Unsteady Heat Research Articles

Influence of heat flow due to concentration gradient on unsteady MHD heat and mass transform dissipative flow with spanwise fluctuating temperature

This study investigates the influence of heat flow due to a concentration gradient on unsteady Newtonian free convective magnetohydrodynamic heat and mass transform dissipative fluid flow over a heated normal porous plate in the presence of radiation absorption and chemical reaction. The plate temperature is assumed to fluctuate in a spanwise cosinusoidal manner over a time and exhibit heat generation with suction velocity. The analysis employs the multiple regular perturbation method to evaluate the governing equations under stipulated boundary conditions. The outcomes are visually depicted to assess the impact of various parameters on the system dynamics. Graphical representations illustrate the physical significance of various parameters on velocity, temperature, and concentration. Additionally, skin friction, mass transfer rate, and heat transfer coefficients are presented in tabular form. The significant findings indicate that velocity, temperature, and skin friction are directly proportional to parameters such as radiation absorption, heat generation, and heat flux due to a chemical potential gradient, whereas Sherwood and concentration are inversely proportional to the Schmidt number and chemical reaction. The outcomes obtained in this study have been cross-referenced with existing scientific literature, demonstrating strong concordance. This alignment provides confidence in the numerical results.

Magnetohydrodynamics flow and heat transfer of novel generalized Kelvin–Voigt viscoelastic nanofluids over a moving plate

In this work, the unsteady magnetohydrodynamics boundary layer flow and heat transfer of novel generalized Kelvin–Voigt viscoelastic nanofluids over a moving plate are investigated. The classical Kelvin–Voigt constitutive relation is generalized to incorporate a time-fractional derivative to characterize the fluid behavior, which is proved to be of significance and physically justified. The newly developed fractional Kelvin–Voigt constitutive correlation and a dual-phase-lagging constitutive equation are applied to the momentum and energy equations, respectively, for a nanofluid model over a moving plate. The formulated integrodifferential velocity and thermal boundary layer equations are solved using the finite difference method together with a fast algorithm, which reduces the consumed central processing unit time significantly. Several numerical examples are presented to illustrate the influence of the critical parameters on the nanofluid motion and thermal characteristics. Compared to the fractional Maxwell nanofluid model, the velocity boundary layer for the fractional Kelvin–Voigt nanofluid model is thinner. Although the fractional indexes show similar effects on the velocity boundary layer, the impacts of the relaxation parameters are in contrast. This work provides valuable insights into the feasibility of using the fractional Kelvin–Voigt viscoelastic model to depict the fluid flow and heat transfer characteristics of nanofluids.

Restoration of unsteady heat flow from a thermal energy accumulator by solving the inverse heat conduction problem

Restoration of unsteady heat flow from a thermal energy accumulator by solving the inverse heat conduction problem

Lightweight insulating oil-well cement filled with hollow glass microspheres and numerical simulation of its unsteady heat transfer process

Lightweight insulating oil-well cement filled with hollow glass microspheres and numerical simulation of its unsteady heat transfer process

Spherical partial differential equation with non‐constant coefficients for modeling of nonlinear unsteady heat conduction in functionally graded materials

AbstractThe objective of this research paper is to propose an exact solution for resolving the transient conduction in a 2D sphere. The coefficients of governing equation are varied according to the material properties. The thermo‐physical properties are regarded as functions that follow a power‐law relationship concerning the radial direction. Both radial and angular thermal conductivity coefficients change with radius. Thermal boundary conditions are considered in a general state, which can cover different thermal conditions, including Dirichlet, Neumann, and Convection surface conditions. Laplace transform and Meromorphic function methods are used in the solution approach to the current unsteady problem. Two unsteady case studies with complex boundary conditions have been considered to show the credibility of the current solution. The results of both case studies have been successfully validated. The results confirm the high capability of the present solution in solving unsteady thermal problems of functionally graded materials in spherical coordinates.

