Solution Of Heat Transfer Research Articles

A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis

This paper presents an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Due to the significant role of fluid flow through non-circular channels in industry and the large number of triangular shapes, a method for solving the heat transfer problem for all triangular shapes is needed. The heat transfer of a fluid flow through a channel with an arbitrary triangular cross-section for the case of constant heat flux at the walls is solved in this work for the first time, considering viscous dissipation. Here, the functionals of flow and heat transfer equations are derived, and the resulting Euler–Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. It is also found that the equilateral triangle exhibits the minimum friction coefficient and the maximum value of the Poiseuille number.

Semi-closed Solutions of Two-Dimensional Nanofluid Flow and Heat Transfer Over a Nonlinear Stretching Sheet Embedded with New Set of Similarity Transformations

Semi-closed Solutions of Two-Dimensional Nanofluid Flow and Heat Transfer Over a Nonlinear Stretching Sheet Embedded with New Set of Similarity Transformations

Theoretical exploration of a free-piston Stirling generator with a gas-compressing self-circulating heat exchanger

The free-piston Stirling generator (FPSG) holds great promise as a thermal-to-electrical conversion device for space applications. However, heat transfer remains a critical factor obstructing its scalability to high power levels. In this study, we propose a high-power FPSG with a gas-compressing self-circulating heat exchanger (GSHX) that utilizes high-pressure helium as the heat transfer fluid, enhancing the reliability of the heat exchanger. By incorporating a built-in gas-compressing device and check valves, the performance degradation caused by significant pressure fluctuations in the resonant self-circulating heat exchanger is effectively addressed. Through detailed simulations, we demonstrate the principle feasibility of the GSHX with a 4 m heat transfer loop, achieving an output electric power of 11 kW and a thermal-to-electric efficiency of 20.4%. Furthermore, the GSHX exhibits similar operating characteristics to traditional FPSGs, as we analyze the systems' stability under various operating conditions. Importantly, our findings reveal that the acoustic characteristics of the loop play a pivotal role in system performance, with operating parameters exhibiting periodic variations related to helium wavelength. By carefully optimizing system parameters, GSHX with a long loop length of 29 m can achieve comparable performance to systems with shorter loops. This study provides valuable insights into the operational characteristics and performance optimization of the GSHX, offering a comprehensive heat transfer solution for long-distance, high-efficiency, and highly reliable applications of high-power FPSGs in the space domain.

Cooling enhancement for engine parts using jet impingement

A computational study has been performed to evaluate the use of jet impingement for cooling applications in the automotive industry. The current study uses an entire internal combustion engine cylinder with its components as a computational domain. An unsteady numerical solution for the Navier-Stokes equations was carried out using Improved Delayed Detached Eddy Simulation (IDDES). The volume of fluid approach is proposed to track and locate the liquid jet surface that is in contact with the air. The conjugate heat transfer approach is used to link the heat transfer solution between the fluid and the solid. The boundary conditions that are employed in the study are provided from lab experiments and one-dimensional simulations. The cooling jet in this study targets the hottest region in the piston, i.e., the region underneath the exhaust valve. Three nozzle sizes with flows at different Reynolds numbers are chosen to examine the thermal characteristics of the cooling jet. The computational study reveals that for a specific Reynolds number, the smaller diameter nozzle provides the highest heat transfer coefficient around the impingement point. The maximum relative velocity location at the impingement point slightly leads the location of the maximum Nusselt number. The maximum temperature in the piston decreases by 7% to 11% as the nozzle diameter changes from 1.0 to 3.0 mm for a jet Reynolds number of 4,500. If a correct selection is made for the nozzle size, the cooling jet can be efficiently used to reduce the temperature and alleviate the thermal stresses in the piston in the region underneath the exhaust valve where the maximum temperature occurs.

