Δ ranging from 2 km to 125 m. At the coarsest resolution, convection remains randomly distributed in space such that the equilibrium statistical mechanics theory proposed by Craig and Cohen in 2006 (CC06; assumes Poisson distributed clouds and exponential mass flux distributions) remains valid. Using classical organization metrics, clustering is already observed at Δ = 1 km, but substantial deviations between the simulated cloud ensemble statistics and CC06 are only observed for grid spacings Δ < 500 m. At these resolutions, the cloud mass flux distributions exhibit heavy tails and cloud counts become overdispersed (higher variance than a Poisson distribution). These changes in ensemble statistics are accompanied by a shift in subcloud organization patterns as well as with the fact that individual cloudy updrafts start to be resolved. Consequently, a horizontal grid spacing no larger than 250 m is recommended, not only to properly resolve the dynamics of individual convective clouds, but also to capture the mesoscale organization of the cloud ensemble. Finally, it is shown that the CC06 theory and our high-resolution results including mesoscale organization may be reconciled if one considers 1) areas smaller than approximately 2 km in size, corresponding roughly to the narrow bands along which clouds develop almost randomly; and 2) individual cloud cores instead of cloud objects, core mass fluxes being shown to generally follow exponential distributions.

Numerical study of nanofluid flow over an exponentially stretching sheet with Hall current considering PEST and PEHF temperatures

We consider the nanofluid flow comprising titanium dioxide and a solid–liquid interfacial layer of ethylene-glycol over an exponentially stretched surface. A strong magnetic field perpendicular to the surface is applied externally while computing the Hall effect. The heat transfer analysis is accomplished by considering the cases of prescribed exponential surface temperature (PEST) and prescribed exponential heat flux (PEHF) amalgamated with thermal radiation. The slip boundary conditions are imposed on the surface. The thermal conductivity model is used to account for the impacts of the nanolayer (solid–liquid interface) and the diameter of the nanoparticles. The envisioned model is unique in its way as no study so far is carried out that discusses the aforementioned impacts altogether. The mathematical model is transmuted into ordinary differential equations (ODEs) by adopting similarity transformations, and the solutions are discovered numerically by using a bvp4c scheme. The consequences of emerging parameters versus associated profiles are numerically tabulated and graphically illustrated. It is noted that by increasing the interfacial layer thickness, the fluid temperature raises for both PEST and PEHF cases. The fluid temperature enhances for strong radiation effect for both PEST and PEHF conditions. The endorsement of the model is also a part of this analysis.

Gyrotactic Motile Microorganisms Impact on Pseudoplastic Nanofluid Flow over a Moving Riga Surface with Exponential Heat Flux

Background: The improvement of the thermal conductivity of nanofluids is practical for different processes such as drug delivery, manufacturing of crystals, polymer processing, food and drink, cancer treatment, oil and gas, paper making and for many more. The bioconvection phenomenon has engrossed the attention of numerous researchers for its many applications in biotechnology, mechanical and electrical engineering. Bioconvection nanofluids are more prominent in the fields of biomedicine, pharmacy, nanodrug delivery, biomedical, automotive cooling and the military. Purpose: The major purpose of the current work was to determine the numerical and statistical analysis of a novel thermal radiation and exponential space-based heat source on the bioconvective flow of a pseudoplastic 3D nanofluid past a bidirectional stretched Riga surface. The behavior of the Arrhenius activation energy (AAE) and thermal radiation are also disclosed. Methodology: Suitable similarity transformations were used to transmute the partial differential equations of the flow-modeled phenomena into the structure of ordinary differential ones. The numerical solutions for the renewed set of ODEs were tackled by the bvp4c shooting algorithm built-in MATLAB software. Furthermore, the statistical analysis was computed by applying response surface methodology (RSM). Research implications: The numerical analysis is valid for the incompressible three-dimensional, magnetized flow of a pseudoplastic bioconvection nanofluid through a bidirectional surface with Riga plate aspects in the occurrence of activation energy. Social implications: The flow across three dimensions has quite important implementations in various fields, for example, polymer production, material production technology, the manufacturing of nano-biopolymer computer graphics, industry, powered engineering, aeroplane configurations, etc. The current analysis is more applicable in nanotechnology. Results: The consequences of flow control parameters over flow profiles were studied and explained under the graphic structures. Numerical outcomes were computed and discussed in detail. From the results, it was noted that the velocity field was increased via a larger mixed convection parameter. The temperature distribution was boosted via the thermal Biot number. The concentration of nanoparticles declined via the greater Lewis number. Furthermore, the motile microorganisms field was reduced via the Peclet number. Originality: Until now, no investigation has been recognized to examine the consequences of the bioconvection flow of three-dimensional pseudoplastic nanofluids past a Riga plate containing motile microorganisms utilizing the shooting method called bvp4c. Conclusions: From the results, it was concluded that nanofluids are more helpful for heat transfer increments. Furthermore, from the experimental design observed, the response declined via the thermophoresis parameter, which was significant from the ANOVA observed model.

