Heat Transfer Formulation Research Articles

Modeling of Metal Matrix Concentrated Solar Receivers for sCO2 Power Blocks

Abstract Supercritical CO2 power blocks for Concentrating Solar Power (CSP) with novel metal matrix solar receivers have the potential to reduce operating expenses while improving overall system efficiencies. These concentrated solar receivers integrated with a metal matrix-based phase change (PCM) thermal storage medium provide the compounding effect of an efficient heat exchanger while also integrating thermal storage within the receiver. Detailed numerical modeling of such devices with enthalpy-porosity-based formulation for phase change and turbulent convective heat transfer for the sCO2 microchannels is described in the current work. With sCO2 power blocks operating at temperatures and pressures beyond 800°C and 200 bar, different high-temperature PCMs are studied. A detailed steady charging followed by discharge and charging transients is simulated to analyze the thermal performance of these devices. In the current work, the energy storage density of PCMs is studied, followed by an analysis of the movement of the melt-pool interface over the streamwise length of a high corrugation wavy microchannel. A scaling analysis is carried out to estimate the heat transfer coefficients while compare them with the numerical model predictions. The results from the current work can be utilized for sizing and detailed design of integrated solar receivers for high-temperature sCO2 power block applications.

Neural networking-based analysis of heat transfer in MHD thermally slip Carreau fluid flow with heat generation

The formulation of heat transfer in non-Newtonian fluid models remains a topic of great interest for researchers. The ultimate flow differential equations in this direction are non-linear and hence difficult to solve analytically. Therefore, we offer state of the art determination of film effectiveness (heat transfer coefficient) by using artificial intelligence (AI). To be more specific, the Carreau fluid model is formulated at a flat surface along with thermal slip, heat generation, velocity slip, chemical reaction, and magnetohydrodynamics (MHD) effects. The developed equations are reduced by the application of the Lie symmetry approach and solved by the shooting method. The artificial neural networking model is built by using 132 sample values of the Nusselt number (NN) as an output. Porosity parameter, Prandtl number, magnetic field parameter, and heat production parameter are all inputs. 92 (70 %) is designated for training, whereas 20 (15 %) is designated for validation and testing. The Levenberg-Marquardt algorithm is used to train the neural network. The constructed artificial neural networking (ANN) is best to predict the NN at a flat surface. It is observed that for large Prandtl numbers, the magnitude of the Nusselt number is greater for porous surface, but the converse is true for magnetic field parameter.

A proposal of models for thermal compensation in machine tools based on a formulation for in-series heat transfer

A proposal of models for thermal compensation in machine tools based on a formulation for in-series heat transfer

Modelling artificial ground freezing subjected to high velocity seepage

Artificial ground freezing (AGF) is a ground improvement technique for ensuring the safety of underground construction works in water-bearing soils. High velocity water transport in coarse-grain soils can prevent the ice wall formation in brine-based ground freezing methods. This can be overcome by using expendable refrigerants such as solid carbon dioxide and liquid nitrogen, which provide much lower temperatures. Presented here is a model for analysis and design of ground freezing by expendable refrigerants under high velocity seepage conditions. Non-local mathematical formulations of heat transfer and water flow in soils are developed within the framework of the Peridynamics theory. Their computational implementation uses an adaptive multi-grid peridynamic approach to analyse large domains efficiently. The simulations are tested successfully against several benchmarks. The developed model enables reliable analyses of the effects of main geological and technological parameters on the ice-wall delivery in the presence of groundwater flow.