Thermal convective transport of nanofluids in a microannulus under electromagnetohydrodynamic and time-periodic pressure gradient

The study of the unsteady flow and heat transfer characteristics of nanofluids in microannulus is crucial for the optimal design and precise operation of microfluidic systems, and microfluidic technology has an important application value in microelectronic engineering. In this article, a theoretical analysis of the heat transfer characteristics of unsteady flow of Water-Al2O3 nanofluids through a microannulus under the coupling of an alternating electric field, a magnetic field, and a time-periodic pressure gradient is presented. Both the thermally completely developed flow assumption and the Debye–Hückel linear approximation are taken into consideration. The microannulus wall is subjected to a consistent heat flow while taking into account the effects of Joule heating and viscous dissipation. A semi-analytical solution of the temperature field is efficiently obtained using the Green’s function method. In addition, the Nusselt number and total entropy generation are further analyzed. The results show that the nanoparticle volume fraction and dimensionless frequency have a significant effect on the heat transfer characteristics of nanofluids. The increase of dimensionless frequency decreases the convective heat transfer and improves the cooling performance of microannulus. On the contrary, increasing the nanoparticle volume fraction improves the heat transfer performance of microannulus. Therefore, the results of this study can be used for electronic cooling of compact and micro-sized circuits. This study is instructive for unsteady flow and heat transfer of nanofluids in microchannels.

Thermo-electrochemical level-set topology optimization of a heat exchanger for lithium-ion batteries for electric vertical take-off and landing vehicles

Developing electric vertical take-off and landing vehicles (eVTOL) that can meet the demanding power and energy requirements entails significant challenges, one of which is due to the weight of the battery packs. To address this challenge, optimization techniques can be employed to achieve lightweight designs while satisfying thermal criteria. This study focuses on optimizing a battery heat exchanger housing a high-energy-densitycylindrical cell using the level-set topology optimization method. To accurately account for heat generation from battery electrochemistry, we investigate both a high-fidelity, the Doyle Fuller Newman (DFN) model, and a low-fidelity electrochemical model, the Single Particle Model (SPM), which are compared to experimental results for an eVTOL flight profile. The novelty of the proposed approach resides in the integration of the electrochemical models within a three-dimensional unsteady thermo-electrochemical topology optimization framework. The battery heat exchanger is optimized considering the heat generated by the batteries at the material scale due to the system power requirements. The heat generated by the battery is incorporated as a source term in an unsteady heat conduction finite element model, forming the basis of the optimization process. Our objective is to minimize the integrated thermal compliance over time while satisfying a volume constraint, employing the level-set method. The SPM proves competent in predicting the voltage profile but underestimates the temperature increase. On the other hand, the DFN model accurately predicts both the temperature increase and the voltage profile, making it suitable for the thermal analysis of cells in eVTOL vehicles. Surprisingly, steady-state optimization turns out to be sufficient to generate optimized topologies that perform similarly to transient cases for the case investigated but at a reduced cost. By integrating electrochemical modeling, level-set topology optimization, and heat transfer analysis, our study contributes to the development of lightweight and thermally efficient battery heat exchangers for eVTOL vehicles, which can be extended to battery packs. Importantly, the presented methodology is versatile and can be applied to different battery chemistries, form factors, and power profiles.

Unsteady slip flow of special second-grade fluid induced by Fe3O4 particles past a movable sheet with magnetic and nonlinear heat source/sink