Study on coupled heat transfer model and enhanced heat transfer law of liquid metals and supercritical fluids

ABSTRACT The supercritical carbon dioxide Brayton cycle system is being considered for application in the power conversion system of advanced liquid metal fast reactors. One important research topic is the coupled heat transfer characteristics and enhanced heat transfer laws between liquid metals and supercritical fluids. However, the traditional Reynolds analogy hypothesis with a constant turbulent Prandtl number is difficult to satisfy the numerical conjugate heat transfer research of liquid metals and supercritical fluids. Therefore, based on the open-source computational fluid dynamics program OpenFOAM, a numerical method suitable for the coupled heat transfer calculation of liquid metals and supercritical fluids was developed, which can achieve precise conjugate heat transfer solutions by applying different turbulence models and heat flux models to liquid metals and supercritical fluids. Subsequently, based on this method, the coupled heat transfer behavior of liquid metals and supercritical fluids in the straight channel of a typically printed circuit heat exchanger was studied. The focus was investigating the conjugate heat transfer characteristics of liquid heavy metal lead-bismuth eutectic and liquid metal sodium with supercritical carbon dioxide. Some sensitive results, including the inlet temperature and Reynolds number of liquid metals and supercritical fluids, were qualitatively and quantitatively analyzed.

The lie group analysis method for heat transfer in steady boundary layer flow field of nanofluid

In order to reveal the mechanism of the abnormal movement (Brownian motion enhances thermal scattering) of nanoparticles on the fluid enhanced heat transfer, the two-phase model was used to study the abnormal convection and diffusion of viscous nanofluids in the flat boundary layer of porous medium. Firstly, for the two-dimensional steady boundary layer stagnation point flow of incompressible Newtonian-nanofluids, the nonlinear governing equations of the flow field and temperature field of nanofluids are established from the Oberbeck-Boussinesq approximate equations. Secondly, the modern Lie group analysis method is introduced, we give the Lie symmetry determining equation of the flow field partial differential equations and the characteristics of the solutions. Further, using the relationship between the Lie symmetries and the conserved quantities, the conservation vector form of the flow field and the group invariant solution are derived in detail, and the reduced order model of the nanofluid flat boundary layer is obtained. Finally, the correctness of the analytical results obtained by the Lie group method was verified for different values of the flow parameter Prandtl. Research has shown that the Lie group method can be used to analytically solve the velocity and temperature distribution functions of abnormal motion of nanoparticles. The fluid temperature increases with the increase of the volume fraction parameter of nanoparticles, but decreases with the increase of the Prandtl value of the base fluid, and decreases with the increase of the plate stretching speed. The Lie group analysis method in this paper provides reference value for numerical simulation solutions of various heat and mass transfer in nanofluids.

Dual solutions for axisymmetric flow and heat transfer due to a permeable radially shrinking disk in copper oxide (CuO) and silver (Ag) hybrid nanofluids with radiation effect

Purpose This study aims to investigate the dual solutions for axisymmetric flow and heat transfer due to a permeable radially shrinking disk in copper oxide (CuO) and silver (Ag) hybrid nanofluids with radiation effect. Design/methodology/approach The partial differential equations that governed the problem will undergo a transformation into a set of similarity equations. Following this transformation, a numerical solution will be obtained using the boundary value problem solver, bvp4c, built in the MATLAB software. Later, analysis and discussion are conducted to specifically examine how various physical parameters affect both the flow characteristics and the thermal properties of the hybrid nanofluid. Findings Dual solutions are discovered to occur for the case of shrinking disk (λ < 0). Stronger suction triggers the critical values’ expansion and delays the boundary layer separation. Through stability analysis, it is determined that one of the solutions is stable, whereas the other solution exhibits instability, over time. Moreover, volume fraction upsurge enhances skin friction and heat transfer in hybrid nanofluid. The hybrid nanofluid’s heat transfer also heightened with the influence of radiation. Originality/value Flow over a shrinking disk has received limited research focus, in contrast to the extensively studied axisymmetric flow problem over a diverse set of geometries such as flat surfaces, curved surfaces and cylinder. Hence, this study highlights the axisymmetric flow due to a shrinking disk under radiation influence, using hybrid nanofluids containing CuO and Ag. Upon additional analysis, it is evidently shows that only one of the solutions exhibits stability, making it a physically dependable choice in practical applications. The authors are very confident that the findings of this study are novel, with several practical uses of hybrid nanofluids in modern industry.