Detection of multiple tumors through temperature response of a human brain using inverse bioheat transfer based on swarm optimization

In this article, an innovative inverse regularized framework has been proposed for a bio-medical problem to detect tumors in the human brain via temperature. Most of the thermal data obtained through infrared thermography is sensitive towards errors, thus a regularized approach is sought from the literature. The best inversion algorithm, WOA, together with a hybrid GWOCS are utilized. Pennes model is used for the formulation of heat transfer within the human brain. Using inverse analysis, the unknown blood perfusion rate ωi is retrieved in the regularized environment. The current research reported that at positions where tumor cells are present, the temperature rises. Moreover, with an increase in time, the temperature of the cancer cells increases, whereas no change in the temperature of tissue without tumor is seen. This observation marks the presence of tumor. Elastic net regularization (λ=0.1, α=10−2) for WOA and (λ=0.9, α=10−4) for GWOCS shows the least relative error. After regularization, the perfusion rate is retrieved. A clear distinction of two tumors from the brain tissue is observed. The obtained perfusion rate is used to reconstruct the temperature profile. An excellent matching of the reconstructed temperature field and the exact field is obtained, even when the forward data contain measurement errors. The obtained set of perfusion rate is appropriate for tumor detection, up to 7% error in the measured data. Thus, the proposed comparative procedure is found suitable for the bio-heat transfer problem.

Heat and mass transfer with chemical kinetics in alcoholic fermentation of multiple sugars: Lumped formulation and dimensional analysis

A consistent non-dimensional lumped-capacitance formulation for heat and mass transfer in alcoholic fermentation has been developed. The formulation stems from a generalization of previous dimensional models, written for an arbitrary number of fermentable species. A comprehensive dimensional analysis of the problem was performed, leading to a concise — and physically meaningful — set of dimensionless groups associated with the occurring physical and chemical phenomena, as well as a set of normalized governing equations. Numerical solutions for the normalized formulations were implemented for both isothermal and non-isothermal fermentation cases, and the results were verified by comparing with experimental data from previous studies. Finally, a parametric analysis was conducted for illustrating the effect of the proposed parameters on the solution of the problem. This analysis was presented for isothermal fermentation – demonstrating the effects of the dimensionless groups related to the Michaelis–Menten kinetics and the inoculation ratios – and for non-isothermal fermentation, demonstrating the effect of the heat transfer coefficient on the fermentation process.

Numerical simulation of the extrusion process of viscoplastic materials using a radial point interpolation method

PurposeFused Filament Fabrication (FFF) is an extrusion-based manufacturing process using fused thermoplastics. Despite its low cost, the FFF is not extensively used in high-value industrial sectors mainly due to parts' anisotropy (related to the deposition strategy) and residual stresses (caused by successive heating cycles). Thus, this study aims to investigate the process improvement and the optimization of the printed parts.Design/methodology/approachIn this work, a meshless technique – the Radial Point Interpolation Method (RPIM) – is used to numerically simulate the viscoplastic extrusion process – the initial phase of the FFF. Unlike the FEM, in meshless methods, there is no pre-established relationship between the nodes so the nodal mesh will not face mesh distortions and the discretization can easily be modified by adding or removing nodes from the initial nodal mesh. The accuracy of the obtained results highlights the importance of using meshless techniques in this field.FindingsMeshless methods show particular relevance in this topic since the nodes can be distributed to match the layer-by-layer growing condition of the printing process.Originality/valueUsing the flow formulation combined with the heat transfer formulation presented here for the first time within an in-house RPIM code, an algorithm is proposed, implemented and validated for benchmark examples.

CFD-DEM coupled simulation of fluidized beds with improved lumped formulation for heat transfer

PurposeThis paper aims to present a novel approach for computing particle temperatures in simulations coupling computational fluid dynamics (CFD) and discrete element method (DEM) to predict flow and heat transfer in fluidized beds of thermally thick spherical particles.Design/methodology/approachAn improved lumped formulation based on Hermite-type approximations for integrals to relate surface temperature to average temperature and surface heat flux is used to overcome the limitations of classical lumped models. The model is validated through comparisons with analytical solutions for a convectively cooled sphere and experimental data for a fixed particle bed. The coupled CFD-DEM model is then applied to simulate a Geldart D bubbling fluidized bed, comparing the results to those obtained using the classical lumped model.FindingsThe validation cases demonstrate that ignoring internal thermal resistance can significantly impact the temperature in cases where the Biot number is greater than 0.1. The results for the fixed bed case clearly demonstrate that the proposed method yields significantly improved outcomes compared to the classical model. The fluidized bed results show that surface temperature can deviate considerably from the average temperature, underscoring the importance of accurately accounting for surface temperature in convective heat transfer predictions and surface processes.Originality/valueThe proposed approach offers a physically more consistent simulation without imposing a significant increase in computational cost. The improved lumped formulation can be easily and inexpensively integrated into a typical DEM solver workflow to predict heat transfer for spherical particles, with important implications for various industrial applications.

