One-dimensional Heat Research Articles

Lumped model for a quasi-continuously operating open metal hydride heat pump system

Hydrogen as a potential future fuel for fuel cell vehicles is mostly stored in high-pressure tanks at 350 or 700 bar, which requires energy-intense compression of typically 15 % of the lower heating value. For the recovery of parts of the compression work, a promising possibility is the usage of an open metal hydride heat pump. Similarly to other sorption-based heat pump systems, in order to reach high specific thermal power, it is crucial to find a trade-off in the design and operation of the reactor between two main factors: enabling fast reaction dynamics and reducing losses due to temperature switches. The present work introduces a steady-state model with lumped metal hydride and reactor mass considering one-dimensional heat and mass transfer, which is able to quickly predict the corresponding specific thermal power and efficiency. A special focus is on the calculation of the non-complete conversion due to an operation at constant gas flow. The model is validated with existing experimental data over a broad range of operation conditions in terms of metal hydride specific hydrogen mass flow (1.6–7.6 gH2 min−1 kgMH-1) and temperature boundary conditions (cold side temperature: 13–25 °C, hot side temperature: 24–42 °C). It is capable of describing the specific thermal power and the efficiency as the two main performance indicators with a suitable accuracy. To give an example of the applicability of the developed tool, a generic discussion of the performance limitations of the selected reactor design is carried out, indicating that the reactor of the validation experiment is mainly mass transport limited.

Determination of Film Cooling Effectiveness and Heat Transfer Coefficient Simultaneously on a Flat Plate

In this paper, flat plate film cooling with two rows of compound angle cylindrical film cooling holes was investigated. A data processing method was evaluated which could determine the film cooling effectiveness and heat transfer coefficient simultaneously from the transient wall temperature data. The method was based on solving an inverse problem of the one-dimensional transient heat conduction equation. To evaluate the performance of the method, wall temperature data were obtained using the known film cooling effectiveness and heat transfer coefficient data as the convection boundary condition. Then, the method was applied to calculate the film cooling effectiveness and heat transfer coefficient based on the wall temperature data. Different blowing ratios, heat transfer coefficients, mainstream temperatures, and material thermal conductivities were investigated. In general, the data and calculation were in good agreement. It was found that the error decreased when the heat transfer coefficient increased and the material thermal conductivity decreased. The percentage error of the span-wise averaged film cooling effectiveness was mainly between 0% and 10%, and the percentage error of the span-wise averaged heat transfer coefficient was mainly between 0% and 4%.

Performance output tracking for a one-dimensional unstable heat equation with input delay

Abstract In this paper, we investigate the performance output tracking for a one-dimensional unstable heat equation with input delay and disturbance. Both the performance output and the disturbance are non-collocated to the controller. By writing the time delay as a transport equation, the control plant becomes a cascade system in which the transport equation can be regarded as the actuator dynamics of the unstable heat equation. As a result, the method of actuator dynamics compensation can be used. The difficulties caused by the non-collocated configuration are figured out in the method of trajectory planning. The full state feedback is presented to realize the output tracking, and an error based observer is constructed successfully. The exponential stability of the closed-loop system and the well-posedness of the observer are proved.

Вероятностно-детерминированный подход к расчету пожарного риска, вызванного воздействием лучистого теплового потока от фронта верхового устойчивого повального лесного пожара на жилой дом

