Heat Transfer Problem Research Articles

Towards more predictive correlations for conjugated mass transfer across a droplet interface

Most studies of heat or mass transfer in dispersed, two-phase flows are either analytical or empirical, and therefore limited to simplified or specific operating conditions. In this frame, Direct Numerical Simulations (DNS) can be a powerful tool to address the needs arising from the development of new liquid–liquid solvent extraction processes, involving e.g., more viscous solvents or different hydrodynamic conditions. In this study, a large parametric study, in the range: Reynolds number Re∈[1,500], Péclet number Pee∈[10,1000], viscosity ratio μ∗∈[0.05,20] and a thermodynamic equilibrium coefficient k∈[0.1,10] , of mass transfer from an isolated droplet is achieved by DNS to propose a physically based correlation of the apparent Sherwood number, Sh, that is sufficiently generic to apply to emerging and future applications. The updated correlations derive first from a solid analysis of the features, in terms of concentration fields inside and outside the droplet and interface properties, to challenge the validity of the assumptions of mass transfer correlations. Then, we propose proper modifications in the formulation of existing models. In a second step, the accuracy and the robustness of the new models have been assessed by comparison with Sh obtained from DNS. The proposed correlations are applicable for mass transfer as well as for heat transfer problems, in most configurations encountered in chemical plants.

Effects of magnetization and heat transfer on electrically conducting magnetohydrodynamics flow with mixed convection flow over porous duct

The effects of magnetic field and heat transfer problem on incompressible magnetohydrodynamics (MHD) mixed unsteady convective flow of an electrically conducting viscous fluid in a duct filled with a porous medium are investigated. The fluid flow is subjected to an applied uniform magnetic field vertical to the duct and uniform free stream of constant velocity and temperature. The system of nonlinear differential equations governing flow and heat transfer phenomena are derived and reduced into a set of ordinary differential equations using the auxiliary variable method. The reduced equations are solved numerically using Runge-Kutta method associated with slip boundary conditions. The graphical results for velocity, temperature and heat transfer rate are obtained using MATLAB software. It is observed that the velocity profiles increase with an increase of similarity parameter (fI) while temperature gradient decreases rapidly with an increase of similarity parameter (θI) for different values of Grosh number, Magnetization and Prandtl number respectively.

A Through Method for Solving Problems of Heat and Mass Transfer in Vapor–Liquid Systems That Takes Account of Many-Particle Interactions

A Through Method for Solving Problems of Heat and Mass Transfer in Vapor–Liquid Systems That Takes Account of Many-Particle Interactions

CFD simulation with analytical verification of discharging of nitrogen and helium from a high-pressure gas vessel

Many applications and industrial processes may necessitate the storage of large amounts of gases at high pressures. These compressed gases could be extremely dangerous if unintentionally released. since they could be poisonous or combustible when mixed with air. This research seeks to create a CFD model and undertake an analytical investigation of the process of de-pressurization of high-pressure gas from a vessel. The vessel to be studied is used in a pneumatic power system used to operate the control surface of a flying vehicle. The study involved two working fluids (nitrogen and helium). The discharging process is considered as a typical mass and heat transfer problem solved analytically by adopting The First Law of Thermodynamics to an unsteady flow control volume and simulated by employing transient flow analysis to the CFD model. The research was carried out on 440 bars (absolute pressure) of pressurized gas vessels. Working gases for the study included nitrogen and helium. Analytical solution results for the two different gases have been compared with the CFD simulation results to assess the CFD model’s accuracy. A good match is achieved when the gas temperature, pressure, density, and outlet mass flow rate variations are compared. The results demonstrated a good match between the CFD and analytical data, proving the validity of the CFD model.

