Conjugate Convective Heat Transfer Research Articles

Research on multi-heat source arrangement optimization based on equivalent heat source method and reconstructed variational autoencoder

The variational autoencoder (VAE) architecture has significant advantages in predictive image generation. This study proposes a novel RFCNN-βVAE model, which combines residual-connected fully connected neural networks with VAE to handle multi-heat source arrangements. By integrating analytical solutions, polynomial fitting, and temperature field superposition, we accurately simulated the temperature rise distribution of a single heat source. We further explored the use of multiple equivalent heat sources to replace adiabatic boundary conditions. This enables the analytical method to effectively solve the two-dimensional conjugate convective heat transfer problem, providing a reliable alternative to traditional numerical solutions. Our results show that the model achieved high predictive accuracy. By adjusting the β parameter, we balanced reconstruction accuracy and latent space generalization. During the stable phase of the multi-heat source optimization iteration, 73.4% of the results outperformed the dense dataset benchmark, indicating that the model successfully optimized heat source coordinates and minimized peak temperature rise. This validates the feasibility and effectiveness of deep learning in thermal management system design. This research lays the groundwork for optimizing complex thermal environments and contributes valuable perspectives on the effective design of systems with multiple thermal sources or for applications like multi-beam lighting equalization.

A fast fluid–solid coupled heat transfer algorithm based on dividing the development stages of the flow field

In this study, a fast numerical method for solving the forced convection conjugate heat transfer problem was developed. The method first proposes a new dimensionless number (Fs) that represents the degree of influence of convection on the temperature field in the flow field. It delineates the stage of development of the flow field by monitoring the change in Fs to determine the moment when the flow field suspends updating and improve the computational efficiency of the transient temperature field. The accuracy of the algorithm is verified by taking the fluid–solid conjugate heat transfer under forced convection conditions as an example, which can accurately capture the changes of the flow field for a given monitoring step number of 100, and classify the flow field into E3, E4 and E5 development stages according to the judgment criteria. The results show that the higher development stages correspond to smaller levels of root mean square error (RMSE) of monitoring point temperatures within 3600 s of physical simulation time, and stages E3, E4, and E5 can reach the levels of E-2, E-3, and E-4, which are 3.4, 3.3, and 3.1 times faster than the traditional coupled calculations, respectively. The algorithm is still applicable at variable time steps, but it will require a higher number of determinations compared to a fixed step. The initial error of the quasi-steady algorithm can be reduced from the E-1 level to E-4 by choosing a higher stage of development. Finally the algorithm is tested under a variety of conditions by varying the inlet temperature and flow rate and is found to be robust to both device warming and cooling.

Simulation of conjugate convective heat transfer in a vertical channel with thermal conductivity property of the solid blocks under the effect of buoyancy force

Currently, the cooling of electronic circuits is one of the most serious problems due to the exponential growth in demand for ever more powerful computer systems; overheating of these components becomes a serious problem. This article presents a number of computational results obtained by simulating a two-dimensional air flow for cooling occurring in a vertical channel. The area under study contains two square blocks simulating a set of electronic elements that are evenly installed in the vertical direction. The 2-D conjugate model of heat transfers between a solid body and an air flow is used with defined boundary conditions. In particular, the basic partial differential equations are approximated by the finite volume method. To study the impact of different parameters on the resulting heat transfer inside the channel, calculations are made for various parameters: Reynolds number, materials, and geometric parameters.

A study on the effect of non-uniform spacing on the performance of forced convection cooling of discrete heaters: A numerical investigation

A numerical simulation of forced convection conjugate heat transfer has been performed for flow over discrete, volumetrically heated rectangular obstacles mounted on the lower wall of a horizontal channel. Non-uniform spacing between the heaters is investigated with the help of isotherms, streamlines, heatlines and entropy generation along with cup-mixing temperature by fixing the geometric parameters for flow Reynolds number between 100 and 1500 (100≤ReL≤1500) and a fixed thermal conductivity ratio of 10 (ks/kf). To quantify heat transfer, local and average Nusselt number have been used. Pressure drop is calculated with the help of the apparent friction factor. Together, these two parameters provide the quality factor, which measures the performance of the discrete heaters. It has been found that the effect of spacing variation is not limited to the proximal heaters. Irregular behaviour in heat transfer has also been noticed in the results. As we move downstream of the flow, the heat transfer will decrease; however, there are a few particular cases where it was noticed that the performance of the last discrete heater is better compared to the heater just upstream of it.