Purpose. The purpose of the article is to create a mathematical model for calculating the fire risk caused by the impact of a radiant heat flux from the front of an independent crown wild fire on the combustible structures of a residential building. A combined calculation method has been developed that combines deterministic and probabilistic approaches. The combination of the above mentioned approaches is due to the fact that the probabilistic approach does not take into account the specific mechanism of the impact of a wild fire on the structure of a building, while the deterministic approach does not take into consideration the probability of a fire starting ABSTRACT and developing, as well as the timeliness of fire units response for fire extinguishing. Methods. The study uses theoretical methods of heat conduction and radiant heat transfer, wild fire statistics analysis, and fire risk theory. Findings. In the deterministic part of the method to calculate the temperature of the irradiated surface of the building structure, a one-dimensional non-stationary heat conduction equation is used, the boundary condition for which is determined by solving the equation of the radiant heat transfer between the wild fire front and the building. The calculated wood (pine) ignition time is compared with experimental data. The agreement between the calculation and experiment is satisfactory. The formula for calculating the fire risk for a residential building resulted from the impact of the radiant heat flux from the front of a wild fire is proposed. The above-mentioned formula takes into account the frequency of crown wild fires occurrence, the probability of ignition of combustible structures of the building when no firefighting measures are taken, as well as the probability of the active and passive fire prevention measures effectiveness. An example of fire risk calculation is presented when constructing a mineralized line, whose increase in width will reduce the fire risk by 1 000 times. Research application field. The results of the study can be applied in the development of fire prevention measures aimed at protecting communities against wild fires impact. Conclusions. The developed probabilistic-deterministic mathematical model for calculating the impact of a radiant heat flux falling from the front of an independent crown wild fire on the combustible structures of a residential building makes it possible to assess the fire risk for a building, considering specific meteorological conditions, pyrological and geometric (tree height, etc.) characteristics of the woodland, the distance from the building to the edge of the forest, as well as fire prevention measures implementation.

Wave-heat coupling in one-dimensional unbounded domains: artificial boundary conditions and an optimized Schwarz method

This paper deals with the coupling between one-dimensional heat and wave equations in unbounded subdomains, as a simplified prototype of fluid-structure interaction problems. First we apply appropriate artificial boundary conditions that yield an equivalent problem, but with bounded subdomains, and we carry out the stability analysis for this coupled problem in truncated domains. Then we devise an optimized Schwarz-in-time (or Schwarz Waveform Relaxation) method for the numerical solving of the coupled equations. Particular emphasis is made on the design of optimized transmission conditions. Notably, for this setting, the optimal transmission conditions can be expressed analytically in a very simple manner. This result is illustrated by some numerical experiments.

Numerical optimization of a multistage sorption compressor

Sorption compressors are driven by thermal cycles and have no moving parts, excluding some passive check valves. Such compressors are suitable for powering Joule-Thomson (JT) cryocoolers and can provide reliable and vibration free active cooling system with a potential for high reliability and long operating life. The thermal cycle consists of cooling and heating a sorbent material which is installed in a sorption cell, where the heating is obtained by an inner electric heater and cooling is obtained by the surrounding via the sorption cell envelope. The investigation and optimization of the sorption cells were conducted in previous work, at steady state conditions, by a one-dimensional heat and mass transfer numerical model. The current paper presents a dynamic numerical model of sorption compressors which consist of several sorption cells. The numerical model allows one to three compression stages, with any number of sorption cells at each stage. The model enables the investigation of dimensional parameters and operational parameters, and provides the low and high pressures, pressure fluctuations, and compressor’s efficiency. The current investigation focuses on a three-stage compressor for nitrogen, with low and high pressures of 0.2 and 8 MPa, respectively, and a mass flow rate of about 11 mg/s.

Feedback exponential stabilization of the semilinear heat equation with nonlocal initial conditions

The present paper is devoted to the problem of stabilization of the one-dimensional semilinear heat equation with nonlocal initial conditions. The control is with boundary actuation. It is linear, of finite-dimensional structure, given in an explicit form. It allows to write the corresponding solution of the closed-loop equation in a mild formulation via a kernel, then to apply a fixed point argument in a convenient space.

Geothermal potential and genetic mechanisms of the geothermal system in the mountainous area on the northern margin of north china