A novel prediction for conjugated heat and mass transfer in falling film and membrane during LiBr absorption

The present investigation is intended to develop an understanding of how the vapor pressure and inlet temperature of the solution affect the absorption rate, which is helpful for the design of absorption heat pump systems. Many conjugated heat and mass transfer processes in falling film and membrane during lithium bromide (LiBr) absorption have not been well addressed. This paper proposes combining the meshless Radial Basis Function (RBF) and Discontinuous Galerkin (DG) methods to solve the conjugated heat and mass transfer in falling film and membrane-based absorption problems. The derivatives in the transverse direction are discretized using the RBF method. Owing to the parabolic nature of the governing equations, the DG methods can be used to discretize the derivatives in the streamwise direction. The efficacy of the proposed method is shown by comparing its results with analytical solutions and experimental data available in the literature. Furthermore, the proposed method is used to evaluate the analytical solutions of the heat and mass transfer problem in a membrane-based absorber. The previous published works simplified the problem to obtain the analytical solutions by providing the mean temperature and concentration values as the boundary conditions at the membrane-solution interface. The comparison of the RBF-DG method and the analytical solutions reveals that there are minor changes in temperature and local concentration values along the streamwise direction, but the profiles and trends are relatively similar across the film. A comparison of mass absorption rate calculations shows that RBF-DG and analytical solutions are compatible. The advantage of the numerical method is that various types of boundary conditions can be handled easily without any simplifications. Moreover, the numerical results of the proposed method are compared with experimental data, and they present good agreement. As a results, the absorption rate of falling film and membrane becomes capable of being accurately predicted.

Higher-Order Difference Schemes in Heat and Mass Transfer Problems

Higher-Order Difference Schemes in Heat and Mass Transfer Problems

Numerical research on contact friction force with different structural brush seal hysteresis characteristics under differential pressure

The problems of leakage, frictional wear, and flow heat transfer caused by the hysteresis characteristics of brush seals are prominent, and existing models for solving the hysteresis characteristics of brush seals have convergence difficulties owing to the extreme degree of nonlinearity caused by additional contacts. In this study, numerical models based on the finite element software ABAQUS were proposed to address the hysteresis characteristics of brush seals with three different structures: basic, low-lag hysteresis, and low-wear high-pressure bearing. The models accounted for the contacts between: the brush, brush and the baffle, and brush and the rotor, while damping was introduced to improve the convergence of the models. The hysteresis of the three structures under differential pressure was investigated and compared with theoretical calculations and experimental test results. The hysteresis of the bristles was normalised by the contact force, the shift of the contact area, and the contact friction force when the hysteresis effect occurred in the brush seal. The results show that the basic model has the most obvious hysteresis characteristics in the presence of differential pressure. Although the low-lag hysteresis model and the low-wear high-pressure bearing model have the weakest hysteresis effect, the deformation variables of the last row of bristles of these two structures are larger than those of the basic model; therefore, the contact position is prone to fatigue fracture. Simultaneously, the hysteresis effect was verified by varying the contact area and contact friction force, and it was found that the larger the contact area and contact friction force, the larger the hysteresis.

Experimental evaluation and quantitative modeling of thermal behavior of surface-attached insulation polymers and steel structures under combustion

The surfaces of liquefied petroleum gas (LPG) storage vessels are usually coated with polymer insulation to maintain low temperatures. However, this insulation layer poses a potential fire risk. This study aimed to investigate the heat feedback mechanism and its impact on steel structures when bonded thermal insulation materials combust. Thermal insulation materials were bonded to Q345 steel surface, which is commonly used in LPG storage tanks, and experiments were conducted by designing a burning experimental rig of the combustible material attached to steel plate. Results revealed the existence of an equivalent temperature layer in the flame zone above the insulation material. Equations for predicting radiative and convective heat feedback were formulated. As combustion of the insulation material stabilized, the predicted heat feedback from the equations closely matched experimental values. A quantitative evaluation method, based on the inverse heat transfer problem, was proposed. This method determines the thermal decay function of heat feedback through the insulation material and steel plate. By establishing three key performance indicators, this work achieved independent quantification of potential thermal concerns and robustness evaluations of steel structures with surface-bonded insulation materials under combustion.

Solution by the self-adjoint operator method for a model of a co/counter-current moving bed heat exchanger with heat losses

