One-dimensional Transient Heat Research Articles

Heat Transfer Characteristics of Cryogenically Frozen Kulfi (A Dairy Dessert)

Kulfi was frozen from concentrated milk as well as from reconstituted dry mix with solids content of 60%. The convective heat transfer coefficients during freezing of kulfi by deep freeze and cryogenic methods were determined using one-dimensional transient heat conduction equation. The heat transfer coefficient for cryogenic freezing of kulfi from milk and dry mix concentrates was 210.57 W m-2K-1 and 216.84 W m-2K-1, respectively when compared to 8.33 W m-2K-1 for conventional deep-frozen kulfi. Freezing was achieved in 267 min in deep freeze method, while it reduced to just 185-190 s under cryogenic conditions. The freezing time was predicted using empirical equations, and the prediction accuracies were compared. Cryogenic freezing was nearly 87.66 times faster than deep freezing, and Pham’s model best-predicted the freezing time. Organoleptic evaluation using fuzzy-logic revealed that the order of ranking of quality attributes of kulfi was body and texture (highly important) > melting characteristics (highly important) > flavour and taste (highly important) > colour and appearance (important), and cryogenically frozen kulfi was statistically (p<0.05) superior to conventionally frozen kulfi.

Effects of heat wave propagation and initial stress on the thermo-elastic behavior of porous-auxetic FG circular plate with variable hybrid foundation

Engineering structures' heterogeneity and porous-auxetic features generate some prominent effects on their thermo-mechanical behavior. In addition, initial stress and heat wave propagation also play important roles in the mechanical behavior of FGM structures. Therefore, this paper investigates the effects of heat wave propagation and initial stress on the thermo-elastic behavior of porous-auxetic FG circular/annular plates with variable hybrid foundations. The one-dimensional transient hyperbolic heat conduction equation is modeled using the Cattaneo-Vernotte (C-V) theory and numerically solved using the Crank-sNicolson (C-N) finite difference scheme. Besides, a mathematical model of the other governing equations is extracted based on the classical thermoporoelasticity theory and semi-analytically solved by employing the state-space method and differential quadrature technique. Numerical examples are provided to illustrate the findings of this investigation graphically. The results reveal that the grading indices, and thermal relaxation time have a significant effect on heat wave propagation in the FG circular plate. Initial stress, porosity, and auxeticity also play an important role in its thermoelastic behavior.

Vibrations of skew cylindrical shells made of FG-GPLRCs under rapid surface heating

Vibrations of skew cylindrical shells made of FG-GPLRCs under rapid surface heating

Exploring energy-saving performance of radiative cooling roofs with a transient heat transfer model

Exploring energy-saving performance of radiative cooling roofs with a transient heat transfer model

Computational Analysis and Regression Laws for Nozzle Erosion Prediction in Hybrid Rockets

The erosion of the nozzle throat can represent one of the major limitations against the future widespread use of hybrid rocket engines (HREs) in the space industry. In fact, nozzle erosion in HREs can be more severe and harder to predict than in solid rockets due to the higher concentration of oxidizing species in the combustion products and to mixture ratio shifts and/or throttling. Therefore, an accurate understanding of the erosion phenomenon is of fundamental importance for the technological advancement of HREs. This work is focused on the investigation of graphite nozzle erosion in HREs burning high-density polyethylene with two different oxidizers, oxygen and nitrous oxide. First, the results of a computational fluid dynamics parametric analysis are used to derive closed-form regression laws for the rapid estimation of nozzle throat erosion and wall temperature depending on chamber pressure and mixture ratio. Then, a one-dimensional transient heat conduction solver is loosely coupled with the aforementioned regression laws, allowing to reconstruct the transient heating process within the solid. The obtained numerical results are validated against experimental data. Finally, the effect of gas-phase reactions on the heterogeneous reactions occurring at the nozzle surface is highlighted when moving from fuel-rich to oxidizer-rich conditions.

Nonlinear vibration analysis of graphene platelets reinforced nanocomposite doubly curved concrete panels subjected to thermal shock: Development of an artificial intelligence technique

When the temperature gradient across a component quickly changes, a phenomenon known as thermal shock occurs that exposes the component to fast variable thermal stresses and large-scale strains. One of the goals of this abrupt loading is to increase the capacity of different systems to withstand thermal shock. The nonlinear thermally induced vibration of doubly curved graphene nanoplatelet reinforced nanocomposite panels subjected to abrupt thermal shock is being studied right now. The bottom portion of the curved panel system is held at a reference temperature while the top portion is thermally shocked. The Crank-Nicholson technique and generalized differential quadrature (GDQ) are used to build up and solve the one-dimensional transient heat equation. The double-curved panel’s thermomechanical characteristics are temperature dependent; hence this equation is nonlinear. Based on the law of decoupled thermoelasticity, Kant’s theory, and von Karman’s assumption of some kind of geometric nonlinearity, the overall function of the doubly curved panel is established. After modeling the current system mathematically and comparing the current approach’s findings to those of earlier research, we revalidated the findings in a Python environment by comparing them to those of the Extreme Gradient Boosting (XGBoost) machine learning algorithm. This approach is founded on the “boosting” idea, which combines additive training techniques with the identification of weak learners to produce strong learners. The findings demonstrate that certain structural geometrical and physical factors are significant contributors to the double-curved GPLRC panel’s nonlinear frequency under thermal shock.

