Problem Of Unsteady Heat Transfer Research Articles

A physics-driven and machine learning-based digital twinning approach to transient thermal systems

PurposeIn this study, the authors propose a novel digital twinning approach specifically designed for controlling transient thermal systems. The purpose of this study is to harness the combined power of deep learning (DL) and physics-based methods (PBM) to create an active virtual replica of the physical system.Design/methodology/approachTo achieve this goal, we introduce a deep neural network (DNN) as the digital twin and a Finite Element (FE) model as the physical system. This integrated approach is used to address the challenges of controlling an unsteady heat transfer problem with an integrated feedback loop.FindingsThe results of our study demonstrate the effectiveness of the proposed digital twinning approach in regulating the maximum temperature within the system under varying and unsteady heat flux conditions. The DNN, trained on stationary data, plays a crucial role in determining the heat transfer coefficients necessary to maintain temperatures below a defined threshold value, such as the material’s melting point. The system is successfully controlled in 1D, 2D and 3D case studies. However, careful evaluations should be conducted if such a training approach, based on steady-state data, is applied to completely different transient heat transfer problems.Originality/valueThe present work represents one of the first examples of a comprehensive digital twinning approach to transient thermal systems, driven by data. One of the noteworthy features of this approach is its robustness. Adopting a training based on dimensionless data, the approach can seamlessly accommodate changes in thermal capacity and thermal conductivity without the need for retraining.

СОВЕРШЕНСТВОВАНИЕ РАСЧЕТА ПРОСТРАНСТВЕННЫХ СТЕРЖНЕВЫХ КОНСТРУКЦИЙ ИЗ ПОЛИМЕРНЫХ МАТЕРИАЛОВ С УЧЕТОМ ТЕМПЕРАТУРНОГО ВОЗДЕЙСТВИЯ.

The influence of temperature effects on the technical condition of cross-bar spatial structures (CSRS) made of polymer building materials (PSM) is considered using the example of tubular elements made of polyvinyl chloride (PVC). From numerous scientific studies by various authors, it is known that low and high temperatures significantly affect the mechanical safety of engineering plastics: tensile-compressive strength, bending, loss of stability, torsion, which ultimately reduces the operational reliability and durability of CSRS. The current regulatory and technical construction documentation on loads and impacts provides only climatic temperature impacts. In the documentation for building structures, technological temperature effects do not take into account the time factor. The general solution to the problem of unsteady heat transfer of a cylindrical element is considered in a nonlinear formulation to calculate the two-dimensional temperature field separately for the rod cylindrical element and the node connection in the “cylinder-cylinder” system. Graphic illustrations of the calculations are provided.

Numerical study of steady and periodic mixed convection of Bingham fluid in a narrow annulus with the exact Bingham model

This article numerically investigates the mixed convection of Bingham fluid in a narrow annulus. The temperature of the inner fixed cylinder ( θ i ) is higher than that of the outer one ( θ o ), which rotates at a constant angular velocity. An OpenFOAM solver, icoFoam, which works based on the finite volume method and the PISO algorithm, is modified to perform the simulations. The modified solver can solve unsteady heat transfer problems for Bingham fluids without using regularization methods. After validating the solver, it solves the problem in different conditions to show the effect of relevant parameters, such as Reynolds number, Bingham number, and aspect ratio, on the flow field and thermal performance of the enclosure for constant amounts of Grashof and Prandtl numbers. The results are presented as streamlines and isotherms, the size and shape of the unyielded regions, the local and mean Nusselt number, and the torque coefficient. The results demonstrate that the flow is steady at Re = 10 for all Bingham numbers, and a decrease in the Reynolds number may result in an unsteady flow depending on the value of the Bingham number. The flow’s time history reveals that at a fixed Reynolds number, the flow shifts from periodic to steady-state by enhancing the Bingham number so that the flow becomes entirely steady for a given Bingham number. An interesting phenomenon is observed, the formation, movement, and disappearance of the plug zones (unyielded regions) for the periodic flow at Re = 1 and Bn = 5 .

Novel methodologies for solving the inverse unsteady heat transfer problem of estimating the boundary heat flux in continuous casting molds.