PurposeFerrofluids are aqueous or non-aqueous solutions with colloidal particles of iron oxide nanoparticles with high magnetic characteristics. Their magnetic characteristics enable them to be controlled and manipulated when ferrofluids are exposed to magnetic fields. This study aims to inspect the features of unsteady stagnation point flow (SPF) and heat flux from the surface by incorporating ferromagnetic particles through a special kind of second-grade fluid (SGF) across a movable sheet with a nonlinear heat source/sink and magnetic field effect. The mass suction/injection and stretching/shrinking boundary conditions are also inspected to calculate the fine points of the features of multiple solutions.Design/methodology/approachThe leading equations that govern the ferrofluid flow are reduced to a group of ordinary differential equations by applying similarity variables. The converted equations are numerically solved through the bvp4c solver. Afterward, study and discussion are carried out to examine the different physical parameters of the characteristics of nanofluid flow and thermal properties.FindingsMultiple solutions are revealed to happen for situations of unsteadiness, shrinking as well as stretching sheets. Greater suction slows the separation of the boundary layers and causes the critical values to expand. The region where the multiple solutions appear is observed to expand with increasing values of the magnetic, non-Newtonian and suction parameters. Moreover, the fluid velocity significantly uplifts while the temperature declines due to the suction parameter.Originality/valueThe novelty of the work is to deliberate the impact of mass suction/injection on the unsteady SPF through the special second-grade ferrofluids across a movable sheet with an erratic heat source/sink. The confirmed results provide a very good consistency with the accepted papers. Previous studies have not yet fully explored the entire analysis of the proposed model.

Polypropylene membranes prepared via non-solvent/thermally induced phase separation: Effect of non-solvent nature

The goal of this work was to investigate the effect of non-solvent nature on the formation of porous membranes via non-solvent/thermally induced phase separation (N-TIPS). The hot solution of polypropylene (PP) in a mixture of dioctyl phthalate (DOP) and dibutyl phthalate (DBP) at 210 °C was placed as a thin film on a polyethylene terephthalate (PET) substrate, and then precipitated by immersion in the non-solvent (water, iso-propanol, 1-hexanol, or 1-decanol) at room temperature. It was found that the non-solvent nature greatly affected the morphology of the thin skin layer of the membrane facing the precipitation bath, which can be attributed to non-solvent induced phase separation (NIPS). The affinity between the polymeric solution and corresponding non-solvent was evaluated by using Hansen solubility parameters of components taken at room temperature and extrapolated to the temperature of 210 °C. An increase in the affinity between the non-solvent and the polymer transformed the surface layer structure from almost monolithic to cellular (with different pore sizes and porosity) and to spherulitic types. The non-solvent nature played a less pronounced role in the formation of the porous structure of the membrane bulk and the back side of the membrane (facing the PET substrate). Since the morphology of the rest of the membrane was correlated with thermophysical properties of non-solvents, it was concluded that the membrane formation took place due to temperature induced phase separation (TIPS). In the case of water, which has the highest cooling rate, the polypropylene crystallized by forming a “smectic” structure, while the standard α-lamellar structure was observed for other non-solvents. To gain insight into the TIPS process, a model of unsteady one-dimensional heat transfer was applied to simulate the change in the temperature profile of the hot, thin film of polymeric solution placed in the corresponding non-solvent. The resulting membranes were mainly in the microfiltration range with a mean through pore size of 0.05–0.61 μm, and iso-propanol permeance of 2.1–8.4 m3 m−2∙h−1∙bar−1. The rejection of 500 nm polystyrene microspheres was in the range of 45–98 %. The tensile strength was in the range of 2.9–3.2 MPa, and elongation at break was 30–190 % with respect to the non-solvent used.

Legendre wavelet integration operational matrix method for the numerical solution of unsteady MHD nanofluid flow between moving parallel plates

This study proposes a novel method based on Legendre wavelet integration operational matrix for solving a system of nonlinear ODE’s to model the two-phase, unsteady nanofluid flow and heat transfer between parallel plates in presence of magnetic field. To validate the applicability of proposed method, system of nonlinear BVP with exact solutions is employed as a test problem. Test problem results are compared with exact solution, and other numerical methods. The governing equations were then changed using similarity transformation into a set of nonlinear ODE’s. . Following this, the LWOMM is applied for the proposed problem. Findings demonstrated that, for a constant Reynolds number, skin friction coefficient value increases with rising Hartmann and squeezing numbers. Furthermore, it is demonstrated that Eckert number is a reducing function of the squeeze number and Nusselt number is an increasing function of Hartmann number.