Non-Local Formulation of Heat Transfer with Phase Change in Domains with Spherical and Axial Symmetries

Describing heat transfer in domains with strong non-linearities and discontinuities, e.g. propagating fronts between different phases, or growing cracks, is a challenge for classical approaches, where conservation laws are formulated as partial differential equations subsequently solved by discretisation methods such as the finite element method (FEM). An alternative approach for such problems is based on the non-local formulation; a prominent example is peridynamics (PD). Its numerical implementation however demands substantial computational resources for problems of practical interest. In many engineering situations, the problems of interest may be considered with either axial or spherical symmetry. Specialising the non-local description to such situations would decrease the number of PD particles by several orders of magnitude with proportional decrease of the computational time, allowing for analyses of larger domains or with higher resolution as required. This work addresses the need for specialisation by developing bond-based peridynamic formulations for physical problems with axial and spherical symmetries. The development is focused on the problem of heat transfer with phase change. The accuracy of the new non-local description is verified by comparing the computational results for several test problems with analytical solutions where available, or with numerical solutions by the finite element method.

Designing an Effective Plate Fin Heat Exchanger and Prediction of Thermal Performance Operated Under Different Water Blends Using Machine Learning

Abstract The main aim of the article is intended to design an effective Plate-Fin Heat Exchanger (PFHX) with composite materials such as SS316 + copper and SS304 + Flyash in a counterflow type. These are brazed together with the method of salt bath brazing and vacuum brazing. The study presents the analytical formulation of heat transfer and fluid flow in PFHX design to predict the enhancement of heat transfer and overall heat transfer coefficient, finite difference method is suggested for analyzing the hot and cold fluids. Moreover, Quantum particle swarm optimization with the radial basis function is proposed for accurate prediction of heat transfer enhancement. The findings of the research demonstrate that the design structure of PFHX with the composite materials is analyzed using a microscopic approach and eroded test. The proposed study is performed using various types of coolants namely MFC, ECSTAR, and TFC anti-freeze coolants with water, and the thermophysical properties of the coolants are also analyzed. The findings demonstrate that the variation between the experimental and theoretical results is less than 3.26%, this indicates that the proposed method is effective for heat exchanger design and the optimization algorithm is more feasible than the analytical results. Hence, the outcome of this study offers a better prediction analysis of heat transfer enhancement using PFHX.

Resonances and near field heat transfer of finite structures

We describe a formulation for near field heat transfer for a finite size system so that the heat conductance can be expressed as sums of contributions from the resonances of the combined structure of the “receiver” and the “source”. Our work opens the door to investigating near field heat transfer between finite systems and in particular metamaterials whose resonances have been well studied. We illustrated our results with an analytically tractable example of energy transfer between two split ring resonantors separated by a distance d on top of each other. When the cuts of the two rings are opposite each other, the heat conductance is smaller than when the cuts of the two rings are on top of each other. This result can only come from a finite system calculation.