In this article, we investigate the estimation of the transient mold-slab heat flux in continuous casting molds given some thermocouples measurements in the mold plates. Mathematically, we can see this problem as the estimation of a Neumann boundary condition given pointwise state observations in the interior of the domain. We formulate it in a deterministic inverse problem setting. After introducing the industrial problem, we present the mold thermal model and related assumptions. Then, we formulate the boundary heat flux estimation problem in a deterministic inverse problem setting using a sequential approach according to the sequentiality of the temperature measurements. We consider different formulations of the inverse problem. For each one, we develop novel direct methodologies exploiting a space parameterization of the heat flux and the linearity of the mold model. We construct these methods to be divided into a computationally expensive offline phase that can be computed before the process starts, and a cheaper online phase to be performed during the casting process. To conclude, we test the performance of the proposed methods in two benchmark cases.

N-Side Cell-Based Smoothed Finite Element Method for Incompressible Flow with Heat Transfer Problems

In this paper, an n-sided cell-based smoothed finite element method (nCS-FEM) is presented to solve the convective heat transfer in incompressible viscous fluid flow. The Characteristic-based-split (CBS) scheme is used to stabilize the spatial and pressure oscillations of CS-FEM that occur during the process of solving incompressible Navier-Stokes equations. Meanwhile, the characteristic-Galerkin method in CBS is adopted as the convective stabilization in the heat transfer equation. In order to verify the proposed method, typical numerical examples are used to test the computational accuracy of CS-FEM. Meanwhile, the investigation of the robustness of highly distorted element is conducted in a natural convection test case. The calculation results of numerical examples show that CS-FEM is qualified to solve the steady and unsteady convective heat transfer problems for incompressible laminar flow with high reliability. The flow across tube banks with complex geometry in the heat sinks is also simulated to prove the capabilities of the proposed method. Well agreed comparison with the results of CFD software, Fluent, proves that the present method can effectively simulate realistic and complex flow with heat transfer problems.

Nonintrusive reduced‐order modeling approach for parametrized unsteady flow and heat transfer problems

AbstractA novel nonintrusive reduced‐order modeling approach is proposed for parametrized unsteady flow and heat transfer problems. A set of reduced basis functions are extracted via a proper orthogonal decomposition (POD) method from a collection of high‐fidelity numerical solutions (snapshots of spatial distribution at a series of time steps) that are computed for properly chosen parameters (e.g., material property, initial/boundary conditions) using a full‐order model (finite‐volume/finite‐element methods). Here, the time dimension is treated separately from other parameters, reflecting the dynamic features of the flow problems. Dynamic mode decomposition is used to decompose the time‐resolved data (POD coefficients) into dynamics modes and reconstruct/predict the dynamic evolution of the flow systems. The POD coefficients at every time step under the condition of a set of parameters are approximated through interpolation with the radial basis function method from those obtained from the snapshots of the chosen parameter space. Hence, the POD coefficients at a set of given time and parameters can be approximated, and the spatial distribution of the solution data can be reconstructed. The current reduced‐order model has been applied to the problems governed by a set of parametrized unsteady Navier–Stokes and heat conduction equations. The model capability has been illustrated numerically by three numerical test cases: flow past a cylinder, melt solidification, and dam break. The model prediction capabilities have been evaluated by varying the material properties (viscosity and density) and the heat transfer conditions on some of the boundaries. An error analysis is also carried out to show the model prediction accuracy.

Optimization and Solution of the Temperature Curve of Reflow

In the production process of electronic products such as process integrated circuit boards, some firmware needs to be heated and soldered to the circuit board through a reflow furnace. In this process, the temperature setting of each temperature zone and the control of the furnace passing speed play a vital role in the quality of the product. By consulting the data, it is known that the reflow heats the welding area by impinging jets, and it is considered that the heat transfer in the reflow is carried out by heat convection. Using Newton’s law of cooling, the three-dimensional heat transfer process is simplified to a two-dimensional unsteady heat transfer problem. Taking into account the lag of the center temperature of the circuit board relative to the surface temperature, it is considered that the heat transfer in the circuit board is carried out by heat conduction, and the physical parameters such as the density and heat transfer coefficient of the circuit board and the soldering area are integrated into a constant τ. The known data is obtained, and the temperature change law model is finally established.