Combining Digital Twin and Machine Learning for the Fused Filament Fabrication Process

In this work, the feasibility of applying a digital twin combined with machine learning algorithms (convolutional neural network and random forest classifier) to predict the performance of PLA (polylactic acid or polylactide) parts is being investigated. These parts are printed using a low-cost desktop 3D printer based on the principle of fused filament fabrication. A digital twin of the extruder assembly has been created in this work. This is the component responsible for melting the thermoplastic material and depositing it on the print bed. The extruder assembly digital twin has been separated into three simulations, i.e., conjugate convective heat transfer, multiphase material melting, and non-Newtonian microchannel. The functionality of the physical extruder is controlled by a PID/PWM circuit, which has also been modelled within the digital twin to control the virtual extruder’s operation. The digital twin simulations were validated through experimentation and showed a good agreement. After validation, a variety of parts were printed using PLA at four different extrusion temperatures (180 °C, 190 °C, 200 °C, 210 °C) and ten different extrusion rates (ranging from 70% to 160%). Measurements of the surface roughness, hardness, and tensile strength of the printed parts were recorded. To predict the performance of the printed parts using the digital twin, a correlation was established between the temperature profile of the non-Newtonian microchannel simulation and the experimental results using the machine learning algorithms. To achieve this objective, a reduced order model (ROM) of the extruder assembly digital twin was developed to generate a training database. The database generated by the ROM (simulation results) was used as the input for the machine learning algorithms and experimental data were used as target values (classified into three categories) to establish the correlation between the digital twin output and performance of the physically printed parts. The results show that the random forest classifier has a higher accuracy compared to the convolutional neural network in categorising the printed parts based on the numerical simulations and experimental data.

A natural convection conjugate heat transfer of Nano-Encapsulated Phase Change Materials (NEPCMs) in an inclined blocked square enclosure

The current investigation deals numerically with a two-dimensional steady laminar flow natural convection heat transfer of a dilute suspension of a base fluid and suspension of Nano Encapsulated Phase Change Materials (NEPCMs) nanoparticles saturated inside an inclined square enclosure with a centered internal conducting square block with a ratio of 0.5. The enclosure inclination angle varies from 0° to 90° with increments of 15°, and block thermal conductivity to the host fluid has been chosen to be 0.2 and 5. The obtained results are in excellent agreement with those available in the literature for validation. The findings reveal that the heat transfer depends considerably on the inclination angle, block thermal conductivity ratio, and Stefan number for all considered ranges. The present results suggest that the average Nusselt number rate is notably enhanced as the inclination angle rises from 0° to 90° for thermal conductivity KR = 0.2 and KR = 5; this enhancement is more evident as the Rayleigh number is increased. The average Nusselt number improves by 5%, 153%, 558%, and 1120% for Rayleigh numbers of 103, 104, 105, and 106, respectively, when the inclination angle varies from 0° to 90° for a thermal conductivity ratio of 0.2. This improvement is somewhat reduced in the case of a thermal conductivity of 5, where the average Nusselt number grows by around 0.4%, 27%, 213%, and 537% for Rayleigh numbers 103, 104, 105, and 106, respectively. The higher value of the latent heat capacity of encapsulated particles enhances the heat transfer rate; the decreased Stefan number induces a notable improvement in the average Nusselt number. This enhancement is more evident as the inclination angle increases. The findings clearly show a considerable influence on the isotherms and heat capacity ratio distributions for all considered block thermal conductivities and Rayleigh numbers.

Enriched immersed boundary method (EIBM) for interface-coupled multi-physics and applications to convective conjugate heat transfer