A solution by the self-adjoint operator method (SAO) (still not widely used in engineering) is presented for a lumped parameter model (LM) of a co/counter-current, indirect heated, diluted, tubular, vertical moving bed heat exchanger (MBHE), with heat loss to surroundings. The self-adjoint formulation of the problem and several mathematical techniques enabled the development of an ingenious methodology capable of solving the difficult problem of establishing the character of the eigenvalues of the MBHE operator - only partially known to date - for co/counter flow.For co-current flow, it is demonstrated that the self-adjoint solution corresponds to a solution from the literature - obtained by the Laplace transform - but with the character of the roots not yet established. Therefore, the work aims to, through analysis, study the character of the eigenvalues of the MBHE operator to generalize results from the literature, allowing the use of the solution in a comprehensive parametric range, as well as for different flow arrangements, discussed within the scope of case studies. From the analysis of the eigenvalue equation, five thermal behaviors of the MBHE could be identified. The model was also solved numerically, and the results show excellent agreement in both calculation methods. The obtained analytical solution reveals a possible inconsistency in a literature solution of the analogous heat transfer problem in a triple tube heat exchanger (the) with thermal losses at the outer surface. The study generalizes previous results and allows its extension, by analogy, to the solution for the TTHE with thermal losses at the outer surface.

A review of regularization strategies and solution techniques for ill-posed inverse problems, with application to inverse heat transfer problems

With the presence of a large number of inversion algorithms for inverse heat transfer problems (IHTPs) and non-IHTPs, a need for review to have a holistic view is seen. An exhaustive literature review, with the motivation of selecting the inversion technique best fit for a given problem, was made for a general inverse problem. For ill-posedness, a classification of available regularization algorithms namely Tikhonov’s regularization, Bayesian regularization, mollification method, Beck’s sequential approach and Alifanov’s iterative approach, has been provided. Inversion methods like singular value decomposition, truncated singular value decomposition, Tikhonov regularization and total variation regularization are explained. Optimization methods namely steepest descent method, conjugate gradient method, Newton method, Levenberg–Marquardt method, Lagrange method, adjoint method, function specification method, genetic algorithm, differential evolution and particle swarm optimization (PSO) are reviewed. Further, a technique based on neural networks is studied, and wavelet methods like shrinking and wavelet vaguelette decomposition are reviewed. Associated literature has also been listed, highlighting the gaps. The usability of various algorithms in IHTP, starting from the golden section search method, for retrieval of a single parameter, to the regularized versions of the inversion technique, for retrieval of multiple parameters with uncertainty, demonstrates real-life applications to fins in IHTP. An inversion algorithm capable to handle every kind of nonlinearity is sought in literature, whose absence raises the research question, “Is there a technique that works globally for every inverse problem?”, is asked prior to, “What if the available techniques were not utilized to an extent that they should?” is posed. In lieu of this gap, a general comparative framework is developed, such that an efficient technique is selected, based on the total minimum error, which can be used in any field of interest.

Analysis of temperature-dependent thermal conductivity and fin efficiency: Direct Akbari-Ganji method

The vast majority of engineering issues, particularly heat transport equations, have a non-linear form. The analytical solution of temperature distribution, fin effectiveness, and fin efficiency of straight convective fins that transport heat with temperature-dependent thermal conductivity convection is derived in this work using the Direct Akbari-Ganji method (DAGM). DAGM is an effective methodology that is very simple and takes less time to solve non-linear temperature distribution fin problems. In the present investigation, Direct Akbari-Ganji technique offers desirable solutions to heat transfer problems. The round-off error is smaller compared to other methods. For the purpose of calibrating the error accuracy of the suggested direct technique, this result is compared with the numerical and earlier solution. The outcomes show that the DAGM for heat transfer equations in engineering situations has excellent validity and considerable promise. Finally, it is clear that when the thermo-geometric fin parameter increases, so does the fin efficiency. The homogeneity of the fin is due to the variable thermal conductivity. Four convection conditions with constant coefficients, growing and decaying convection coefficient with fin temperature are discussed.

A convergence criterion for elliptic variational inequalities

We consider an elliptic variational inequality with unilateral constraints in a Hilbert space X which, under appropriate assumptions on the data, has a unique solution u. We formulate a convergence criterion to the solution u, i.e. we provide necessary and sufficient conditions on a sequence { u n } ⊂ X which guarantee the convergence u n → u in the space X. Then we illustrate the use of this criterion to recover well-known convergence results and well-posedness results in the sense of Tykhonov and Levitin–Polyak. We also provide two applications of our results, in the study of a heat transfer problem and an elastic frictionless contact problem, respectively.