Physics-Assisted Deep Neural Network for Inverse Unsteady Heat Transfer Problems

Physics-Assisted Deep Neural Network for Inverse Unsteady Heat Transfer Problems

Finite Difference Analysis of Unsteady Heat and Flow of an Incompressible Third Grade Fluid

An unsteady flow and heat transfer problem with viscous dissipation of a third order fluid placed within two long parallel flat porous walls is studied in present work. The governing equations are non- dimensionalized and finally a non-linear coupled system of partial differential equation is obtained. An approximated solution is obtained using finite difference method of fully implicit form. With help of high speed MATLAB programming numerical solution is procured and presented graphically. Investigation is made on effect of different physical parameters on flow and heat profile. The notable finding in the current work is that for smaller values of visco-elastic parameter ®, the velocity rises with raising the values of ®. But for larger visco-elastic parametric values of ®, a reversed effect is seen on velocity field. Also with the increase of viscous-dissipation parameter, more viscous-dissipation heat generated that increases the temperature field.

Numerical study for the unsteady space fractional magnetohydrodynamic free convective flow and heat transfer with Hall effects

In this paper, a numerical research for the problem of unsteady space fractional magnetohydrodynamic (MHD) free convective flow and heat transfer with Hall effects is investigated. We firstly establish a space fractional MHD flow and heat transfer model, which is coupled by the incompressible space fractional Navier–Stokes equations and the heat conduction equation. Then we develop a finite difference spectral decomposition method based on the pressure correction algorithm to solve this nonlinear coupled model. The validity of the proposed numerical scheme is verified and some flow field, temperature field are obtained. We also detailedly analyze the effects of relevant parameters on the space fractional MHD flow and heat transfer.

Novel Method of Fast Measurement of Thermal Conductivity in Wide Range of Temperatures

Theoretical aspects and practical realization of a new method of fast measurement of thermal conductivity of coating materials (like deposits on wall and tubes of the boilers using fossil fuel, or high-temperature ceramics and adhesive materials) are presented. The method is based on analytical solution of the problem of unsteady heat transfer from the heated probe with coating to the environmental air. Several models of the phenomenon, taking into account convection and thermal radiation components of heat transfer, are described. The records of the probe temperature are processed numerically and compared with calculated values based on analytical solution. The best fit between the curves of recorded and calculated temperatures yields thermal conductivity value used as a parameter of the best fitting. This approach was applied to measurement of thermal properties of Fouling deposition in a coal-firing boiler. It was also demonstrated how extended version of the method allows one to represent the thermal conductivity of coating as a piecewise constant function of temperature, using a single record of the probe cooling curve. With a specially designed software for efficient calculation according to developed mathematical model, the whole experiment in the range 1500 °K–300 °K takes no more than 35–40 min, including processing on a regular PC. Validation of the suggested method was carried out in a special experiment with the substance of known thermal conductivity (Corn oil). The method was applied to Fouling depositions of two kinds of fuel—Columbian bituminous coal and Russian bituminous coal. It was demonstrated that Fouling in these two cases is characterized by significantly different thermal conductivity which also changes markedly with temperature.

Expanding/contracting fin of rectangular profile

PurposeThe purpose of this paper is to study an expandable or contractible metallic fin and heat transfer process. The fin is assumed to be thin having a rectangular cross section. It is attached to a hot surface with a time-dependent temperature, and its tip extends to a medium (fluid) of an ambient temperature. With the insulated wall constraint at the tip, the tip of the metallic fin has the property of expanding or contracting in time at a specific rate.Design/methodology/approachThe corresponding physical problem is so formulated that the unsteady heat transfer problem is governed by means of a similarity variable represented by a second-order ordinary differential equation. The system can be reduced to the traditional well-documented steady state fin problem often studied in the literature, if the unsteadiness is turned off from the formulated system.FindingsThe system is then solved analytically for the temperature distribution through the fin. The fin tip temperatures are calculated, and the heat transfer analysis is made with varying physical parameters. And finally, observations are discussed leading to better fin efficiency and heat transfer enhancement.Originality/valueAn expandable or contractible metallic fin and heat transfer process are analyzed for the first time in the literature. Full solutions are presented, whose numerical correspondence is discussed through graphical and tabular forms.

