Dimensional Heat Research Articles

Numerical and experimental study on the evolution of thermal contrast for infrared detection of debonding in concrete filled steel tubular structure

Debonding in Concrete-Filled Steel Tubes (CFST) can reduce bridges’ overall load-bearing capacity and thus threaten the bridge’s structural safety. Infrared thermography (IRT) is widely used for CFST debonding detection due to its efficiency and non-contact advantages. However, IRT is often affected by complex environmental factors and faces challenges in achieving quantitative evaluation only based on thermal contrast. This study aims to reveal the relationship between thermal indicators and thermal contrast through numerical and experimental investigations of CFST debonding under varied mimicked climatic conditions. A 3-dimensional (3-D) heat transfer transient model of CFST is established to simulate the evolution of thermal contrast of debonding under different daily temperature variations and seasonal solar irradiance. Based on the finite element analysis results, the internal interface heat flux is found as a strong linear indicator correlating the thermal contrast to environmental factors. Model experiments then were conducted to verify the validity of this indicator. Finally, an infrared evaluation method for CFST debonding is proposed, which can linearly quantify the relationships among debonding sizes, environmental factors, and thermal contrast.

The Geometry of Vector Fields and two Dimensional Heat Equation

The Geometry of Vector Fields and two Dimensional Heat Equation

3-D geometric design of microwaveable food products for optimal heating uniformity based on machine learning-supervised multiphysics models

Multiphysics models can assist in geometric design of frozen microwaveable foods, but the conventional 'parametric-sweeping' strategy is computationally intensive. This study develops an online machine learning (ML)-supervised multiphysics modeling strategy to simultaneously optimize multiple geometrical parameters (e.g., top surface width, top surface length, and the ratio of top-to-bottom dimensions) for optimal microwave heating uniformity. First, one or more paired geometric dimensional parameters and heating uniformity results obtained from multiphysics modeling are used as initial training data for the ML optimization process that integrates Gaussian Process Regression (GPR) and Bayesian optimization. Then, the multiphysics modeling procedure is supervised by an ML process to generate new paired geometry-heating uniformity results to expand the training dataset. The loop of multiphysics modeling and ML optimization is conducted to effectively identify geometry designs with good heating uniformity. Results indicate that the ML-supervised optimization strategy can efficiently identify good geometric designs with low heating uniformity by using much fewer multiphysics models than the parametric sweep approach. The ML-supervised approach also exhibits great robustness, delivering good performance even with small (as little as one model) and randomly selected initial training data. This ML-supervised approach is flexible and can be modified to meet specific needs for broad industrial implementation in the development of microwaveable food.

KPZ equation limit of sticky Brownian motion

We consider the motion of a particle under a continuum random environment whose distribution is given by the Howitt-Warren flow. In the moderate deviation regime, we establish that the quenched density of the motion of the particle (after appropriate centering and scaling) converges weakly to the (1+1) dimensional stochastic heat equation driven by multiplicative space-time white noise. Our result confirms physics predictions and computations in [66,7] and is the first rigorous instance of such weak convergence in the moderate deviation regime. Our proof relies on a certain Girsanov transform and works for all Howitt-Warren flows with finite and nonzero characteristic measures. Our results capture universality in the sense that the limiting distribution depends on the flow only via the total mass of the characteristic measure. As a corollary of our results, we prove that the fluctuations of the maximum of an N-point sticky Brownian motion are given by the KPZ equation plus an independent Gumbel on timescales of order (log⁡N)2.

Infinite time blow-up for the three dimensional energy critical heat equation in bounded domains