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

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

Mathematical Model of Parabolic Trough Collector with Fresnel Lens as Second Collector

Parabolic trough collectors (PTCs) have came out as a promising technology for harnessing solar energy for various applications including electricity generation and thermal heating. However, improving their thermal performance remains a critical challenge to maximize energy conversion efficiency. This paper presents a mathematical model for enhancing the thermal performance of PTCs by using a curved Fresnel lens as a second collector over the top side of the receiver. This enhancing has taken advantage of the space above the top side of receiver and increased the thermal efficiency of PTCs. The unsteady heat transfer equations with one dimension are used to simulate the effect of Fresnel lens on the receiver components beside the heat transfer fluid and compared with that without Fresnel lens. The results of this model are based on parameters of LS-2 model and environment of installation place whereas the water was chosen as heat transfer fluid with physical properties depending on Temperature. Al-Baydha city in Yemen is chosen as an installation place taking in consideration the variation of environment temperature in each month of the year and the inlet temperature of water and receiver‘s components are taken as the minimum temperature of the air. Keywords: Mathematical Model; Parabolic Trough Collector; Fresnel Lens ; Solar

Unsteady magnetohydrodynamic free convection and heat transfer flow of Al2O3‒Cu/water nanofluid over a non-linear stretching sheet in a porous medium

This article investigates the impact of time-dependent magnetohydrodynamics free convection flow of a nanofluid over a non-linear stretching sheet immersed in a porous medium. The combination of water as a base fluid and two different types of nanoparticles, namely aluminum oxide (Al2O3) and copper (Cu) is taken into account. The impacts of thermal radiation, viscous dissipation and heat source/sink are examined. The governing coupled non-linear partial differential equations are reduced to ordinary differential equations using suitable similarity transformations. The solutions of the prin-cipal equations are computed in closed form by applying the MATLAB bvp4c method. The velocity and temperature pro-files, as well as the skin friction coefficient and Nusselt number, are discussed through graphs and tables for various flow parameters. The current simulations are suitable for the thermal flow processing of magnetic nanomaterials in the chemical engineering and metallurgy industries. From the results, it is noticed that the results of copper nanofluid have a better impact than those of aluminium nanofluid.

An Implementation of LASER Beam Welding Simulation on Graphics Processing Unit Using CUDA

The maximum number of parallel threads in traditional CFD solutions is limited by the Central Processing Unit (CPU) capacity, which is lower than the capabilities of a modern Graphics Processing Unit (GPU). In this context, the GPU allows for simultaneous processing of several parallel threads with double-precision floating-point formatting. The present study was focused on evaluating the advantages and drawbacks of implementing LASER Beam Welding (LBW) simulations using the CUDA platform. The performance of the developed code was compared to that of three top-rated commercial codes executed on the CPU. The unsteady three-dimensional heat conduction Partial Differential Equation (PDE) was discretized in space and time using the Finite Volume Method (FVM). The Volumetric Thermal Capacitor (VTC) approach was employed to model the melting-solidification. The GPU solutions were computed using a CUDA-C language in-house code, running on a Gigabyte Nvidia GeForce RTX™ 3090 video card and an MSI 4090 video card (both made in Hsinchu, Taiwan), each with 24 GB of memory. The commercial solutions were executed on an Intel® Core™ i9-12900KF CPU (made in Hillsboro, Oregon, United States of America) with a 3.6 GHz base clock and 16 cores. The results demonstrated that GPU and CPU processing achieve similar precision, but the GPU solution exhibited significantly faster speeds and greater power efficiency, resulting in speed-ups ranging from 75.6 to 1351.2 times compared to the CPU solutions. The in-house code also demonstrated optimized memory usage, with an average of 3.86 times less RAM utilization. Therefore, adopting parallelized algorithms run on GPU can lead to reduced CFD computational costs compared to traditional codes while maintaining high accuracy.