A general unsteady Fourier solution for orthotropic heat transfer in 2D functionally graded cylinders

In the present research, an analytical solution is presented for unsteady heat transfer in a two‐dimensional finite cylinder made of functionally graded Materials (FGM). The governing equation, as an unsteady partial differential equation (PDE), is solved with general boundary conditions (BCs). The thermal conductivity coefficients are considered as a power function of the radius, both in the longitudinal and radial directions of the FGM cylinder. The presence of non‐constant coefficients and general BCs will confront us with the challenge of solving an unsteady problem with high complexity. A combination of Laplace transform, Fourier transform, and meromorphic functions are utilized to deal with this complex PDE. The Laplace transform was applied to transform to the frequency domain, the Sturm–Liouville equation was used to extract the orthogonal basis Fourier series, and the meromorphic function was deployed to transform back from the frequency domain to the time domain. Results were well verified against previous research works. Results showed that the proposed analytical solution could well predict the temperature distribution. The current analytical solution is useful to better understand unsteady heat transfer in FGMs.

Modeling Of 3D Integrated Circuits, Heat Transfer Solutions and Application

As transistor sizes approach the quantum limit, the cost of further shrinking them becomes prohibitively high. To overcome this limitation and surpass Moore's Law, 3D (Integrated Circuits) IC technology has emerged. However, while 3D ICs offer advantages like high integration, they also present challenges related to thermal management. This paper introduces and discusses partial differential equations and modeling methods for heat transfer in 3D ICs. It explores solutions to address thermal conduction problems and analyzes the potential application areas and prospects of 3D ICs. By utilizing different modeling methods, we can optimize the heat transfer problem during the design stage. To enhance the thermal conduction of 3D ICs, this study proposes the use of copper thermal conductive materials, graphene thermal conductive layers, and phase-change material cooling. As technology advances and costs decrease, 3D ICs are expected to find broader applications in high-performance computing, artificial intelligence, the Internet of Things, and other fields. Despite its numerous advantages, 3D integrated circuit technology still faces challenges such as cost, heat, and silicon vias. To address these issues, further technological innovations and updates to Computer Aided Design (CAD) tools are necessary. Overall, this study holds significant social and scientific importance as it promotes the development of 3D IC technology, improves electronic device performance, and advances scientific research.

Mixed convective flow of nanofluid across exponential surface: A numerical assessment of the impact of Darcy-Forchheimer and nanoparticle aggregation

Improving heat transmission is a modern difficulty faced in a multitude of areas, incorporating but not limited to electronics, heat exchangers, biochemical reactors, and other similar areas. In their capacity as cutting-edge heat transfer fluids, nanofluids have the promise of becoming a useful instrument in the pursuit of greater energy transfer efficiency. So, the focus of this work is on how it is possible to enhance heat transmission by using nanofluids. Using a stretched exponentially accelerating surface, this analysis investigates the effect that nanoparticle aggregation with thermal radiation has on the nanofluid of mixed convective stagnation point flow through Darcy-Forchheimer porous surfaces. The aggregation of nanoparticles may be assessed using modified Krieger-Dougherty and Maxwell-Bruggeman models. By using the right similarity transformations, the controlling equations of this problem were turned into a numerical model that can be unraveled. Mathematica was used to resolve the issue numerically by using the shooting with Runge-Kutta (RK-IV) procedure. nanoparticles with base fluid under aggregation effect boost heat transfer performance. A diversity of parameter estimates, including the mixed convection, mass suction, solid volume fraction of nanoparticles, thermal radiation, and stretching, were used to provide solutions for heat transfer and lower skin friction coefficients, as well as velocity and temperature curves. In addition to the findings, there were graphs and tables with explanations. The increase in heat transfer rates was 6.7021% when the suction parameters were set between 2.0 to 2.5 with =0.01. When the amount of nanoparticles volume fraction went from 0% to 1% by volume, the ineptitude of heat transfer went by an average of 4.249%. Aggregation models are often favored over non-aggregation models due to their ability to provide more accurate velocity and skin fraction profiles. Because of their superior precision, they are often used in situations where accuracy is paramount.