Application of graded phase change materials for solar energy inter-seasonal storage heating and thermal storage characteristics

Abstract In this paper, firstly, the heat transfer characteristics of the stepped phase change accumulator are studied, and the location of the solid-liquid phase interface is determined by the phase fraction in a fixed grid scheme, while the phase change heat transfer process is simulated using Fluent. Secondly, for the phase change heat transfer problem, the enthalpy-porosity method in the Solidification/Melting model is used to treat the solid-liquid mixed paste region of the phase interface as a porous media region, and the evaluation system is constructed in terms of heat storage and discharge efficiency, heat storage, and heat recovery efficiency. Then the mathematical model, boundary conditions and solution parameters of the stepped phase change heat accumulator are set, and the data analysis of the effect of the pool height-to-diameter ratio on the heat storage in the solar inter-seasonal storage heating system is carried out by using ANSYSCFD software. The results show that the heat storage of the system also shows an overall increasing trend with the increase of the pool height-to-diameter ratio, and the heat storage of the system increases faster when the height-to-diameter ratio increases from 0.2 to 1.0 in sequence, and the heat storage of the system increases less when the height-to-diameter ratio changes between 0.9 and 1.8, and basically tends to be stable. This study realizes the graded heat storage and graded heat use of solar energy, which is useful for the research of solar heat supply and heat storage.

Sequential Deep Operator Networks (S-DeepONet) for predicting full-field solutions under time-dependent loads

Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to solution functions in contrast to classical neural networks that need re-training for every new set of parametric inputs. In this work, we have extended the classical formulation of DeepONets by introducing sequential learning models like the gated recurrent unit (GRU) and long short-term memory (LSTM) in the branch network to allow for accurate predictions of the solution contour plots under parametric and time-dependent loading histories, known as Sequential DeepONets (S-DeepONets). Two example problems, one on transient heat transfer and the other on path-dependent plastic loading, were shown to demonstrate the capabilities of the new architectures compared to the benchmark DeepONet model with a feed-forward neural network (FNN) in the branch. Despite being more computationally expensive, the GRU- and LSTM-DeepONets lowered the prediction error by half (0.06% vs. 0.12%) compared to FNN-DeepONet in the heat transfer problem, and by 2.5 times (0.85% vs. 3%) in the plasticity problem. In all cases, the proposed DeepONets achieved a prediction R2 value of above 0.995, indicating superior accuracy. Results show that once trained, the proposed S-DeepONets can accurately predict the final full-field solution over the entire domain and are at least two orders of magnitude faster than direct finite element simulations, rendering it an accurate and robust surrogate model for rapid preliminary evaluations.

A new hybrid approach to study heat and mass transfer in porous medium influenced by imprecisely defined parameters

The present work discusses a hybrid approach of Successive Overrelaxation (SOR) with Finite Element Method (FEM) in presence of non-probabilistic uncertainties. In order to address the heat and mass transfer problem in porous media with fuzzy environment, the proposed SOR FFEM has been applied. Here, the imprecise parameters have taken in terms of TFNs and the convergence analysis of the proposed technique is performed. The parameters viz. Rayleigh number (Ra), Radiation parameter (Rd) and Lewis's number (Le) are considered as uncertain and discussed in case study. Different combinations of uncertain parameters are considered for investigation and the sensitivity analysis of the same is observed. It is noted that the stream function (ψ‾) is sensitive when Ra is fuzzy. Similarly, the stream function (ψ‾) and temperature (T‾) both are exhibiting sensitivity when Rd is fuzzy. Additionally, the stream function (ψ‾) is sensitive when Le is fuzzy. As comparing all the cases, it is observed that, stream function (ψ‾) is more sensitive in all three circumstances that is a small change in value can be affect more.

A methodology using a non-increasing sequence applied in the solution of heat transfer problems

This research aims to propose a numerical methodology that employs a non-increasing sequence to approximate the solution for a large class of ordinary differential equations like the ones described in complex non-linear heat transfer through porous fins. It also aims to compare this proposed methodology with an earlier one using a non-decreasing sequence of elements and to provide an upper-bound estimation for the error. The comparison between the non-increasing and non-decreasing sequences showed excellent agreement when applied to an example of convection and radiation in porous fins.