Natural convective heat transfer of Al2O3-Cu/water hybrid nanofluid in a rectotrapezoidal enclosure under the influence of periodic magnetic field

This study seeks to examine quantitatively the two-dimensional unsteady free convective heat transfer enhancement of Al2O3-Cu/H2O hybrid nanofluid within a rectotrapezoidal-shaped structure. The lower wall is both uniformly and non-uniformly heated with different thermal boundary conditions, the top horizontal wall is adiabatic, and the vertical and inclined walls are assumed chilly. The enclosure is penetrated by a periodic magnetic field. A set of variable transformations is used to render the governing equations dimensionless, which makes it possible to identify the model parameters that control it. The finite element method is then used to numerically solve these equations. To verify the code's numerical precision, comparisons with formerly available works are performed and, a high level of agreement is obtained among the results. The generated outcomes are shown for the principal parameters that control the flow in the context of streamlines, heat lines, isotherms, average Nusselt number, friction factor, and thermal efficiency index. The findings demonstrated that the efficiency index, friction factor, and heat transmission are all considerably influenced by the Rayleigh number (Ra). The lowest Ra yields the maximum thermal efficiency. The results also revealed that the hybrid nanoparticle volume fraction and period of the magnetic field amplified the heat transfer rate and efficiency index due to the increased pumping force. It is observed that when the percentage of the mixing ratios for Cu nanoparticles rises from 0% to 100%, the heat transport in Al2O3-Cu/H2O hybrid nanofluid increases for a fixed volume fraction of hybrid nanoparticles. As compared to parabolic and sinusoidal boundary conditions, the uniform temperature boundary setting for Ra = 105 exhibits the highest average rate of heat transport of 10.04. The average Nusselt number increases by 25.12% at Ra = 103 with a 3% volume fraction of hybrid nanofluid as compared to pure water and the mixing ratios of Al2O3:Cu = 0:300 gives the highest increased rate of 16.30%. The results further illustrate that Al2O3-Cu/H2O hybrid nanofluid has the highest heat transfer rate compared to the pure water and Al2O3– H2O nanofluid.

Acoustic Design Parameter Change of a Pressurized Combustor Leading to Limit Cycle Oscillations

When aiming to cut down on the emission of nitric oxides by gas turbine engines, it is advantageous to have them operate at low combustion temperatures. This is achieved by lean premixed combustion. Although lean premixed combustion is a proven and promising technology, it is also very sensitive to thermoacoustic instabilities. These instabilities occur due to a coupling between the unsteady heat release rate of the flame and the acoustic field inside the combustion chamber. In this paper, this coupling is investigated in detail. Two acoustic design parameters of a swirl-stabilized pressurized preheated air (300 °C)/natural gas combustor are varied, and the occurrence of thermoacoustic limit cycle oscillations is explored. The sensitivity of the acoustic field as a function of combustion chamber length (0.9 m to 1.8 m) and reflection coefficient (0.7 and 0.9) at the exit of the combustor is investigated first using a hybrid numerical and analytical approach. ANSYS CFX is used for Unsteady Reynolds Averaged Navier-Stokes (URANS) numerical simulations, and a one-dimensional acoustic network model is used for the analytical investigation. Subsequently, the effects of a change in the reflection coefficient are validated on a pressurized combustor test rig at 125 kW and 1.5 bar. With the change in reflection coefficient, the combustor switched to limit cycle oscillation as predicted, and reached a sound pressure level of 150 dB.

Experimental Investigation of Tip Design Effects on the Unsteady Aerodynamics and Heat Transfer of a High-Speed Turbine

Abstract While modern engine manufacturers devote significant efforts to the development of reliable and efficient machines, the introduction of novel, optimized components in the hot gas path represents a risky opportunity. Accurate experimental and numerical data are critical to assess the impact of new technologies on the harsh engine environment. The present study addresses the impact of a selection of high-performance rotor blade tips on the aerodynamic and heat flux field of a high-pressure turbine (HPT) stage. A combined numerical and experimental approach is employed to characterize the interaction of the tip leakage flow with the rotor secondary flows and the casing heat transfer mechanisms for each individual tip geometry. The turbine stage is tested at engine-scaled conditions in the rotating turbine facility of the von Karman Institute. In the present study, the turbine rotor is operated in rainbow configuration to allow the simultaneous testing of multiple blade tip geometries. Reynolds-averaged Navier–Stokes (RANS) simulations are employed to predict the aerodynamic and thermal fields of the individual profiles using test-calibrated boundary conditions. Isothermal steady computations are performed at different wall temperatures to compute the adiabatic wall temperature and the heat transfer convective coefficient. Low-order models are used to represent the over-tip thermal field and the driving heat transfer mechanisms. The time-resolved outlet flow is characterized using a vortex tracking technique and high-frequency aerodynamic measurements to identify the rotor secondary flow structures.