AbstractWe consider the Dirichlet problem for the energy-critical heat equation $$\begin{aligned} {\left\{ \begin{array}{ll} u_t=\Delta u+u^5 &{} \text {in} \quad \Omega \times \mathbb {R}^+,\\ u=0 &{}\text {on} \quad \partial \Omega \times \mathbb {R}^+,\\ u(x,0)=u_0(x) &{} \text {in} \quad \Omega , \end{array}\right. } \end{aligned}$$ u t = Δ u + u 5 in Ω × R + , u = 0 on ∂ Ω × R + , u ( x , 0 ) = u 0 ( x ) in Ω , where $$\Omega $$ Ω is a bounded smooth domain in $$\mathbb {R}^3$$ R 3 . Let $$H_\gamma (x,y)$$ H γ ( x , y ) be the regular part of the Green function of $$-\Delta -\gamma $$ - Δ - γ in $$\Omega $$ Ω , where $$\gamma \in (0,\lambda _1)$$ γ ∈ ( 0 , λ 1 ) and $$\lambda _1$$ λ 1 is the first Dirichlet eigenvalue of $$-\Delta $$ - Δ . Then, given a point $$q\in \Omega $$ q ∈ Ω such that $$3\gamma (q)<\lambda _1$$ 3 γ ( q ) < λ 1 , where $$\begin{aligned} \gamma (q) :=\sup \{ \gamma>0: H_\gamma (q,q)>0 \}, \end{aligned}$$ γ ( q ) : = sup { γ > 0 : H γ ( q , q ) > 0 } , we prove the existence of a non-radial global positive and smooth solution u(x, t) which blows up in infinite time with spike in q. The solution has the asymptotic profile $$\begin{aligned} u(x,t)\sim 3^{\frac{1}{4}} \left( \frac{\mu (t)}{\mu (t)^2+\vert x-\xi (t)\vert ^2}\right) ^{\frac{1}{2}} \quad \text {as}\quad t \rightarrow \infty , \end{aligned}$$ u ( x , t ) ∼ 3 1 4 μ ( t ) μ ( t ) 2 + | x - ξ ( t ) | 2 1 2 as t → ∞ , where $$\begin{aligned} -\ln (\mu (t))= 2\gamma (q) t(1+o(1)),\quad \xi (t)=q+O(\mu (t)) \quad \text {as}\quad t \rightarrow \infty . \end{aligned}$$ - ln ( μ ( t ) ) = 2 γ ( q ) t ( 1 + o ( 1 ) ) , ξ ( t ) = q + O ( μ ( t ) ) as t → ∞ .

Numerical investigation of flow boiling characteristics of R134A in a smooth horizontal tube

Three-dimensional transient simulations using ANSYS Fluentʼs mixture multiphase model was conducted to investigate the impact of heat flux, mass flux, and saturation temperature variations on pressure drop behaviour and heat transfer characteristics during flow boiling of R134a refrigerant in smooth horizontal tubes of different diameters. The simulations employ an implicit numerical method to solve the governing equations, with relevant source terms for mass and energy transfer, incorporating the continuum surface force (CSF) and shear stress transport (SST) κ-ω models to account for surface tension and flow turbulence respectively. The results are presented in both dimensional (heat transfer coefficient and pressure drop) and non-dimensional (Nusselt number and two-phase frictional factor) forms. The Nusselt number shows a direct relationship with the Reynolds number, while the two-phase friction factor exhibits different behaviour. At higher vapor quality, mass flux significantly affects heat transfer performance and pressure drop. Heat flux plays a crucial role in heat transfer, but its impact on pressure drop is negligible. Higher saturation temperatures enhance heat transfer while reducing pressure gradients. The obtained results demonstrate good agreement with existing correlations, with mean absolute deviations (MAD) as low as 1.2 % for the heat transfer coefficient and 23.7 % for the pressure drop behaviour. This highlights the model's accuracy in predicting flow boiling behaviour of R134a in smooth horizontal channels, providing valuable insights for thermal analysis. The findings contribute to the understanding of flow boiling processes and aid in designing and optimizing efficient heat exchangers for various engineering applications.

On a family of nonzero solutions to the heat equation ut = △u on ℝn+1 which vanish on an arbitrary n-dimensional hyperplane P ⊂ ℝn+1

Motivated by the paper Rosenbloom–Widder [A temperature function which vanishes initially, Amer. Math. Mon. 65(8) (1958) 607–609], we construct a more general family of nonzero solutions to the [Formula: see text]-dimensional heat equation [Formula: see text] on [Formula: see text] with zero initial data. These solutions are analytically more manageable than the well-known Tychonoff power series solution. Nonzero solutions to the [Formula: see text]-dimensional heat equation [Formula: see text] on [Formula: see text] with zero initial data (i.e. vanishing on the hyperplane [Formula: see text]) can be easily obtained as a consequence of the examples on [Formula: see text] Finally, given an arbitrary hyperplane [Formula: see text], we can construct a family of nonzero solutions which vanish on [Formula: see text]

Extended symmetry analysis of (1+2)‐dimensional fine Kolmogorov backward equation

AbstractWithin the class of (1+2)‐dimensional ultraparabolic linear equations, we distinguish a fine Kolmogorov backward equation with a quadratic diffusivity. Modulo the point equivalence, it is a unique equation within the class whose essential Lie invariance algebra is five‐dimensional and nonsolvable. Using the direct method, we compute the point symmetry pseudogroup of this equation and analyze its structure. In particular, we single out its essential subgroup and classify its discrete elements. We exhaustively classify all subalgebras of the corresponding essential Lie invariance algebra up to inner automorphisms and up to the action of the essential point‐symmetry group. This allowed us to classify Lie reductions and Lie invariant solutions of the equation under consideration. We also discuss the generation of its solutions using point and linear generalized symmetries and carry out its peculiar generalized reductions. As a result, we construct wide families of its solutions parameterized by an arbitrary finite number of arbitrary solutions of the (1+1)‐dimensional linear heat equation or one or two arbitrary solutions of (1+1)‐dimensional linear heat equations with inverse square potentials.