Numerical investigation of double diffusion heat flux model in Williamson nanofluid over an exponentially stretching surface with variable thermal conductivity

This investigation examines the Williamson nanofluid flow over an exponentially stretched surface with variable thickness. Cattaneo-Christov double diffusion (CCDD) heat flux model is applied while examining two cases of heat transfer, i.e., prescribed exponential surface temperature (PEST) and prescribed exponential heat flux (PEHF). A mathematical model of the problem based on momentum, mass, and energy conservation. The governing non-linear partial differential equation (PDEs) are converted into non-linear ordinary differential equations (ODEs) via similarity transformations. The velocity, temperature, and concentration profiles are obtained numerically. Additionally, the impacts of numerous physical parameters of engineering significance are visually depicted through graphs and tables. It is noted that by raising the thermal relaxation parameter γ 1 , the temperature profile decreases. When the concentration relaxation parameter γ 2 rises, then the concentration distribution also decays. When the magnetic parameter M increases, then the velocity profile decreases. For the selected numeric values of the Prandtl number Pr , the temperature profile decreases for both PEST and PEHF cases.

Corrigendum: Transient Heat Transfer Characteristics of Twisted Structure Heated by Exponential Heat Flux

Corrigendum: Transient Heat Transfer Characteristics of Twisted Structure Heated by Exponential Heat Flux

Transient Heat Transfer Characteristics of Twisted Structure Heated by Exponential Heat Flux

This study was conducted to investigate the transient heat transfer characteristics of a twisted structure. The twisted structure was heated according to exponential function (Q=Q0×exp(t/τ), where Q0 is the initial heat generation rate, W/m3; t is time, s; and τ is the period of heat generation rate). A wide range of τ from 37 ms to 14 s was applied for the experimental study. A platinum plate with five pitches (each was 180° twisted with 20 mm in length) was used in the experiment. Helium gas with inlet temperature of 298 K under 500 kPa was used as the coolant. The heat transfer coefficient is found to increase with the decrease of τ, and the transition point was estimated to be at τ≈1s, which means that, when the increasing ratio of heat generation rate satisfies dQdt≥Q0⋅et, the heat transfer enhancement phenomenon will be observed. The response analysis for transient heat transfer at fluid-solid interface was conducted by applying the concept of penetration depth. It is considered that, when the penetration depth is smaller than the thermal boundary thickness, the heat transfer from the interface (wall surface) to the fluid domain is not fully developed during the disturbance.

Modified Morris–Lecar neuron model: effects of very low frequency electric fields and of magnetic fields on the local and network dynamics of an excitable media

A Morris–Lecar neuron model is considered with electric and magnetic field effects where the electric field is a time-varying sinusoid and magnetic field is simulated using an exponential flux memristor. We have shown that the exposure to electric and magnetic fields have significant effects on the neurons and has exhibited complex oscillations. The neurons exhibit a frequency-locked state for the periodic electric field and different ratios of frequency-locked states with respect to the electric field frequency is also presented. To show the impact of the electric and magnetic fields on network of neurons, we have constructed different types of network and have shown the network wave propagation phenomenon. Interestingly, the nodes exposed to both electric and magnetic fields exhibit more stable spiral waves compared to the nodes exhibited only to the magnetic fields. Also, when the number of layers is increased, the range of electric field frequency for which the layers exhibit spiral waves also increases.