Nonlinear transient responses of lattice core sandwich plates under a sudden heat flux

Nonlinear transient responses of lattice core sandwich plates under a sudden heat flux

Numerical modeling of soil temperature variation under an extreme desert climate

Numerical modeling of soil temperature variation under an extreme desert climate

Numerical Analysis of Airfoil Flow Control Using a Nanosecond Pulsed Plasma Actuator

The control mechanism of a nanosecond dielectric barrier discharge (NS-DBD) actuator for suppressing laminar separation on airfoils was investigated using two-dimensional scale-adaptive simulations. To model the control effect of the NS-DBD actuator, a surface heating approach based on the analytical solution for transient one-dimensional heat conduction has been used. The focus of the investigation lies in the study of vortex formation and evolution induced by the actuator. A NACA 0015 profile was simulated at 14° with 250,000 chord-based Reynolds number. Regarding energy deposition, a low-energy case and a high-energy case were simulated. Several actuation parameters were varied, including the electrode position and surface temperature. In addition, the influence of constant and temperature-dependent modeling of the kinematic viscosity was investigated. The results for the time-averaged pressure coefficients show excellent agreement with measurement results. High grid resolution in the boundary layer allowed a detailed investigation of the vortex formation process. The main finding is that vortices are generated by baroclinic torque and vortex dilatation and not by a Kelvin–Helmholtz instability. Initially, tiny vortices form at the beginning of the separation region. Subsequently, these vortices are carried downstream and grow in size, thus preventing full separation due to momentum transfer from the external flow.

Application of GDQ method to large amplitude response of FGM joined spherical-conical shells under rapid surface heating

Geometrically non-linear thermally induced vibrations of functionally graded material (FGM) joined spherical-conical shells are analyzed in the current research. Thermo-mechanical properties of the shells are assumed to be temperature and position dependent. The system of joined spherical-conical shells is subjected to thermal shock on the ceramic-rich surface, whereas the metal-rich one is kept at reference temperature. The one-dimensional transient heat conduction equation is established and solved via the generalized differential quadrature (GDQ) and Crank-Nicolson methods. This equation is non-linear since the thermo-mechanical properties of the shells are temperature dependent. The total functional of the shells is obtained under the assumptions of uncoupled thermoelasticity laws, first order shear deformation shell theory, and the von Kármán type of geometrical non-linearity. Non-linear coupled equations of motion are solved via the iterative Picard method accompanied with the β-Newmark time approximation technique. Numerical results are well-validated with the available data for the case of single FGM spherical shell. Parametric studies are conducted to examine the influences of conical and spherical shell geometries, material composition, temperature dependence, in-plane and out-of-plane mechanical boundary conditions, various configuration of conical/spherical shell system, and thermal boundary conditions. It is highlighted that thermally induced vibrations indeed exists.

A simplified one-dimensional transient heat transfer model for rocket thrust chamber

The heat transfer model is essential to rocket engine thrust chamber, for it determines the accuracy of chamber wall temperature and heat flux distribution. In order to predict the transient temperature field during startup and shutdown, we introduce a simplified one-dimensional model of transient heat transfer for thrust chamber. The heat transfer process is divided into two parts: the convective heat transfer from hot gas to the inner wall and the heat conductance through the chamber wall. The Bartz formula modified with constant coefficient C is used to characterize the convective heat transfer and the one-dimensional transient heat transfer model of slab is the calculative foundation of the heat conductance. Finally, we propose a strategy to iteratively solve the model. To verify the model, it is implemented in a series of hot run experiments for a LOX/Methane heat sink thrust chamber. The average error of wall temperature evaluated at different locations of the thrust chamber inner wall can be reduced up to a 1.76%. The application of our novel method provides an accurate and efficient tool to calculate chamber wall temperature and heat flux distribution in the thrust chamber design. In addition, through inverse analysis of the proposed model, we can also estimate the near-wall gas temperature, which is difficult to obtain in a hot run test, by acquiring wall temperature data.