Heat transfer augmentation in a diamond shaped enclosure utilizing CNT-water Nanofluid

A numerical analysis has been investigated for unsteady natural convection heat transfer problem in diamond shaped cavity. Carbon nanotube (CNT)-water nanofluid is used to analyze the heat transfer and compared with the pure water as working fluid. The lower right wall is kept at heated surface with constant heat flux and upper left wall is kept cold. Both the bottom left and upper right wall are kept adiabatic. The considered physical problem is characterized mathematically by a set of governing equations along with the corresponding boundary conditions. Galerkin weighted residual method of finite element analysis is used to solve the governing equations. Calculations are done for pertinent parameters such as the solid volume fraction (ϕ = 0.0–0.12) and Rayleigh number (Ra = 104–108) at dimensionless times (τ = 0.01 and 1.0) and fixed Pr = 6.2. Obtained results are presented in terms of average Nusselt number and maximum fluid temperature, streamlines and isotherms in graphs, charts and related contours. It has been observed that increase of Rayleigh number and solid volume fraction enhance the heat transfer rate and reduce the maximum fluid temperature. In this investigation the highest amount of overall heat transfer reaches up to 115%.

A parallel inverted dual time stepping method for unsteady incompressible fluid flow and heat transfer problems

The simulation of unsteady incompressible fluid flow and heat transfer problems is a huge time-consuming task and has been becoming one of the hottest topics in the fields of computational fluid dynamics and numerical heat transfer. Pure spatial parallelization has been so far the most widely used parallel strategy to speed up unsteady simulations but suffers from the problem of speedup saturation as parallel scale increases. In order to further speed up unsteady simulations and exploit the concurrency in temporal dimension, we propose a novel temporal parallelization strategy, i.e., parallel inverted dual time stepping method, by simply inverting the sequence of the inner loop (pseudo time) and the outer loop (physical time) within the dual time stepping framework. The parallel performance of the proposed method is verified and validated with three steady/unsteady problems. Parallel results of the proposed method agree well with those of the dual time stepping method and the available benchmark solutions. The parallel efficiency of the proposed method is about 96%, 81%, 62%, 51%, 45% for 4, 8, 12, 16, 20 CPU cores, respectively, which is considerably higher than that of the widely used parareal method. The proposed method has potential in further increasing parallel scale as spatial parallelization is saturated.

Unsteady theory of heat transfer and fluid flow during instantaneous transition to film boiling

The paper deals with the problem of unsteady convective heat transfer during instantaneous transition to film boiling over a flat vertical surface, when heat flux is suddenly switched on. This heat flux exceeds the critical value, which corresponds to the onset of the film boiling regime. As a result, instantaneous transition to film boiling takes place. To solve the problem, two sets of the initial and boundary conditions were used. The first set was used in the classical solution of the film condensation problem derived by Nusselt. The second set was proposed by Ellion for a stationary liquid at the vapor-liquid interface. The analytical solution of the problem enabled obtaining unsteady temperature distributions, Nusselt numbers, velocity profiles and friction coefficients. Results obtained based on the Laplace transform and the self-similar solution are analyzed.

Optimization of structural solutions building envelopes of industrial buildings operated in variable thermal conditions

The article presents the methodology of thermo-technical calculation of low-heat enclosing structures industrial buildings operated in conditions of variable thermal conditions. According to the proposed methodology, the thickness of the sandwich panel of the outer wall of the industrial building is determined on the basis of the fulfillment of energy saving conditions and the given time of room’s heating. To solve the problem of unsteady heat transfer through the outer wall was applied an approximate analytical method developed by the authors of this article. The presented analytical method by choosing a building envelope allows taking into account not only heat-shielding but also the dynamic characteristics of the fence. This calculation method can be applied at the stage of developing structural solutions for the external fence and detailing of building units in this construction. The results of the heat engineering calculation of the outer wall of a production building under construction are presented as an example. Based on the presented calculation results, it becomes possible to determine the optimal thickness of the insulation layer, at which the designed enclosing structure will satisfy not only the modern requirements of thermal protection, but also provide a given time for the heating of the room.