Exact solutions for magnetohydrodynamic nanofluids flow and heat transfer over a permeable axisymmetric radially stretching/shrinking sheet

We report on the magnetohydrodynamic impact on the axisymmetric flow of Al2O3/Cu nanoparticles suspended in H2O past a stretched/shrinked sheet. With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles, the physical flow process is illustrated. The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations. The transformed differential equations are solved analytically. Impacts of the magnetic parameter, solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically. The skin friction and Nusselt number were also evaluated. In addition, existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one. Further, Al2O3/H2O nanofluid flow has better thermal conductivity on comparing with Cu/H2O nanofluid. Furthermore, it was found that the first solutions of the stream are stable and physically realizable, whereas those of the second ones are unstable.

An analytical solution for convective heat transfer in conical gaps with either cone or disk rotating

This study is devoted to solving two problems of laminar fluid flow in a conical gap with small conicity angles up to 4°: cone rotation with a fixed disk, and disk rotation with a fixed cone. A new improved asymptotic expansion method for energy equation was used to obtain an approximate analytical solution to the convective heat transfer equation. The characteristic Reynolds number ranged from 0.001 to 1.0, the Prandtl number took values 0.71, 1, 5, and 10, and the exponent n* in the power-law for the disk temperature was 0 (constant disk temperature) or 2 (strongly radially increasing disk temperature). A novel model for the asymptotic expansion of the temperature profile and a novel expansion parameter Sv = Re2Pr, which is a new dimensionless number proposed for the first time in the known scientific literature, was developed. For the first time, new approximate analytical solutions were obtained for temperature profiles and Nusselt numbers on the disk and cone for both problems that agree well with the self-similar solution, if the Re and Pr numbers do not exceed threshold values. These analytical solutions are advantageous in analysis of experimental data and further development of one-dimensional models for gases, water, and aqueous solutions (Pr = 0.71–10).

Effect of viscous dissipative fluid in a slit micro-channel with heated super-hydrophobic surface

The analytical solution of heat transfer and hydro magnetic flow for an incompressible, electrically-conducting, and viscous dissipative fluid traveling vertically through an isothermally heated parallel plate in a slit micro-channel is performed. One channel surface was super-hydrophobic slip and temperature jump, whereas the other did not. This study also examined the effects of super-hydrophobic slip and a temperature jump on characteristic flow of magneto-hydrodynamics (MHD) free convection flow with viscous dissipative fluid. The perturbation technique was used to solve the coupled nonlinear and coupled equations analytically. With the aid of illustrative graphs, the results were presented, and the effects of the relevant controlling parameters namely Brinkman number, magnetic field, velocity slip condition and temperature jump effects were analysed for temperature, velocity, skin friction and Nusselt number distributions when either wall is heated by constant wall temperature. The result demonstrated that the activities of Brinkman number, Br, substantially increase fluid velocity, whereas growing levels of magnetic field effect was seen to slow down the flow movement. In addition, the fluid velocity is higher for greater values of temperature jump and velocity slip effects respectively. Furthermore, this research can prove very useful for designers in improving the performances of mechanical systems when viscous dissipation is involved, as well as heat transfer in micro-channels, as it is in combustion.

Theoretical Examination of the Volume Concentration and Nanoparticles Density Influence on the Convective Heat Transfer Enhancement of Nanofluid in 2D Cavity Including the Square Heater