Geothermal resources as clean and renewable energy can be utilized for agriculture, tourism, and industry. The assessment of geothermal potential and the study of genetic mechanism of the geothermal system is an essential part of geothermal resource development. In this study, 16 steady-state temperature logs are obtained in the mountainous area on the northern margin of North China. Thermal conductivity and heat production rates are tested or collected from more than 200 rock samples of these wells and outcrops around the study area. Based on these data, for the first time, the detailed delineations of temperature distributions, genetic mechanisms of geothermal systems, and resource potential of Hot Dry Rock in the study area are achieved. The heat flow map indicates a low heat flow state with an average value of 53.1 mW/m2 in the study area, which is lower than the average value of 62.5 mW/m2 in mainland China. The distribution of hot springs in the area is mainly controlled by fault systems. Heat flow only exhibits a minor effect on the temperature of hot springs and geothermal wells. On this basis, the deep temperature distribution within 3–10 km depths of the study area is calculated using the one-dimensional steady-state heat conduction equation. With it, the reservoir depths of hot springs are estimated to be 3–5 km with temperatures ranging from 70°C to 110°C. Furthermore, a conceptual model for the geothermal system in the study area is derived. According to the results, Northeastern Chengde and northern Beijing exhibit the highest temperatures at all depths. Similar patterns are observed in the temperature distribution maps and the heat flow map, which suggest that the deep temperature distribution is mainly controlled by regional heat flow. With the depth increases, the temperature shows larger variation at each depth level, which is possibly caused by the heterogeneity of crustal composition. According to our resource assessment by volumetric method, the exploitable potential of Hot Dry Rock within the depth of 7–10 km of the study area is equivalent to about 3.1 × 1011 tons of standard coal, but the barrier is still existing for development under the current technical and economic conditions.

ON FUZZY PARTIAL FRACTIONAL ORDER EQUATIONS UNDER FUZZIFIED CONDITIONS

This paper is devoted to investigating or computing the solution to one-dimensional partial fuzzy fractional order heat equation. In particular, one-dimensional fuzzy partial heat equation is hybridized into two equations by hybrid techniques along with the concept of parametric fuzzy number. For this investigation, a hybrid method of decomposition due to Adomian and Laplace transform is used. The considered techniques are presented for the computation of series of solutions of partial fractional order heat equation. The applied techniques have also provided the accuracy, simplicity and efficiency as compared to other existing methods. Finally, some illustrations are solved for the justification of our theoretical solution.

Development of an Efficient Conjugate Heat Transfer Modeling Framework to Optimize Mixing-Limited Combustion of Ethanol in a Diesel Engine

Abstract Mixing controlled combustion of alcohol fuels has been identified as a promising technology based on their low propensity for particulate and NOx production, but the higher heats of vaporization and auto-ignition temperatures of these fuels make their direct use in diesel engine architectures a challenge. To realize the potential of alcohol-fueled combustion, a computational fluid dynamics (CFD) modeling framework is developed, validated, and exercised to identify designs that maximize engine thermal efficiency. To evaluate the use of thermal barrier coatings (TBCs), a simplified one-dimensional (1D) conjugate heat transfer (CHT) modeling framework is employed. The addition of the 1D CHT model only increases the computational expense by 15% relative to traditional approaches, yet offers more accurate heat transfer predictions over constant temperature boundary conditions. The validated model is then used to explore a range of injector orientations and piston bowl geometries. Using a design of experiments (DoE) approach, several designs were identified that improved fuel–air mixing, shortened the combustion duration, and increased thermal efficiency. The most promising design was fabricated and tested in a Caterpillar 1Y3700 single-cylinder oil test engine (SCOTE). Engine testing confirmed the findings from the CFD simulations and found that the co-optimized injector and piston bowl design yielded over 2-percentage point increase in thermal efficiency at the same equivalence ratio (0.96) and over 6-percentage point increase at the same engine load (10.1 bar indicated mean effective pressure (IMEP)), while satisfying design constraints for peak pressure and maximum pressure rise rate.

Numerical solution of coupled radiative and conductive heat transfer’s equations in PolyMethylMethAcrylate by the finite difference method

ABSTRACT This study has been conducted to illustrate combined heat transfer in a PolyMethylMethAcrylate (PMMA) sample. PMMA is a promising polymer utilized to optical, pneumatic actuation, sensor, analytical separation, and conductive devices. Combined radiation and conduction is considered, corresponding to the problem of one-dimensional transient heat transfer. Numerical results have been obtained by computer implementation, considering the effect of radiation, based on implicit finite difference formulation. Data have been provided from a nonlinear heat conduction equation using Kirchhoff transformation, centered the finite difference scheme by considering temperature conditions applied to the boundaries and monochromatic radiation intensity. In the present study, the temperature distribution and combined heat transfer equation are derived for PMMA. The temperature distribution is verified by the data of other studies that were done before. A comparison of the results showed a very good agreement with others. The results showed a great temperature gradient in the primary positions which cause a large amount of Conductive heat flux. The conductive heat flux was similar to radiative heat flux in terms of behavior but approximately twice in amount. On the other hand, total heat flux was constant at a specific time when it was an approximated steady-state condition.