Investigation of a solar assisted heat pump wheat drying system with underground thermal energy storage tank

Storage of solar energy in underground Thermal Energy Storage (TES) tank during sunny days and extraction of the energy in the TES tank and its surrounding ground by a heat pump through the year for drying systems is an attractive subject for effective use of solar energy and ground as heat sources. It is possible to store solar energy in the TES tank and ground to use it for heating systems. In this study, modeling of a wheat drying system with a heat pump and underground TES tank charged by solar energy is developed using energy analysis of the drying system to investigate its long-term performance parameters. The drying system has four components, which are wheat dryer, underground TES tank, solar collectors, and a heat pump. The analytical model consists of a solution of unsteady heat transfer problem around the TES tank and energy expressions for the other components. A MATLAB code is developed to examine the performance parameters hour by hour along the years. These parameters are water temperature in the tank, Coefficient of Performances for the heat pump (COP) and system (COPs), Specific Moisture Evaporation Rate (SMER), and energy fractions for the system. When wheat mass flow rate and Carnot efficiency are selected as 50 kg h−1 and 40% respectively, collector area, TES tank volume, COP, COPs and SMER are 70 m2 and 200 m3, 4.43, 4.3 and 6.05 respectively when the system attains periodic operation time from the 5th year onwards for 10 years of operation.

Analysis of Unsteady Heat Transfer Problems with Complex Geometries Using Isogeometric Boundary Element Method

Numerical analysis of unsteady heat transfer problems with complex geometries by the isogeometric boundary element method (IGABEM) is presented. The IGABEM possesses many desirable merits and features, for instance, (a) e... | Find, read and cite all the research you need on Tech Science Press

Meshless Method for Nonuniform Heat-Transfer/Solidification Behavior of Continuous Casting Round Billet

Numerical simulation is the primary approach to evaluate the complex solidification behavior for the continuous casting (CC) process, in which the methods based on the mesh and topology technique have been widely used to solve field variables. For the traditional techniques, such as the finite difference, finite element, and boundary element methods, it is arduous or even impossible to deal with complicated problems that involve multiphase coupling, interface tracking/reconstruction, and self-adaptation due to the inherent weaknesses in the grid structure and mesh dependence. Hence, the present work explores a meshless calculation method for the two-dimensional unsteady heat-transfer problem and proposes an element-free Galerkin (EFG) model for solving heat transfer inside the CC mold based on the moving least-squares approximation. The temperature functions are approximated and constructed by a linear basis and cubic spline weight function over a set of rectangular supporting domain; then, the discrete heat-transfer governing equation based on the EFG method is deduced. The heat flux measured in the real casting process is set as the boundary condition to calculate the nonuniform solidification of the round billet. The calculated results demonstrate that the shell thickness is consistent with that obtained by the square root law of solidification. In addition, the high heat flux region near the meniscus directly determines the growth characteristics of the initial billet shell, which ultimately results in the overall nonuniformity of the shell. The EFG method has the characteristics of fast convergence, high computational accuracy, and great discrete flexibility; it also provides a novel and effective approach for subsequent thermomechanical coupling and crack propagation analysis in the CC process.

Full-scale experimental study of moisture condensation on the glazing surface: condensation rate characterization

Excessive indoor moisture promotes the growth of mold and condensation on building envelope, which lead to severe IAQ problems. Given the transient, unsteady heat and mass transfer problem, studies dealing with the condensation phenomenon are generally lacking in the literature, especially studies on the condensation rate prediction. Consequently, this paper presents a method to quantify experimentally the condensation rate of droplets formed on a cold glazing surface in a full-scale entirely controlled test room (6.2 x 3.1 x 2.5 m). The condensation qualitative characterization, i.e. the moment of its appearance and its growth mechanism, is achievable using a macro-photography technique. From the time-series of droplet images captured, an image post-processing method is used to detect the droplet contours and to estimate the condensation mass flow rate. Comparisons between experimental and theoretical results show some agreement, which could validate the feasibility of imaging techniques in full-scale condensation studies. Those first results are encouraging and valuable since there were no similar studies in the literature at such the scale. Further investigations are needed in order to clarify all these aspects related to the accuracy of the condensation rate quantification methodology developed in this work.