Application of the adaptive method to determine the process noise in the extended Kalman filter to estimate the parameters of the two dimensional inverse heat transfer problem

To deal with inverse nonlinear heat transfer problems in a two-dimensional heat conduction problem, this paper presents a hybrid approach combining fuzzy logic and the extended Kalman filter (EKF). The proposed algorithm has been applied to the real-time reconstruction of the temperature field, time-varying convective heat transfer coefficient, and time-varying boundary heat flux using temperature data from a set of sensors. The effects of the covariance of the initial estimation error, the time step of data acquisition by the sensors, and the number of installed sensors on the precision and stability of the estimation results has been investigated by numerical experiments. To compare and validate the results, all these parameters were investigated using the EKF method. The results show that the adaptive fuzzy extended Kalman filter (FEKF) method for estimating temperature, convection coefficient, and heat flux at the boundaries is precise and stable. The comparison shows that the performance of the FEKF method in parameter estimation is better than the EKF method, and the highest increase in precision and stability of the results is related to the convective heat transfer coefficient.

Groundwater–surface water exchange from temperature time series: A comparative study of heat tracer methods

The importance of the interaction between groundwater and surface water is increasingly being recognized for both understanding and managing water systems. Many efforts have been made to characterize and quantify groundwater–surface water exchange. In particular, temperature–based methods have quickly established themselves given their monetary and practical advantages. In the last 15 years, several methods for interpreting passive temperature time series measured in the streambed have been developed. Still, the benchmarking of these methods has only been carried out in specific and distinct hydrological conditions.This article aims to fill this research gap by benchmarking the performance of six commonly used methods for deriving seepage fluxes using a two-year-long temperature time series covering various meteorological and thermal conditions. This work compares three analytical methods that calculate seepage flux using the amplitude and/or phase of the temperature signals, and three numerical methods that use different schemes to inversely solve the one–dimensional heat transport equation in the streambed. The temperature measurements were made in the context of an international dispute between Chile and Bolivia over the status and use of the waters of the Silala River, Northern Chile. Flux estimations are tested against Darcy’s flux derived from measured hydraulic gradient and hydraulic conductivity.Flux estimations from the benchmarked methods ranged from −0.5 to 3.5 m/d (with positive fluxes directed downwards), whereas fluxes estimated using Darcy’s law ranged from 0.5 to 6 m/d. Results show that the amplitude method is the best–performing method. This method is best suited for estimating the direction of the fluxes, while the method using both the thermal amplitude and phase is best suited for monthly flux trends, and the combination of a Local Polynomial (LP) method and a Maximum Likelihood Estimator (MLE) method (LPMLEn) is appropriate for estimating flux in transient conditions.The use of heat as a tracer proved to be an effective tool for monitoring groundwater–surface water exchange in a river reach for two years, and yielded exchange flux estimates with lower point-scale variability than Darcy’s law.

Infinitely Fast Heterogeneous Catalysis Model for Premixed Hydrogen Flame-Wall Interaction