NLFEM WITH HIGHER ORDER INTERPOLATION FUNCTION FOR EFFICIENT ANALYSIS OF IRREGULAR DOMAIN

This study proposes a new approach to developing a more efficient numerical technique by coupling the non-uniform rational B-spline (NURBS) with the higher-order polynomial basis functions under the framework of the Finite Element Method (FEM). In this technique, denoted as NURBS-Lagrange FEM (NLFEM), the NURBS basis functions are employed to represent the geometry of the problem domain, while the Lagrange interpolation functions are employed for the higher-order polynomial functions to interpolate the field variables. The NURBS is a mathematical model which provides a numerically stable algorithm to exactly represent all conic sections, and the Lagrange interpolation function allows for higher-order basis functions resulting in a faster convergence rate of analysis. By taking advantage of both models, the objective of this study is to propose a new approach, i.e., NLFEM, which can improve the accuracy of the analysis of the irregular domain with more efficient consumption of computer resources. A steady heat transfer formulation for a curved boundary problem is presented to demonstrate the validity and accuracy of the developed technique. The performance is verified against converged solutions obtained using higher-order FEM (FEM/Q9) and NURBS-Augmented FEM (NAFEM). The presented result shows that the NLFEM provides a favorable comparison against other methods. The converged solution is achieved 20% faster than the FEM/Q9 and 80 % faster than the NAFEM. This highlights the potential of the NLFEM as a new approach in numerical techniques for solving problems with irregular boundaries.

Determination of Cooling Load for a Solar Cooled Building in Khartoum Using a Simulation Method

Cooling load calculations are normally carried out assuming steady state conditions. This is a simple but conservative approach that leads to overestimation of the cooling capacity. For more accurate estimation of cooling loads, one has to take into account the thermal capacity of the walls and internal heat sources, which makes the problem more complicated. In this paper, the unsteady state heat transfer formulation has been used to determine the air conditioning cooling load for a building in Khartoum for a hot summer day. An explicit method was used to calculate the nodal temperatures at each time step of the thermal network. A simulation program was developed to calculate the cooling load at each time step. The building is cooled by absorption cooling system comprised mainly of an evacuated tube solar collector, a lithium bromide –water absorption air conditioner, a storage tank fitted with an auxiliary heater. A mathematical model is built to simulate the absorption cooling system for the solar cooled building and the results showed that the absorption system driven by solar energy from the evacuated tubes solar collector is enough to cover the cooling load demand by the building more than ten hours.

Nonlocal thermal effects on biological tissues and tumors

• Analysis of heat distribution of tumor growth based on nonlocal rang effects. • The long-range kernel approach generalizes the Pennes bioheat equation. • Temperature is affected by nonlocal effects and by the localization of the neighbouring tumors. • The nonlocal kernel approach may imitate what is going on biologically within a tumor where cancer cells reside. Tumors consist of heterogeneous populations of cells. The cell–cell interactions processes play a critical role in cancer invasion and could be influenced by the mutation of cancerous tumor. This study is devoted to the analysis of the temperature distribution of tumor growth based on nonlocal range effects mainly the tumor-tumor influence incorporated in a kernel. The long-range kernel approach generalizes the Pennes bioheat equation which is the most commonly used formulation of heat transfer in biological systems. It was observed that the temperature is affected by nonlocal effects and by the localization of the neighbouring tumors. The nonlocal kernel approach may imitate what is going on biologically within a tumor where cancer cells reside. This may assist to the nonlocal treatment of cancer invasion in a human body.

Sensitivity Analysis for Transient Thermal Problems Using the Complex-Variable Finite Element Method

Solving transient heat transfer equations is required to understand the evolution of temperature and heat flux. This physics is highly dependent on the materials and environmental conditions. If these factors change with time and temperature, the process becomes nonlinear and numerical methods are required to predict the thermal response. Numerical tools are even more relevant when the number of parameters influencing the model is large, and it is necessary to isolate the most influential variables. In this regard, sensitivity analysis can be conducted to increase the process understanding and identify those variables. Here, we combine the complex-variable differentiation theory with the finite element formulation for transient heat transfer, allowing one to compute efficient and accurate first-order sensitivities. Although this approach takes advantage of complex algebra to calculate sensitivities, the method is implemented with real-variable solvers, facilitating the application within commercial software. We present this new methodology in a numerical example using the commercial software Abaqus. The calculation of sensitivities for the temperature and heat flux with respect to temperature-dependent material properties, boundary conditions, geometric parameters, and time are demonstrated. To highlight, the new sensitivity method showed step-size independence, mesh perturbation independence, and reduced computational time contrasting traditional sensitivity analysis methods such as finite differentiation.