It is challenging to develop numerical methods that simultaneously maintain accuracy of resolving boundary conditions and mesh flexibility to handle the interface in interface-coupled multi-physics problems involving large property discontinuity. On the one hand, boundary-fitted methods possess high accuracy in capturing the interfacial phenomenon but involve complicated volumetric mesh generation, mesh-motion, and even re-meshing procedures. On the other hand, immersed boundary methods (IBM) provide mesh flexibility but sometimes suffer from inferior interface representations, leading to poor enforcement of boundary conditions. This paper presents an enriched immersed boundary method (EIBM) to overcome this challenge and demonstrates its efficacy in conjugate heat transfer, a representative example in interface-coupled multi-physics systems that have implications for many industrial processes. The core technique of the method is to enhance IBM’s accuracy of the fluid–solid interface by enriching the degrees of freedom of the cut elements to enforce temperature and flux compatibilities and resolve all the physical unknowns on the background mesh to simplify the volumetric mesh generation. We implement the EIBM under the framework of a variational multiscale formulation for coupled Navier–Stokes and thermodynamics equations. The enriched DoFs enable better enforcement of temperature and flux compatibilities with large conductivity ratios across the fluid–solid interface. At the same time, the immersed nature of the proposed method still attains mesh flexibility. The EIBM’s accuracy is thoroughly evaluated through a set of examples, ranging from benchmark problems with analytical solutions to real-world cooling processes of a moving metallic structure with complex geometry.

Computational multi-phase convective conjugate heat transfer on overlapping meshes: a quasi-direct coupling approach via Schwarz alternating method

Computational multi-phase convective conjugate heat transfer on overlapping meshes: a quasi-direct coupling approach via Schwarz alternating method

Inverse estimation of heat flux under forced convection conjugate heat transfer in a vertical channel fully filled with metal foam

In this work, for the first time, a heat flux at the boundary is estimated for a conjugate heat transfer under forced convection in the presence of high porosity metal foams. For the forward problem a vertical channel experimental set up reported in the literature is considered. The metal foam placed in the vertical channel is subjected to constant heat flux through aluminum plate and airflow of various velocities is passed through vertical channel for removal of heat from the high porosity metal foam placed in the vertical channel. Six different velocities are considered and the required temperature distribution of the aluminum plate is obtained by solving Darcy extended Forchheimer and Local Thermal non-equilibrium models for metal foams. The forward problem, created using computational fluid dynamics in ANSYS-FLUENT, is substituted with Neural Network for faster computation of the forward problem. The maximum errors between the computational fluid dynamics and Artificial Neural Network models for the heat flux values of 466.66, 666.66 and 1133.3 W/m 2 are found to be 0.086, 0.043, 0.092 respectively. The heat flux to the forward problem is treated as unknown and the same is estimated using an inverse method that couples Particle Swarm Optimization with Bayesian framework. The result of inverse estimation of exact temperature data shows that for a heat flux of 1266.64 W/m 2 the error is found to be 1.6e−4%. Similarly, for the noise added temperature data, the absolute % error in heat flux of 599.985, 733.315 and 1266.635 W/m 2 is 4.80e−2%, 2.20e−2%, 2.30e−2% respectively. • Inverse estimation of boundary heat flux using particle swarm optimization method. • Forward problem is a conjugate heat transfer problem in a vertical channel. • Darcy–Forchheimer, Local Thermal Non-equilibrium models for modelling porous medium. • Different Artificial Neural Network models to facilitate faster computations. • Particle Swarm Optimization combined Bayesian framework to quantify modeling error.

Analysis of conjugate heat transfer for forced convective flow through wavy minichannel

PurposeThe purpose of this paper is to analyze numerically forced convective conjugate heat transfer characteristics for laminar flow through a wavy minichannel.Design/methodology/approachThe mass and momentum conservation equations for the flow of water in the fluidic domain and the coupled energy conservation equations in both the fluid and solid domain are solved numerically using the finite element method. The exteriors of both the walls are subjected to a uniform heat flux.FindingsThe results reveal that the theoretical model without consideration of the effect of wall thickness always predicts a lower value of average Nusselt number () as compared to the case of conjugate analysis, although it varies with the thickness as well as material of the wall. For the low amplitude of the wall (α = 0.2), the performance factor (PF) becomes very high for Re in the regime of 5 (⩽) Re (⩽) 15. For any geometrical configurations, conjugate heat transfer analysis predicts higher PF as compared to that of nonconjugate analysis.Practical implicationsThe present study finds relevance in several applications, such as solar collectors and heat exchangers used in chemical industries and heating-ventilation and air-conditioning, etc.Originality/valueTo the best of the authors’ knowledge, the analysis of combined influences of the thickness and the material of the wall of the channel together with the geometrical parameters of the channel, namely, amplitude and wavelength on the heat transfer and fluid flow characteristics for flow through wavy minichannel in the laminar regime is reported first time in the literature.