Nanofluid is one of the solutions of heat transfer, which can apply in devices fields as nuclear power, Nano-electronics systems, and solar fluid heating. In this work, the natural convection of Cuwater nanofluid is examined using the Lattice Boltzmann Method (LBM) as a mesoscopic approach. The main objectives of this work are to study the performance and pattern of Cu-water nanofluid and to demonstrate that the nanofluids behave differently while improving their energy transfer compared to pure fluids. The set goal was achieved by solving the tasks: based on the streamlines and isotherms profiles to demonstrate how the convection process and temperature gradients improve. Also, conducting study on heat transfer of nanofluid by calculate the Nusselt number. Depending on the nanoparticle volume percentage, the Grashof number Gr , and the hot obstacle have a significant impact on the convection flow and rate of heat transfer. The most important result is the enhancement of heat transfer with the increasing of volume fraction for a particular Grashof number, also it improves with the rising of Grashof number for a particular nanoparticles volume fraction. Therefore, the aspect ratios of the enclosure have played a significant part in Nusselt number variation. In addition, we found that the Nusselt number avg Nu is higher in the case of cavity without hot obstacle more than for cavity with hot obstacle, so the heat transfer improves in the case of cavity without hot obstacle. The significance of the obtained results consists that the nanofluid is one of the ways to improve heat transfer due to its specific characteristics and properties.

Microfluidic systems with a pulsating heat pipe

This research addresses a critical issue in modern microelectronics, which arises from increased miniaturization and heat generation, necessitating effective temperature control. The study focuses on pulsatile heat pipes, offering a passive and highly efficient heat transfer solution by utilizing fluid and vapor phases within a closed capillary channel. To enhance temperature regulation, microfluidics are employed with integrated separation barriers to improve capacity and efficiency. Altering the flow pattern of liquid and vapor plugs through droplet generation may enhance thermal performance. The study demonstrates the accuracy of the heat transport model through mathematical and empirical data comparison, achieving a remarkable 90.9% accuracy and efficiency. Pulsatile flows, especially in microfluidic systems, exhibit advantages over steady flows, promising avenues for future physics-based research.

Analytical and numerical (FEA) solution for steady-state heat transfer in generic FGM cylinder coated with two layers of isotropic material under convective-radiative boundary conditions

An investigation was carried out in order to develop an accurate analytical solution and a numerical (FEA) solution for steady-state heat transfer in a circular sandwich structure incorporated with convective-radiative boundary conditions. The dimensional governing equations and boundary conditions were developed in the form of a 4th order algebraic equation, and then the solution was obtained using Ferrari's method. By solving for the roots of the quartic equation, we were able to determine the dimensionless temperature fields of the FG sandwich composite. The findings obtained utilizing the exact analytical solution for the FG sandwich composite under thermal loads were satisfactorily validated against those data obtained using the Galerkin finite element approximation. The impact of geometric and thermo-physical characteristics, such as Biot number (Bii=1,2), Inner and outer surface thickness ratio (ri=1,2Ro), ambient temperature ratio (θd), radiation-conduction parameter (Nr), and thermal conductivity ratio (λ3λ1) on the efficiency of heat transfer, has also been studied. This study reveals the distinct effect of Biot number on the inner and outer layers of the composite cylinder. It shows that Bi1 has a negligent effect on temperature distribution; on the other hand, the outer surface (Bi2≤1) minimizes temperature variation. However, for design consideration, a thicker inner face sheet is not recommended in high thermal load, as Nr>4 has an insignificant impact on inner surface thickness on top surface temperature. Moreover, the outer surface temperature appears to be more sensitive to θd than the radiation-convection side. Furthermore, the given analytical solution is adequately verified against the proposed FEA method, having an error of less than 1.5%.

Similarity solutions of heat transfer in shear flow over an otherwise still fluid

Thermal energy and momentum transport in two-fluid systems are investigated. The hydrodynamic part of the problem was considered by Wang [“The boundary layers due to shear flow over a still fluid,” Phys. Fluids A 4, 1304–1306 (1992)] and Andersson and Mukhopadhyay [“Boundary layers due to shear flow over a still fluid: A direct integration approach,” Appl. Math. Comput. 242, 856–862 (2014)], whereas the accompanying heat transfer analysis is new and fills a gap in the literature. Momentum and thermal boundary layers form on both sides of the planar interface between a shear-driven upper fluid and an underlying still fluid. Similarity transformations reduce the governing partial differential equations to sets of ordinary differential equations for each fluid, coupled by boundary conditions at the interface. The thermal part of the transformed two-fluid problem depends explicitly on the ratios between the kinematic viscosities, the thermal conductivities, the Prandtl numbers, and the temperatures of the lower and upper fluids. Moreover, an implicit dependence on the density ratio appears due to the fluid velocities. Similarity solutions obtained by means of a direct integration approach are presented for six different two-fluid systems. The computed results show that the temperature and velocity fields in the upper and lower fluid depend crucially on the mechanical and thermophysical properties of the two fluids, as does the heat flux through the interface between the two immiscible fluids.