Enhancement of methodology for protection of structures in contradiction of thermal effects

The research paper is devoted to protection of structures against heat and temperature effects. The necessity of improving the calculation of multilayered fence structures is shown. The solution of a one-dimensional unsteady heat conduction equation with constant and variable coefficients allowing to use of inhomogeneous and anisotropic materials as the fence material is given. An example of the solution of a fence made of inhomogeneous and anisotropic material is given. Solution of heat conduction equation is obtained by the recurrence-operator method. The solution of one-dimensional unsteady heat conduction equation with variable coefficients is obtained using the recurrence-operator method. The possibility of using the solution of the equation for multilayered inhomogeneous anisotropic fence materials is indicated.

Numerical modeling of laser ablation of materials

In this paper, we report a numerical simulation of laser ablation of a material by ultrashort laser pulses. The thermal mechanism of laser ablation is described in terms of a one-dimensional nonstationary heat conduction equation in a coordinate system associated with a moving evaporation front. The laser action is taken into account through the functions of the source in the thermal conductivity equation that determine the coordinate and time dependence of the laser source. For a given dose of irradiation of the sample, the profiles of the sample temperature at different times, the dynamics of the displacement of the sample boundary due to evaporation, the velocity of this boundary, and the temperature of the sample at the moving boundary are obtained. The dependence of the maximum temperature on the sample surface and the thickness of the ablation layer on the radiation dose of the incident laser pulse is obtained. Numerical calculations were performed using the finite difference method. The obtained results agree with the results of other works obtained by their authors.

Approximate Controllability for Degenerate Heat Equation with Bilinear Control

This paper investigates the nonnegative approximate controllability for the one-dimensional degenerate heat equation governed by bilinear control. Both non-controllability and approximate controllability are studied for the system. If the control is restricted to act on a fixed domain, it is not controllable. If the control is allowed to mobile, it is approximately controllable.

Simulation of Nonlinear Heat Conduction in Perforated Material by Improved Moving Particle Semi-Implicit Method

Abstract An improved moving particle semi-implicit (MPS) method is presented to simulate heat conduction with temperature-dependent thermal conductivity. Based on Taylor expansion, a modified Laplacian operator is proposed, and its accuracy in irregular particle distributions is verified. Two problems are considered: (1) heat conduction in a one-dimensional (1D) slab and (2) heat conduction in a perforated sector with different boundary conditions. Consistent results with a mesh-based method are obtained, and the feasibility of the proposed method for heat conduction simulation with temperature-dependent conductivity is demonstrated.

A holistic consideration of turbocharger heat transfer analysis and advanced turbocharging modeling methodology in a 1D engine process simulation context

The focus on transient engine operation will increase to fulfill future emission requirements in the commercial vehicle sector. Accordingly, the transient turbocharger matching process is becoming increasingly important. The one-dimensional fluid dynamics (1D-CFD) simulation is established as an important development tool for matching the exhaust gas turbocharger to a combustion engine. The optimization of the modeling methodology of the combustion process and the turbocharger modeling are two key parameters to improve the reliability of the dynamic engine process simulation. In this paper, the advanced turbocharger (TC) methodology is described. This includes the determination of the adiabatic turbocharger performance from conventional hot gas test stand (HGS) measurement data, the derivation of an one-dimensional (1D) turbocharger heat transfer model and a method to physically extend the turbine map range. The adiabatic efficiencies of the turbocharger are determined with a model-based heat transfer correction of the conventional measured efficiencies from HGS measurement data. These adiabatic efficiency maps were used as a baseline to extend the conventional TC model with a heat transfer model taking into account of the engine boundary conditions in terms of temperature, pressure and mass flow rate. To assess the temperature distribution and the thermal inertia of the TC main components, in both stationary and transient engine operations, the variable geometry turbine (VGT) turbocharger hardware, installed on a medium-duty diesel engine, was equipped with several thermocouples on all accessible surfaces to make comprehensive surface temperature surveys. A 1D lumped capacitance heat transfer model (HTM) of the VGT TC was developed and validated against the experimental data from the engine test bench. To complete the advanced TC modeling, the turbine map is extended using experimental measurement data, based on extended HGS measurements, in combination with mathematically supported extrapolation. The results from the advanced turbocharger simulation methodology significantly improves the prediction of the temperature drop over the turbine in comparison to the conventional adiabatic TC simulation methodology. The validated heat transfer model also allows the analysis of the heat flow breakdown of the turbocharger. Based on the advanced turbocharger model, a tool for the improved transient turbocharger-engine matching process is given.