Experimental and numerical study of innovative plate heat exchanger design in simplified hot box of SOFC

The inverse computational fluid dynamics simulation combined with experimental temperature measurements is applied to investigate the three-dimensional natural convection of an innovative plate heat exchanger in a hot box. This natural convection conjugate heat transfer separated by all insulating walls of the hot box is solved by couping. The upper low-temperature duct is located between the lower high-temperature duct and the top wall of the hot box. If the root mean square error between the obtained numerical results of the air temperature and the experimental data at the selected measurement locations is the smallest among all flow models, then the appropriate flow model and wall function can be predicted. Furthermore, more accurate natural convection heat transfer characteristics and the heat transfer rate applied to the two ducts can be determined. An important finding is that the realizable k-ε model combined with the standard wall function and the zero-equation model are suitable for problems with smaller and larger duct spacings, respectively. This means that the location of the two ducts may influence the selection of an appropriate flow model. In addition, increasing the number of grid points does not necessarily lead to more accurate results. An optimal total grid points can be obtained. The obtained heat transfer coefficients on the upper surfaces of the two ducts are also in good agreement with the existing correlation. This comparison further verifies that the present results and the selected flow model are accurate. Due to the blocking, buoyancy and heat dissipation effects of the two ducts, the formation of the main vortex, the velocity patterns and air temperature contours obtained by the two selected appropriate flow models are slightly different. The two gaps between the edges of the ducts and the side walls of the hot box can destroy the structure of natural circulation and improve the heat accumulation under the two ducts. The air flows slightly in the direction of the larger gap so that the velocity pattern and the temperature contour become asymmetric. As far as we know, these findings have not yet appeared in the public literature. Therefore, this study is novel and innovative.

Conjugate heat transfer analysis for forced convective flow through a parallel plate microchannel: Effect of nonuniform asymmetric heating

We analyze numerically the influence nonuniform asymmetric heating on the forced convective conjugate heat transfer characteristics for two-dimensional, steady flow of Newtonian fluid through a parallel plate microchannel. A parametric study is carried out by varying the phase difference, amplitude and period of fluctuation of the imposed heat flux, thickness and thermal conductivity of the walls as well as Reynolds number in the range of 25–600. Results reveal that there exists a complex interaction between the imposed heat flux profile and the physico-thermal properties of the walls in altering the thermal transport characteristics. The impact of asymmetric heating in altering the overall thermal transport rate is greater than the effect of nonuniform heating.

Numerical studies of nonstationary conjugate convective heat transfer in vertical layers of liquid and gas separated by a thin metal partition

Numerical studies of nonstationary conjugate convective heat transfer in vertical layers of liquid and gas separated by a thin metal partition

Shape control of the crystal-melt interface in the Bridgman method

The processes of silicon crystallization in flat-bottomed cylindrical graphite crucibles in the modes of conjugate convective heat transfer with allowance for latent heat are numerically investigated. The influence of hydrodynamics and heat transfer on the local shape of the crystal-melt interface has been studied. The hydrodynamics of a silicon melt is investigated in the modes of thermogravitational and thermal gravitational-centrifugal convection. First, the effect of the velocity of lowering the crucible into the cold zone was studied. Then, at the set crucible lowering velocity, the influence of the crucible angular velocity was studied. The problems were solved in a nonstationary formulation by the finite element method.

Effect of thermal conductivity of thin walls limiting the inclined liquid layer on non-stationary conjugate natural convective heat exchange and temperature fields in thin walls

Non-stationary conjugate convective heat transfer in a rectangular cavity at an angle of 45 degrees is studied numerically in the conjugate formulation. A liquid layer with a Prandtl number of 25.66 is located in a cavity with thin metal or low-heat walls. The outer surface of the lower wall is suddenly heated, and the outer surface of the upper wall is maintained at the original temperature. The system of equations of non-stationary thermogravitation convection is solved in the Boussinesq approximation in a dimensionless form. The time evolution of convective flows and temperature fields in the liquid and in the walls is studied. It is shown that the thermal conductivity of walls significantly affects the spatial shape of convective flows and the regularities of conjugated convective heat exchange.