Inverse Estimation of Time-Dependent Heat Flux in Stagnation Region of Annular Jet on a Cylinder Using Levenberg–Marquardt Method

All solving methods available in literature are formulated for direct solution of stagnation point flow and its heat transfer impinging on the surfaces with known boundary conditions. In this paper for the first time, a numerical code based on Levenberg–Marquardt method is presented for solving the inverse heat transfer problem of an annular jet on a cylinder and estimating the time-dependent heat flux using temperature distribution at a specific point. For this purpose, the numerical solution of the dimensionless temperature and the convective heat transfer in a radial incompressible flow on a cylinder rod is carried out as a direct problem. Using similarity variable and appropriate transformations, momentum and energy equations are converted into Semi-similar equations. The heat flux is then estimated by applying the Levenberg–Marquardt approach. This technique is an iterative approach based on minimizing the least-square summation of the error values, the error being the difference between the estimated and measured temperatures. Results of the inverse analysis indicate that the Levenberg–Marquardt algorithm is an efficient and acceptably stable technique for estimating heat flux. This method also exhibits considerable stability for noisy input data. The maximum value of the sensitivity coefficient is related to the estimation of exponential heat flux and its value is 0.1619 also the minimum value of the sensitivity coefficient is 5.6210-6 which is related to the triangular heat flux. The results show that the parameter estimation error in calculating the triangular and trapezoidal heat flux is greater than the exponential and sinus–cosines heat flux because the maximum value of RMS error is obtained for these two cases, which are 0.481 and 0.489, respectively the reason for the increase in the errors in estimating these functions is the existence of points where the first derivative of the function does not exist.

Inverse analysis of the time-dependent heat flux in stagnation point flow of incompressible fluid impinging on a cylinder with uniform surface suction-blowing using Levenberg–Marquardt method

ABSTRACT In this paper for the first time, a numerical code based on Levenberg–Marquardt method is presented for solving inverse heat transfer problem of axisymmetric stagnation flow impinging on a cylinder with uniform transpiration and to estimate the time-dependent heat flux using temperature distribution at a point. The effect of noisy data on the final result is studied. The maximum value of the sensitivity coefficient is related to estimation of exponential heat flux and its value is 0.1718 also the minimum value of the sensitivity coefficient is 7.50 × 10−6 which is related to the triangular heat flux. The results show that the parameter estimation error in calculating the triangular and trapezoidal heat flux is greater than the exponential and sinus–cosines heat flux because the maximum value of RMS error is obtained for these two cases, which are 0.458 and 0.492, respectively the reason for the increase in error in estimating these functions is the existence of points where the first derivative of the function does not exist. This method also exhibits considerable stability for noisy input data. In most cases, surface blowing decreases the prediction accuracy by removing the boundary layers from the surface whereas suction acts vice versa.

Mathematical modeling of consolidation in unsaturated poroelastic soils under fluid flux boundary conditions

The spatiotemporal variability in precipitation could have a significant impact on ground subsidence. In this paper, we utilize a previously developed one-dimensional theory of consolidation for a two-fluid system, the generalization of Biot's theory, to investigate the impact of a time-dependent fluid flux across the surface of an unsaturated soil on the solid deformation and pore pressure responses. We consider three prescribed fluid flux patterns and the associated gradient of pore water pressure: constant, periodic, and exponential flux patterns. We employ a Fourier series representation and Laplace transformation in the space and time domains to derive a complete set of closed-form analytical solutions, including the complementary and particular solutions, describing both transient and steady-state excess pore water and pore air pressure responses as well as the total settlement induced by the fluid flux. Using two different types of soil, i.e. clay and sand, we demonstrate the dependence of the solution on the initial water saturation and hydraulic conductivity in the saturated and unsaturated regimes. Results of this study reveal that the fluid flux across the surface could have a significant impact on the dissipation of excess pore water pressure and the time evolution of the total settlement of the ground surface. The effect on the pore water pressure is more significant for sand than for clay irrespective of moisture content, mainly because of the much higher hydraulic conductivity of sand. Finally, we show that the hydraulic conductivity has a dominant effect on the consolidation behaviors of saturated and unsaturated soils subjected to surface fluid flux.

Ignition of polymers under exponential heat flux considering both surface and in-depth absorptions