A Method for Evaluation of Thermal Characteristics of Complex Heat-Shield Assembles at Extremely High Energy Fluxes

A suitable laboratory test procedure is developed where a small fragment of the relatively thick multilayer heat shield is exposed to the extreme heat flux of up to several kW/cm2 in order to evaluate its performance. A nearly one-dimensional test condition has been achieved, where thermal behavior of a small fragment of a large shield became representative for the large heat-shield panel. A cylindrical test sample made of carbon-carbon composite has been surrounded by high-temperature thermal isolation made of zirconia concrete. The high heat flux has been provided by a power CW-laser. The conditions of one-dimensional axial heat flux through the cylindrical fragment of the heat shield are confirmed by the mathematical modeling of the experiment using experimentally measured temperature excursions along the sample axis.

One Dimensional Heat Transfer through a Uniform Plane Wall by Using Finite Volume Method

In this paper, the finite volume method has been used to investigate one-dimensional conductive heat transfer throw a uniform plane wall. Then the step by step procedures of this numerical solution is described and implemented in a real-world problem where tri-diagonal matrix algorithm and Gaussian elimination matrix method are applied to solve the system of our discretized algebraic system of equations. Finally, to check the accuracy of our method, a comparison between the numerical solution obtained by finite volume techniques and the exact solution is presented which shows a minimum error compared to other existing methods.

The Numerical Method of Lines facilitates the instruction of unsteady heat conduction in simple solid bodies with convective surfaces

The present study on engineering education addresses the Method of Lines and its variant the Numerical Method of Lines as a reliable avenue for the numerical analysis of one-dimensional unsteady heat conduction in walls, cylinders, and spheres involving surface convection interaction with a nearby fluid. The Method of Lines transforms the one-dimensional unsteady heat conduction equation in the spatial and time variables x, t into an adjoint system of first-order ordinary differential equations in the time variable t. Subsequently, the adjoint system of first-order ordinary differential equations is channeled through the Numerical Method of Lines and the powerful fourth-order Runge–Kutta algorithm. The numerical solution of the adjoint system of first-order ordinary differential equations can be carried out by heat transfer students employing appropriate routines embedded in the computer codes Maple, Mathematica, Matlab, and Polymath. For comparison, the baseline solutions used are the exact, analytical temperature distributions that are available in the heat conduction literature.

Simplified Theoretical Model for Temperature Evaluation in Tissue–Implant–Bone Systems during Ultrasound Diathermy

Deep heating procedures are helpful in treating joint contractures that frequently occur with fractures and joint diseases involving surgical implants and artificial joint prostheses. This study uses a one-dimensional composite medium model consisting of parallel slabs as a simplified approach to shed light on the influences of implants during ultrasound diathermy. Analytical solutions for the one-dimensional transient heat generation and conduction problem were derived using the orthogonal expansion technique and a Green’s function approach. The analytical solutions provided deep insight into the temperature profile by therapeutic ultrasound heating in the composite system. The effects of the implant material type, tissue thickness, and ultrasound operation frequency on temperature distribution were studied for clinical application. In addition, sensitivity analyses were carried out to investigate the influences of material properties on the temperature distribution during ultrasound diathermy. Based on the derived analytical solutions, the numerical simulations indicate that materials with high density, high specific heat, and low thermal conductivity may be optimal implant materials. Among available implant materials, a tantalum implant, which can achieve a lower temperature rise within the tissue (hydrogel) and bone layers during ultrasound diathermy, is a better choice thanks to its thermodynamics.