Analytical solution for the temperature field of cold region tunnels that considers thermal resistance

The temperature field is a crucial factor in the design and research of cold region tunnels. However, current research has focused on the effects of insulation, ventilation and heating on heat transfer, while disregarding the effect of thermal resistance from embedded components on heat conduction. In this study, a new analytical solution for transient heat transfer that considers interfacial thermal resistance is developed. This solution employs the shifting function method and finite integral transform technique. The proposed solution is highly versatile and can accommodate arbitrary time-varying ambient temperature, the convective heat transfer coefficient at the air-solid interface of the tunnel and the heat source power of embedded heating components. Furthermore, the consistency and accuracy of the proposed solution are validated by comparing with the finite element method solutions for two tunnel examples: (1) only concrete linings are applied; and (2) concrete linings are applied, along with an insulation layer and an embedded heat source. The new solution can provide valuable insights into the design and optimization of anti-frost systems in cold region tunnels and exhibits high potential for engineering applications.

Multi-objective optimization design of TRISO-based fully ceramic microencapsulated fuel

Fully Ceramic Microencapsulated (FCM) fuel is a new type of material in nuclear energy field. It has become a promising accident tolerant fuel (ATF) candidate due to its advantages of high radiation stability, high fission product containment capacity and excellent thermo-mechanical performance. During operation, the temperature, stress, deformation and other key parameters will change significantly, which directly affect the safety of nuclear reactor. Therefore, it is necessary to carry out a multi-physics fully-coupled analysis suitable for the multi-scale, multi-component, multi-phase and nonlinear coupling processes in the reactor, so as to sort out the influences of material properties, radiation behavior, thermo-mechanical performance from numerous influencing factors. In this paper, based on the irradiation-thermo-mechanical coupling method, the performance of TRISO-based FCM fuel under irradiation conditions was analyzed, key thermo-mechanical parameters and other influencing factors of the fuel were obtained, failure behavior of the fuel element was evaluated. On this basis, the theoretical and numerical model of multi-objective optimization method were established, the optimum parameters including material properties, fuel geometry and particle arrangement were found by optimization method. The optimization results showed that the multi-objective optimization results could provide multiple Pareto optimal solutions for the FCM fuel. Specifically, when the TRISO particle spacing is 200 µm and 150 µm, the objective function difference between the optimal heat transfer solutions is only about 1.7%, meanwhile the mechanical properties vary significantly (the difference between the objective functions of the optimal solutions is about 12.4% ∼26.5%), indicating the response of stress is more sensitive than temperature. When the TRISO particles are tightly packed (particle spacing less than 100 µm), the difference of objective function between the optimal solutions is less than 5%, illustrating the optimization has limited improvement on the thermo-mechanical performance of the fuel, namely the optimization space is limited.

Numerical Study on the Optimal Thermally Affected Region of a Buried Oil Pipeline.

Crude oil pipeline transportation is usually a closed process under a certain depth of burial, and the condition of oil in the pipeline changes with the continuous decline of temperature during the transportation process. The safety and energy consumption of pipeline transportation are closely related to the accurate prediction of oil temperature. It is a popular technique to use the thermally affected region to overcome the problem of an unclosed calculation domain caused by the semi-infinite soil around the pipeline. However, there is no clear and unified guidance on the thermally affected region at present, and improper region size may lead to a loss of the accuracy of the pipeline system. Therefore, our study answers two questions about the optimal form of the thermally affected region and its economic scope of application. The coupled solution of heat transfer and flow in a tridimensional numerical model is carried out, and the thermodynamic influences of the geometric shape and range of the thermally affected region on the buried pipeline system are investigated. The results show that the rectangular region is more suitable for the modeling of buried oil pipelines, and a region with 16 m width and 9 m height is recommended for the conventional case.