Simulation of discharging by loading various sizes of nano-powders utilizing numerical method for analyzing unsteady heat transfer

Simulation of discharging by loading various sizes of nano-powders utilizing numerical method for analyzing unsteady heat transfer

A physics‐informed machine learning prediction for thermal analysis in a convective‐radiative concave fin with periodic boundary conditions

AbstractThe present research is focused on the inspection of unsteady heat dissipation through a radiative‐convective concave profiled fin along with the periodic boundary conditions. Additionally, the long‐short‐term memory machine learning (LSTM‐ML) approach is used in this study to examine the periodic fluctuation in the temperature of the fin. The current research is devoted to solving the highly non‐linear equation using a physics‐informed neural network (PINN) approach. Using the proper dimensionless terms, the associated fin problem is transformed into a non‐dimensional system, and the resulting partial differential equation (PDE) is then numerically solved using the finite difference method (FDM). Using the data‐driven LSTM‐ML technique, the time‐dependent periodic heat transmission in the concave fin is also examined. The impact of various factors on the temperature profile of the concave extended surface is explained, and the results are visually displayed. The temperature distribution in the concave fin diminishes as the convection‐conduction parameter and radiation‐conduction parameter rise. As the amplitude and thermal conductivity parameters improve, so does the temperature of the concave fin. Furthermore, it is demonstrated that although LSTM‐ML and PINN closely matched the FDM findings during the training domain, only PINN with designed characteristics has the potential to predict accurately beyond the trained region by capturing the physics of the problem.

Coupled Axisymmetric Thermoelectroelasticity Problem for a Round Rigidly Fixed Plate

Introduction. To describe the operation of temperature piezoceramic structures, the theory of thermoelectroelasticity is used, in which the mathematical model is formulated as a system of nonself-adjoint differential equations. The complexity of its integration in general leads to the study of problems in an unrelated formulation. This does not allow us to evaluate the effect of electroelastic fields on temperature. The literature does not present studies on these problems in a three-dimensional coupled formulation in which closed solutions would be constructed. At the same time, conducting such studies allows us to understand the interaction picture of mechanical, thermal and electric fields in a structure. To solve this problem, a new closed solution of a coupled problem for a piezoceramic round rigidly fixed plate has been constructed in this research. It provides for qualitative assessment of the cross impact of thermoelectroelastic fields in this electroelastic system.Materials and Methods. The object of the study is a piezoceramic plate. The case of unsteady temperature change on its upper front surface is considered, taking into account the convection heat exchange of the lower plane with the environment (boundary conditions of the 1st and 3rd kind). The electric field induced as a result of the thermal strain generation is fixed by connecting the electrodated surfaces to the measuring device. The thermoelectroelasticity problem includes the equations of equilibrium, electrostatics, and the unsteady hyperbolic heat equation. It is solved by the generalized method of finite biorthogonal transformation, which makes it possible to construct a closed solution of a nonself-adjoint system of equations.Results. A new closed solution of the coupled axisymmetric thermoelectroelasticity problem for a round plate made of piezoceramic material was constructed.Discussion and Conclusion. The obtained solution to the initial boundary value problem made it possible to determine the temperature, electric and elastic fields induced in a piezoceramic element under arbitrary temperature axisymmetric external action. The calculations performed provided determining the dimensions of solid electrodes, which made it possible to increase the functionality of piezoceramic transducers. Numerical analysis of the results enabled us to identify new connections between the nature of external temperature action, the deformation process, and the value of the electric field in a piezoceramic structure. This can validate a proper program of experiments under their designing and significantly reduce the volume of field studies.