Unsteady conjugate convective heat transfer in a vertical channel at a sudden heating of the bottom

The processes of unsteady heat transfer in the mode of thermogravitational convection in a vertical channel with solid walls of finite thermal conductivity after a sudden heating from bottom was studied numerically by the finite element method in three-dimensional problem statement. The system of thermogravitational convection equations was solved in the Boussinesq approximation in the variables of vortex–vector potential of the velocity field and temperature. The calculations were performed with the Prandtl number of 10, the Grashof number of 5000, and the ratio of the thermal conductivity of solid walls to the thermal conductivity of the liquid equal to 6.29. Distributions of the unsteady temperature field into the liquid and solid walls, temperature gradient fields, and velocity fields in the liquid were obtained. The process of formation, loss of axial symmetry and subsequent development of the rising stream was shown.

Numerical analysis of 2-D laminar natural convection heat transfer from solid horizontal cylinders with longitudinal fins

Proper thermal management through an effective cooling mechanism is essential for improving the reliability of operation of various electronic devices. A number of cooling methods are available among which passive cooling by natural convection has been deemed appropriate since it has distinctive advantages over active cooling or forced convection like high reliability, low maintenance cost, energy efficiency and noise-free nature. In the present study, natural convection from solid horizontal cylindrical heat sources of the geometry and dimensions of heat sinks of LED bulbs with external longitudinal plate fins have been modelled. Numerical computations of continuity, momentum and energy equations to solve the two dimensional incompressible natural convection conjugate heat transfer from such cylinders has been studied in the laminar regime (4.5×105<RaD<5.2×105). The diameter of the cylinder is kept at 60 mm whereas the length is kept at 50 mm. The number of fins has been varied from three to 36, the height of fins kept at 10, 20 and 30 mm and thickness at one mm. The effect of fin geometry parameters and Rayleigh number on total heat transfer, heat transfer exclusively from fin surface and from bare cylinder surface, heat transfer per fin and Nusselt number based on cylinder diameter have been studied in detail. Finally, optimum fin spacing for a particular fin height has been evaluated. Contour plots to capture temperature and velocity vectors around the heat source have also been developed. Numerical correlations of Nusselt number as a function of Rayleigh number, non-dimensional fin spacing and non-dimensional fin height reveal that the scaling laws of RaD1∕3 and RaD1∕4 are valid both for the computational data of our present analysis and experimental data even though the experiments are for a slightly different boundary condition.

Evaluation of artificial neural network in data reduction for a natural convection conjugate heat transfer problem in an inverse approach: experiments combined with CFD solutions

Evaluation of artificial neural network in data reduction for a natural convection conjugate heat transfer problem in an inverse approach: experiments combined with CFD solutions

Influence of conjugate convective heat transfer on temperature fields in thin walls that organize liquid layers of various orientations

Numerical studies of unsteady conjugate natural convective heat transfer in the model of a thin-walled fuel tank are carried out in the conjugate formulation. The fields of temperature in liquid and in solid walls of the tank are calculated. The evolution of convective flows and temperature fields after a sudden supply of heat to the base of the tank is investigated. Flat layers of liquid enclosed between flat walls of different orientations with inclination angles of 0, 30, 45, 60 and 90 degrees are considered. With the angle of inclination of 0 degrees the outer surface of the side walls is insulated. The outer surface of the lower wall heats up suddenly, the outer surface of the upper wall is isothermally cold. The system of equations of thermogravitation convection in the Boussinesq approximation in dimensionless form, written in terms of temperature, vector potential of the velocity field and velocity vortex, is solved. It is shown that an inhomogeneous temperature field is formed inside the solid walls of the finite thermal conductivity. The thermal conductivity of walls and conditions at the upper boundary of the liquid layer affect significantly the spatial form of convective fuel flows in fuel tanks and laws of conjugated natural convective heat exchange.

The influence of Prandtl numbers of melts and crucible materials on the features of crystal growth by the Bridgman method

The processes of crystallization of silicon and heptadecan in flat-bottomed cylindrical crucibles in conjugate convective heat transfer regime were studied numerically by the finite element method. Crystallization of silicon was investigated in a graphite crucible. Crystallization of heptadecane was investigated in a Plexiglas crucible. The possibility of existence of two convective vortices over a solidification front during the crystallization of silicon and heptadecane has been discovered. Crystallization of heptadecane was studied at two rates of lowering the crucible into the cold zone. Lowering of the crucible was simulated by moving the breakpoint in the temperature distribution on the outer side of the crucible walls. The breakpoint was the boundary of transition from the wall area heated to the initial temperature to the area with a given temperature gradient. Adaptive grids on triangles tracking the position of the crystallization front at each time step were used. The software package of developed by the authors was used.