Semi-analytical solutions of flow and heat transfer of fluid along expandable-stretching horizontal cylinder

In the presence of suction/injection, a mathematical formulation for laminar boundary layer flow and heat transfer of an incompressible viscous fluid along an expandable-stretching horizontal cylinder is provided. The partial differential equations governing system is reduced to a system of ordinary differential equations. With the aid of Mathematica, semi-analytical solutions for the resultant system of ordinary differential equations are obtained using the OHAM (Optimal Homotopy Asymptotic Method) and the Legendre-Galerkin method. It is found that the suction process increases surface stiffness and strength while the injection process reduces surface skin friction. Also, other flow and thermal factors are discussed graphically.

Thermal model of precast concrete curing process: Minimizing energy consumption

Worldwide, precast concrete elements are becoming the primary construction materials, and there have been conducted numbers of studies on their manufacturing process, mechanical properties and curing regime. However, the energy consumption of the precast concrete manufacturing process and specifically the curing process is ignored by researchers. In this study, a thermal model of a curing unit, including three main sections: a curing room, a steam transfer system and a boiler, is developed. Besides, based on the mathematical formulation of heat transfer, a MATLAB code is prepared to determine the heat transfer, the mass of steam, the mass of fuel and the annual fuel cost. By the MATLAB code, the effect of different parameters on the curing process energy consumption and the fuel cost is investigated. Eventually, a smart control system that is based on the condition of the curing unit in every moment is suggested. This system leads to a reduction of 30% of energy consumption and the annual fuel cost.

Entropy Generation Rate for Stationary Ballistic-Diffusive Heat Conduction in a Rectangular Flake

Thermodynamic irreversibility in low dimensional flake is considered and entropy generation rate in two-dimensional thin film is examined, Equation of phonon radiative transfer is solved for two-dimensional and rectangular diamond flake. Volumetric and total entropy generation rate are evaluated incorporating the formulation of thermal radiation heat transfer. The influence of flake aspect ratio (width to height) on the entropy generation rate is explored while keeping the Diamond flake area constant for all aspect ratios considered. The findings reveal that the entropy generation rate increases with increasing aspect ratio for fixed boundary conditions.

Temperature monitoring of milling processes using a directional-spectral thermal radiation heat transfer formulation and thermography

Temperature is an important property to be monitored during cutting operations, such as in the milling of metals, because it affects the workpiece mechanical properties, the machining tool performance, and the process efficiency. For this reason, authors have used thermography to monitor thermal and spatial gradients, and to estimate temperature. The problem is that IR cameras native applications are mostly based on the diffuse-gray approximation, with emissivity set as a constant value. The diffuse-gray approach is a reasonable choice for opaque surfaces with emissivity approximately constant in respect to the wavelength, which is not the case in most of the time for metals under cutting operation. In this work we propose a more suitable methodology that uses radiative heat transfer directional-spectral relations to estimate cutting process temperatures during face milling of metals, using the full electrical response of commercial infrared cameras as an input. AISI H13 steel was used as the workpiece material. In the first part of the experiments, emissivity was estimated for eight different temperatures from 50 °C to 250 °C, using both directional-spectral and diffuse-gray approaches. Temperature was measured using a thermocouple type T, calibrated using a PT-100 reference from 50 °C to 250 °C. In the second part, we used the emissivity obtained in the first part to estimate the temperature for twelve different cutting conditions, again using both directional-spectral and diffuse-gray approaches. We compared the results of both methods, also with the direct application of emissivity provided in infrared cameras manuals. The temperature deviation between the different approaches were up to 41%, which demonstrates that the temperature estimation procedure affects the results substantially.

A scuffing model for spur gear contacts

This study proposes a scuffing model for spur gear contacts. A heat transfer formulation is devised to evaluate gear bulk temperature, with frictional heat flux yielded from thermal mixed elastohydrodynamic lubrication (EHL) analysis. In return, the bulk temperature is fed back into the EHL modeling to determine tribological behavior within contact zone, including flash temperature. After bulk temperature stabilizes, the bulk and flash components are added to arrive the total surface temperature, whose maximum is compared to a scuffing limit for failure determination. Utilizing the model, a set of simulations is performed to demonstrate the influences of surface roughness and rotational speed on scuffing load.