In most computations of reacting flows, walls are considered as inert. This approach can produce non-physical results that lead to very large values of heat release at the wall for hydrogen Flame-Wall Interaction (FWI). This paper confirms this unexpected behavior at walls for H2 flames. It also explores the possibility that the problem does not come from a deficiency of the chemical scheme at low temperatures but from the wall boundary condition: due to the large amount of radical species produced by H2 flames, the “inert” assumption may not be valid anymore. The purpose of this study is twofold: (1) to propose a simplified model named Infinitely Fast Heterogeneous Catalysis (IFHC) that mimics surface reactions and (2) to test it on the canonical Head-On Quenching (HOQ) configuration. A large set of parameters is investigated: a skeletal (San Diego) and a detailed (Burke) chemical schemes are tested, the grid-dependence and the influence of operating conditions (ϕ, Tw and P) are assessed. Results show that the IFHC model can inhibit the chemical pathways that are responsible for the heat generation peak observed on the wall in hydrogen FWI with inert surfaces. The IFHC model also allows computations to converge when the mesh is refined, a property that cannot be reached for inert wall treatments. Using IFHC, neither the predicted quenching distance nor the flame structure are altered. However, the maximum wall heat flux is significantly decreased when compared to inert walls. Over the range of operating conditions studied, the maximum wall heat flux is reached at high pressure, low wall-temperature and equivalence ratios close to the maximum of reactivity of H2 flames (ϕ≈1.7). This study shows that, for H2 FWI, walls should be at least modeled with simple surface reactions – such as IFHC – and that assuming inert walls is not possible.Novelty and significance statementThe work presented in this paper is new, original and of interest at the present time as many groups simulate near-walls H2/Air flames. The IFHC model is relevant for all premixed hydrogen combustion close to walls and is, thus, relevant for most realistic premixed hydrogen combustion scenarios. Besides being conservative in terms of mass, momentum, energy and atom balance, IFHC allows to reach mesh convergence during quenching contrary to simplistic inert wall treatments. It also allows to describe walls at an affordable computational cost compared to a full set of heterogeneous reactions. This work also opens the discussion with experimentalists since, to the best of the authors’ knowledge, the dimensional maximum wall heat fluxes are not yet available in the literature and are, thus, provided here for future comparison.

Enhancing the high-temperature thermal evacuation of Cf/C-Mo30Cu joint via grooving 3D heat transfer interface

The joining of Cf/C composite to Mo30Cu alloy plays an important practical role in a bias filter for thermonuclear fusion. In this study, the Cf/C composite is joined to Mo30Cu alloy at 860 °C/10 min using AgCu4.5Ti braze after fabricating the three dimensional (3D) heat transfer interface along the Cf/C interface. The effect of interface grooving on the thermal conductivity of the joint is investigated and compared with the original brazed joint. The results demonstrate that the room temperature thermal conductivity of the joint reached a maximum of 132 W·m−1·K−1 at a grooving depth of 200 μm, which is 17.8 % higher than that of the original joint (112 W·m−1·K−1). The thermal conductivity of the joint is still as high as 100 W·m−1·K−1 at a temperature of 500 ℃. The excellent high-temperature thermal conductivity significantly reduces the Cf/C damage and extends the service life of the joint. And the shear strength of the joint has also been significantly increased by 252 % from 13.1 MPa to 33.1 MPa. Grooves prepared along the Cf/C interface provide channels for braze penetration, increasing the contact area between the brazing seam and the Cf/C matrix. Ultimately, the thermal evacuation performance of the joint is improved by increasing the heat exchange area across the joint. Also, grooves along the Cf/C interface enable mechanical interlocking with the brazing seam, achieving an enhanced joint strength. The heat transfer process of the brazed joint is simulated and analyzed by the finite element method. The analysis indicated that the thermal evacuation across the joint can be enhanced by pre-fabricating a 3D heat transfer interface in the joint. This research can provide a reference for solving the problem of heat accumulation in the first wall materials inside thermonuclear reactors.

Heat and Mass Transfer on Unsteady MHD Chemically Reacting Rotating Flow of Jeffrey Fluid Past an Inclined Plates under the Impact of Hall Current, Diffusion Thermo and Radiation Absorption

An analytical solution for two dimensional unsteady MHD free convective double diffusive heat and mass transfer rotating flow of viscous incompressible optically thin non Newtonian fluid (jeffrey fluid) past a semi-infinite porous plate in the presence of generation of heat absorption with hall current, radiation absorption and Dufour effects are presented in this paper. Lorentz force is applied perpendicular direction to the plate with a first-order chemical reaction. The governing PDEs transformed into ODEs by applying the perturbation technique. The effects of various physical parameters like Hall current, heat absorption, radiation parameter, radiation absorption parameter, Grashof number, modified Grashof number, Dufour effect, magnetic field parameter, inclined angle, chemical reaction parameter, etc., are studied with graphically. Temperature profile is increased by raising the values of Dufour effect, radiation absorption parameter and reverse effect of the heat absorption parameter and also concentration profile distribution is downfall by raising the values of Schmited number, chemical reaction parameter. Another significant finding of the current study is that the numerical data are displayed with the use of Matlab programmes to investigate the outcomes of the skin friction solution. the rate of heat and mass transfer at the wall rising under the influence of Dufour effect. Tables, graphs, and reports can be used to display the impact of all pertinent parameters.