Analytical models addressing ignition of solids under constant heat flux have been developed in previous studies utilizing surface or in-depth absorption or combination of them. When encountering time-dependent heat flux, the majority of the studies focused on polynomial heat flux and surface absorption assumption. However, in-depth absorption also should be taken into account under time-dependent heat flux in analytical models especially for infrared translucent solids. In this work, an analytical model aiming at revealing the ignition mechanism of translucent polymers under exponential time-increasing heat flux is established considering both surface and in-depth absorptions. Critical temperature is employed as ignition criterion. Four typical non-charring polymers, polymethyl methacrylate (PMMA), polyoxymethylene (POM), polyamide 6 (PA 6) and polypropylene (PP), are utilized as the reference materials, and a numerical solver is employed to validate the analytical model. The results show that the developed analytical model provides accurate predictions of surface temperature and ignition time. Surface heat loss by convection and reradiation has little effect on surface temperature, ignition time and critical energy, but it affects the ignition heat flux greatly. Thermal penetration depth differs from the one under constant heat flux, and it gets smaller as the surface heat loss is considered. The ignition time, thermal penetration depth and critical energy decrease as the heat flux increasing rate gets larger. Meanwhile, the ignition heat flux for in-depth absorption is higher than that for surface absorption, and both increase with heat flux increasing rate. Furthermore, the linearity between ignition time and the squared critical energy, proposed in constant and linear heat flux scenarios, is also found valid under this exponential heat flux condition.

Heat transfer of three-dimensional micropolar fluid on a Riga plate

In this article, we deal with prescribed exponential surface temperature and prescribed exponential heat flux due to micropolar fluids flow on a Riga plate. The flow is induced through an exponentially stretching surface within the time-dependent thermal conductivity. Analysis is performed inside the heat transfer. In our study, two cases are discussed here, namely prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). The governing systems of the nonlinear partial differential equations are converted into nonlinear ordinary differential equations using appropriate similarity transformations and boundary layer approach. The reduced systems of nonlinear ordinary differential equations are solved numerically with the help of bvp4c. The significant results are shown in tables and graphs. The variation due to modified Hartman number M is observed in θ (PEST) and [Formula: see text] (PEHF). θ and [Formula: see text] are also reduced for higher values of the radiation parameter Tr. Obtained results are compared with results from the literature.

Birth and death of spiral waves in a network of Hindmarsh–Rose neurons with exponential magnetic flux and excitable media

Spiral waves are spatiotemporal patterns, observed in complex networks of biological oscillators such as heart and brain. In this paper, at first a modified Hindmarsh–Rose model with external electromagnetic radiation and discontinuous exponential flux coupling is introduced. Then a 2-dimensional network of the proposed model is constructed. The spatiotemporal patterns of the network are investigated in two different cases of periodic and quasi-periodic external magnetic excitations, by varying the external force parameters. As a consequence, the effective factors on the formation and elimination of spiral waves are reported.

Polynomial approximate solutions of an unconfined Forchheimer groundwater flow equation

We consider a one-dimensional, unconfined groundwater flow equation for the horizontal propagation of water. This equation was derived by using a particular form of the Forchheimer equation in place of Darcy’s Law. Such equations can model turbulent flows in coarse and fractured porous media. For power-law head, exponential head, power-law flux and exponential flux boundary conditions at the inlet, the problems can be reduced, using similarity transformations, to boundary-value problems for a nonlinear ordinary differential equation. We construct quadratic and cubic approximate solutions of these problems. We also numerically compute solutions using a new modification of a method of Shampine, which exploits scaling properties of the governing equation. The polynomial approximate solutions replicate well the numerical solutions and they are easy to use. Last, we compare the predicted wetting front positions from our quadratic and cubic polynomials to predictions based on Adomian polynomials of the same degrees. The work demonstrates the value of polynomial approximate solutions for validating numerical solutions and for obtaining good approximations for water profiles and the extent of water propagation. This work also presents a new application of Shampine’s method for this type of groundwater flow equation. We note that this paper introduces additional classes of approximate solutions for the Forchheimer equation. Up to this date, not many solutions are known, especially for the transient cases considered here.

Simulation of Heat Flux to the DEMO First Wall Due to Filamentary Transport in the Far SOL

A simplified model describing turbulent plasma transport in the far scrape-off layer has been proposed for calculation of the plasma heat and particle fluxes to the first wall (FW) of the DEMO tokamak. The model has been implemented in the TOKES code for simulation of the heat flux distribution along the tokamak FW. First simulations of the wall heat flux, using this model, predict more pronounced “hot spots” at the top of the DEMO wall in comparison with the exponential heat flux decay model, commonly used for simulation of the flux.

Blow-up of multi-componential solutions in heat equations with exponential boundary flux

This paper deals with heat equations coupled via exponential boundary flux, where the solution is made up of $n$ components. Under certain monotone assumptions, necessary and sufficient conditions are obtained for simultaneous blow-up of at least two components for each initial datum. As for two components blowing up simultaneously, it is interesting that the representations of blow-up rates are quite different with respect to the different blow-up mechanisms and positions between the two components.