A new procedure for rapid convergence in numerical performance calculations of electrochemical cells

This paper introduces a novel coupled region-to-region numerical procedure for electric field potential calculations. A conventional segregated scheme is also introduced to illustrate the coupling issues that exist in performance calculations in electrochemical devices. Numerical simulations are conducted for a solid oxide cell operating in both fuel cell and electrolysis modes. The cell performance is predicted with both segregated and coupled methods. A comparison between the coupled and segregated schemes shows that the former greatly outperforms the latter, reducing convergence times (from 5000 to 300 iterations) and improving stability. A smaller coupling coefficient contributes to the convergence as well, however, less markedly. The coupled region-to-region approach may readily be applied to numerous other scenarios, e.g., heat transfer problems between multiple phases and regions.

Numerical study on coupled multiphase thermal and mass transfer of moving surface impacted by jet array in semi-enclosed space

The problems of fluid flow, heat transfer and mass transfer involved in the process of impinging jet belt transportation are very common in engineering applications. However, the array jet forms thermal disturbances on the moving impact surface, which leads to the unclear turbulent flow characteristics and the heat and moisture distribution mechanism on the moving surfaces. In this paper, a multi-phase flow model is established for coupled heat and moisture transfer of the array impacting a moving surface in a semi-enclosed space. Based on considering the multi-phase component transmission, the effects of height-to-diameter ratio (H/d), impinging jet velocity (Vjet), and surface moving speed (Vs) on heat and moisture transfer are investigated. The results show that increasing the jet velocity strengthens the phase change evaporation process on the impact surface. The movement of the impact surface makes asymmetric vortices appear on both sides of the peak Reynolds number and Nusselt number in the vertical direction of the space flow field. At the same time, a horseshoe-shaped vortex is formed on the impact surface. When the moving speed of the impact surface increases, the downstream boundary layer becomes thicker due to the disturbance effect of multiple airflows, increasing the uneven distribution of temperature and moisture on the impact surface. The accuracy of the model is examined by making comparisons with experimental results, where the error remains less than 10 %. The results in this paper provide a theoretical basis for parameter optimization and improvement of the process quality in belt transmission equipment.

A diffuse interface–lattice Boltzmann model for conjugate heat transfer with imperfect interface

A diffuse interface-lattice Boltzmann model is proposed for modeling conjugate heat transfer problems with imperfect interfaces. According to the continuity condition of heat flux and jump condition of temperature across the imperfect interface, a unified sharp interface equation of the temperature field with a singular source term in the composite media domain is established. Then a diffuse interface equation is obtained by making a smoothed approximation of the unified sharp interface equation. The novel diffuse interface equation is restructured into a second-order heat diffusion equation with an anisotropic diffusion coefficient tensor. To numerically solve the second-order anisotropic diffusion equation, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) scheme is employed. Several numerical simulations of benchmark test examples with analytical solutions are carried out to demonstrate the accuracy of the present model, including the steady-state heat diffusion in a two-layer medium with a flat interface, steady heat diffusion in a square domain with a curved interface and unsteady-state temperature diffusion with two-layer media. The numerical results show that the phenomenon of temperature jump across the imperfect interface can be successfully and correctly captured. Moreover, as an example of practical application, the new proposed diffuse interface model is utilized to predict the effective thermal conductivity of porous media with thermal contact resistance at pore scale. The variation law of the effective thermal conductivity is obtained for each parameter by studying the effects of thermal conductivity ratios of the dual-component material, the shape and volume fraction of blocks in the material, the interfacial thermal conductance coefficient, and the number of blocks on the effective thermal conductivity. Both uniform and random pore structures are considered. The previous theoretical equations strongly support the validity of the present model.

Estimation of soils thermophysical characteristics in a nonlinear inverse heat transfer problem

It is well known that knowledge of thermophysical parameters is a leading strategy to research effects of energy transfer in soils. The present article proposes an inverse analysis for numerical solving of nonlinear heat transfer problem to determine the thermophysical properties of two different soil types: sand and chernozem. First, estimation of thermophysical parameters is performed using temperature data from experimental set-up, which is two-chambered container for two soil types. Second, numerical algorithm is based on implicit Euler scheme for discretization, Newton method to solve nonlinear system of equations and Levenberg-Marquardt method to minimize nonlinear estimator with Tikhonov's regularization technique. Simulations have been efficiently carried out for two different soil types, showing that the reliability of the model is satisfying with a discrepancy between numerical predictions and experimental observations remaining within the measurement error.