Uniform Regularity Estimates for Three Dimensional Nonhomogeneous Incompressible Heat Conducting Navier–Stokes Flows

Uniform Regularity Estimates for Three Dimensional Nonhomogeneous Incompressible Heat Conducting Navier–Stokes Flows

Quantitative Rapid and Finite Time Stabilization of the Heat Equation

The finite time stabilizability of the one dimensional heat equation is proved by Coron-Nguyên [J.-M. Coron and H.-M. Nguyen, Arch. Ration. Mech. Anal. 225 (2017) 993–1023], while the same question for multidimensional spaces remained open. Inspired by Coron-Trélat [J.-M. Coron and E. Trélat, SIAM J. Control Optim. 43 (2004) 549–569] we introduce a new method to stabilize multidimensional heat equations quantitatively in finite time and call it Frequency Lyapunov method. This method naturally combines spectral inequality [G. Lebeau and L. Robbiano, Comm. Partial Diff. Equ. 20 (1995) 335–356] and constructive feedback stabilization. As application this approach also yields a constructive proof for null controllability, which gives sharing optimal cost CeC/T with explicit controls and works perfectly for related nonlinear models such as Navier–Stokes equations [S. Xiang, Ann. Inst. H. Poincaré C Anal. Non Lineaire 40 (2023) 1487–1511.].

Laser induced temperature-jump time resolved IR spectroscopy of zeolites.

Combining pulsed laser heating and time-resolved infrared (TR-IR) absorption spectroscopy provides a means of initiating and studying thermally activated chemical reactions and diffusion processes in heterogeneous catalysts on timescales from nanoseconds to seconds. To this end, we investigated single pulse and burst laser heating in zeolite catalysts under realistic conditions using TR-IR spectroscopy. 1 ns, 70 μJ, 2.8 μm laser pulses from a Nd:YAG-pumped optical parametric oscillator were observed to induce temperature-jumps (T-jumps) in zeolite pellets in nanoseconds, with the sample cooling over 1-3 ms. By adopting a tightly focused beam geometry, T-jumps as large as 145 °C from the starting temperature were achieved, demonstrated through comparison of the TR-IR spectra with temperature dependent IR absorption spectra and three dimensional heat transfer modelling using realistic experimental parameters. The simulations provide a detailed understanding of the temperature distribution within the sample and its evolution over the cooling period, which we observe to be bi-exponential. These results provide foundations for determining the magnitude of a T-jump in a catalyst/adsorbate system from its absorption spectrum and physical properties, and for applying T-jump TR-IR spectroscopy to the study of reactive chemistry in heterogeneous catalysts.

Numerical Solution for the Heat Equation Using Crank-Nicolson Difference Method

Abstract: In this paper, the Crank-Nicolson difference method is applied to a simple problem involving one dimensional heat equation. Numerical solution to the heat equation using Crank-Nicolson difference equation is obtained. The method of solving the problem is implemented by using Python Programming. We have discussed the local truncation error and stability analysis of Crank-Nicolson difference method difference method of heat equation.

A New Nonlinear One-Dimensional Shape Function applied to Simulate a Steady State Heat Transfer Problem

Generally linear shape functions are considered for two noded elements as coefficients of higher order polynomial cannot be determined from two nodes. In the present work, attempts have been made to fit a non-linear trigonometric shape function for one dimensional two noded elements. As in case of nonlinearity, the dependent variable varies nonlinearly with the independent one, consideration of linear shape function may lead to erroneous results. Here, a one dimensional heat transfer problem is solved analytically, with the help of linear shape functions and with the help of newly developed nonlinear shape functions. Analysis shows that results obtained by considering nonlinear shape functions have quite good match with that by linear shape functions.

Effects of Chemical Reaction on Unsteady MHD Free Convective Flows past a Vertical Porous Plate Embedded in a Porous Medium with Variable Suction

In the present analysis we study two dimensional unsteady MHD free convection laminar heat and mass transfer flows past a vertical porous plate embedded in a porous medium with variable suction in the presence of chemical reaction and soret effects. Perturbation technique is applied to transform the non linear coupled governing partial differential equations in dimensionless form into a system of ordinary differential equations. The equations are solved analytically and the solutions for velocity, temperature and concentration fields are obtained. The effects of various parameters on velocity, temperature and concentration fields are presented graphically.

Numerical Solution for the Heat Equation Using Forward Time Centered Space Difference Method

Abstract: In this paper, the forward time centered space is applied to a simple problem involving one dimensional heat equation. Numerical solution to the heat equation using forward time centered space difference equation is obtained. The method of solving the problem is implemented by using Python Programming. We have discussed the local truncation error and stability analysis of explicit forward time centered space difference method of heat equation.