Geometrically nonlinear response of FGM joined conical–conical shells subjected to thermal shock

Geometrically nonlinear thermally induced vibrations of functionally graded material (FGM) joined conical–conical shells is analyzed in the current research. Thermo-mechanical properties of the shell are assumed to be temperature and position dependent. The system of joined conical–conical shells is subjected to thermal shock on the ceramic-rich surface, whereas the metal-rich one is kept at reference temperature. The one-dimensional transient heat conduction equation is established and solved via the generalized differential quadrature (GDQ) and the Crank–Nicolson methods. This equation is nonlinear since the thermo-mechanical properties of the shell are temperature dependent. The total functional of the shell is obtained under the assumptions of uncoupled thermoelasticity laws, first order shear deformation shell theory, and the von Kármán type of geometrical non-linearity. Non-linear coupled equations of motion are solved via the iterative Picard method accompanied with the β -Newmark time approximation technique. Numerical results are well validated with the available results for the case of FGM single conical shell. Parametric studies are conducted to examine the influences of conical geometry, material composition, temperature dependence, in-plane and out-of-plane mechanical, various configuration of joined shell system, and thermal boundary conditions.

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%.

Analysis of spray/wall impingement using an ECN single-hole injector and a controlled-temperature wall under realistic engine conditions

Spray–wall interactions (SWI) directly affect fuel–air mixture and emissions formation. Therefore, they are considered among the most critical physical processes in engine research nowadays. However, the physics of the wall film formation, propagation, and breakup is not fully understood yet. This work aims to use a thermoregulated steel wall to study the spray–wall interaction phenomenon and its influence on the macroscopic spray behavior. A single-hole injector known as “Spray D” in the Engine Combustion Network was used. n-Dodecane was employed as fuel and the wall has been positioned in four different configurations, varying angle and distance respect to the injector tip. For this work, not only diesel combustion is reproduced in the test rig due to ambient gas engine-like thermodynamic conditions, but wall temperature has been controlled to emulate characteristic values that could be found in the piston of an internal combustion engine. This implies that the spray–wall heat transfer is simulated and its effects on ignition and spray development can be analyzed. Heat flux was measured by employing high-speed thermocouples fitted in the wall and by the use of an one-dimensional transient wall heat model. Three high speed cameras were simultaneously used to observe the SWI, one for the Schlieren optical technique which allows to study the vapor phase of the spray and to determine the ignition delay, another one to observe the natural luminosity of the flame, and finally, an intensified camera was used to determine the lift-off length by observing the chemiluminescence of the OH*. An interesting finding obtained in this work was a boundary layer formation due to the thermal diffusion that contributes to cool down the spray and to delay the high-temperature chemical reactions. Results show a substantial increment of the heat flux and the wall temperature variation with both ambient temperature and density by increasing the flame temperature and gas entrainment. The exposure to the cold wall affects the ignition delay variation with the injection pressure and the wall distance. It was found that the wall temperature (in the range of tested conditions) did not affect the lift-off length location. • The exposure to the cold wall delayed the ignition. • Flame thickness around the wall undergoes a narrowing at lower wall temperatures. • The injection pressure increments the convective coefficient. • A boundary layer due to thermal diffusion was formed on the wall.

Thermophysical properties of balsa wood used as core of sandwich composite bridge decks exposed to external fire

The load-bearing performance of sandwich bridge decks comprising a balsa core and fiber-reinforced polymer composite face sheets exposed to fire is a main concern regarding the application of these deck systems. In order to obtain the thermal responses of the balsa core exposed to fire, the temperature-dependent values of thermal conductivity and specific heat capacity are required. Furthermore, information about the char depth and charring rate and the temperature-dependent coefficient of thermal expansion is also needed for the subsequent thermomechanical modeling. In the current study, the effective thermal conductivity and specific heat capacity of balsa up to 850 °C were obtained from one-dimensional transient heat transfer models and experimental data using an inverse heat transfer analysis. The results showed that both properties depend significantly on the stages of combustion, direction of heat flow (in the tracheid or transverse direction) and density. Moreover, charring temperatures and rates were obtained, again as a function of direction and density. Finally, the coefficient of thermal expansion was measured in the transverse direction during evaporation and pyrolysis.

An Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes

With the increasing engineering applications of geothermal borehole heat exchangers (BHEs), accurate and reliable mathematical models can help advance their thermal design and operations. In this study, an analytical model with a time-dependent heat flux boundary condition on the borehole wall is developed, capable of predicting the thermal performance of single, double, and multiple closed-loop BHEs, with an emphasis on solar- and waste-heat-assisted geothermal borehole systems (S-GBS and W-GBS) for energy storage. This analytical framework begins with a one-dimensional transient heat conduction problem subjected to a time-dependent heat flux for a single borehole. The single borehole scenario is then extended to multiple boreholes by exploiting lines of symmetry (or thermal superposition). A final expression of the temperature distribution along the center line is attained for single, double, and multiple boreholes, which is verified with a two-dimensional finite-element numerical model (less than 0.7% mean absolute deviation) and uses much lesser computational power and time. The analytical solution is also validated against a field-scale experiment from the literature regarding the borehole and ground temperatures at different time frames, with an absolute error below 6.3%. Further, the thermal performance of S-GBS and W-GBS is compared for a 3-by-3 borehole configuration using the analytical model to ensure its versatility in thermal energy storage. It is concluded that our proposed analytical framework can rapidly evaluate closed-loop geothermal BHEs, regardless of the numbers of boreholes and the type of the heat flux on the borehole wall.

Heat Transfer and Recovery Factor of Aerodynamic Heating on a Flared Cone

This paper investigates aerodynamic heating on a flared cone in a Mach 6 wind tunnel. Two data processing methods to calculate the Stanton number and recovery factor simultaneously are presented, using the experimentally measured wall temperature in a hypersonic wind-tunnel test. The first method is the linear fitting of the measured temperature and calculated heat flux. The second method is to solve an inverse problem of a one-dimensional transient heat conduction equation with the convection boundary condition. Distributions of heat flux, Stanton number, and recovery factor for the flared cone with a smooth wall or wavy wall are obtained. Compared with the smooth wall, the wavy wall can remove the local high Stanton number region before the boundary-layer transition. In addition, the wavy wall can reduce the growth rate of Stanton number in the boundary-layer transition and delay the transition process.

Eagle Strategy Based on Modified Barnacles Mating Optimization and Differential Evolution Algorithms for Solving Transient Heat Conduction Problems

Solving time-dependent heat conduction problems through a conventional solution procedure of iterative root-finding method may sometimes cause difficulties in obtaining accurate temperature distribution across the heat transfer medium. Analytical root-finding methods require good initial estimates for finding exact solutions, however locating these promising regions is some kind of a black-box process. One possible answer to this problem is to convert the root-finding equation into an optimization problem, which eliminates the exhaustive process of determining the correct initial guess. This study proposes an Eagle Strategy optimization framework based on modified mutation equations of Barnacles Mating Optimizer and Differential Evolution algorithm for solving one-dimensional transient heat conduction problems. A test suite of forty optimization benchmark problems have been solved by the proposed algorithm and the respective solution outcomes have been compared with those found by the reputed literature optimizers. Moreover, five challenging real-world constrained optimization problems have been solved to further scrutinize the effectiveness of the proposed framework. Finally, two case studies associated with a transient heat conduction problem have been solved. Results show that Eagle strategy can provide efficient and feasible results for various types of solution domains.

Modeling of cooling and heat conduction in permanent mold casting process

Motivated by the need to understand the heat transfer process in permanent mold casting, the heat conduction problem in the casting and the mold is modeled as transient one-dimensional heat flow in a double-layer cylinder with radial interfacial heat flux to emulate the cooling process of the casting. The cylinder is cooled down by dissipating heat to surrounding by convection. Green's function method, which obtained by separation of variables technique, is used to obtain a closed form solution of temperature distribution. The results of the derived analytical expressions are verified with numerical results of finite-element analysis and the published experimental results. The simulations are performed for different casting/mold materials with diversified thermo-physical properties to figure out the relationship between those properties and heat transfer process. The analytical results are justified by their good agreement with both of numerical and experimental results and its time efficiency in computation which offers advantages in potential real-time application to casting process monitoring. The mean absolute percentage error between the obtained temperatures using the developed analytical model and the measured ones was 14.5% and 2.4% for the casting and mold, respectively.

Research on Temperature Change of Reflow Furnace Based On Mathematical Modeling

After referring to many documents, this article comprehensively considers various heat transfer methods, analyzes the heat transfer process of welded components, and establishes a temperature field distribution model based on one-dimensional transient heat transfer equation by ignoring some irrelevant conditions, and useing the finite difference method. We solve it and apply it to the optimization of furnace temperature curve. Due to the many types of reflow furnaces, this article mainly considers hot-air reflow furnaces. The heating methods are mainly heat convection and heat conduction, ignoring heat radiation. The welding area is established by the transient heat transfer equation. The temperature field distribution model is established, and the initial conditions and thermal boundary conditions are determined. Related heat transfer analysis is done for the front area, back area and gap areas. Finally, through the experimental data and the idea of least squares, the parameters of the electronic devices used in this experiment are obtained, and it also provides an idea to check whether the relevant parameters of the experimental materials are accurate. In order to make it easier for the staff to operate, this article proposes a method to find the maximum speed of conveyor belt, which has great practical significance.