Uniform Heat Flux Distribution Research Articles

Two-dimensional turbulent convection in a toroidal duct of a liquid metal blanket of a fusion reactor

Convection in a horizontal duct aligned with a uniform magnetic field is analysed computationally. The motivation of the study is the concept of a liquid metal blanket for a tokamak fusion reactor, in which ducts are oriented toroidally, i.e. parallel to the main component of the magnetic field. Computations of two-dimensional (streamwise-uniform) flows appearing at very strong magnetic fields and of three-dimensional flows in long domains are conducted. Non-uniform volumetric internal heating is applied, while the walls are maintained at a constant temperature. Two-dimensional or nearly two-dimensional turbulent convection is found at high Grashof and Hartmann numbers typical for fusion reactor conditions. The turbulence results in stronger mixing and more uniform distribution of wall heat flux, indicating promising potential of this concept of the blanket.

A two dimensional approach for temperature distribution in reactor lower head during severe accident

In order to evaluate the safety margin during a postulated severe accident, a module named ASAP-2D (Accident Simulation on Pressure vessel-2 Dimensional), which can be implemented into the severe accident simulation codes (such as ATHLET-CD), is developed in Shanghai Jiao Tong University. Based on two-dimensional spherical coordinates, heat conduction equation for transient state is solved implicitly. Together with solid vessel thickness, heat flux distribution and heat transfer coefficient at outer vessel surface are obtained. Heat transfer regime when critical heat flux has been exceeded (POST-CHF regime) could be simulated in the code, and the transition behavior of boiling crisis (from spatial and temporal points of view) can be predicted.The module is verified against a one-dimensional analytical solution with uniform heat flux distribution, and afterwards this module is applied to the benchmark illustrated in NUREG/CR-6849. Benchmark calculation indicates that maximum heat flux at outer surface of RPV could be around 20% lower than that of at inner surface due to two-dimensional heat conduction. Then a preliminary analysis is performed on the integrity of the reactor vessel for which the geometric parameters and boundary conditions are derived from a large scale advanced pressurized water reactor. Results indicate that heat flux remains lower than critical heat flux. Sensitivity analysis indicates that outer heat flux distribution is more sensitive to input heat flux distribution and the transition boiling correlation than mass flow rate in external reactor vessel cooling (ERVC) channel, and the correlation for molten vessel and ERVC coolant inlet temperature.According to the results achieved, the new developed module shows good applicability to simulate the pressure vessel behavior during melt pool formation. Thus it can be applied for the future study of the severe accidents relating to lower head integrity.

Achieving Heat Flux Uniformity Using an Optimal Arrangement of Impinging Jet Arrays

In order to achieve uniform distribution of heat flux over an isothermal heated target surface, a numerical algorithm is developed to obtain an optimized array of four laminar impinging slot jets. Root mean square deviation of the local Nusselt distribution from the desired Nusselt number is considered as the objective function. Jets' widths, jet-to-jet and jet-to-surface spacings, and the overall flow rate are chosen as design variables. Conjugate gradients method along with backtracking line search is applied to optimize the objective function calculated by numerical simulation for three different cases of Nu = 7, 9, and 11. For each of these desired Nusselt numbers, an almost uniform distribution of local Nusselt number with percent of root mean square error less than 2.5% is achieved in fewer than 12 iterations. An experimental study using a Mach–Zehnder interferometer (MZI) has been performed. The measured distribution of local Nusselt number is in good agreement with numerical results in all three optimal configurations.

Study the effect of Gaussian and Uniform heat flux on laser forming of Bi-layer sheets

Laser forming process is one of the newest methods of sheet metal bending which no mechanical force needs. Although lots of investigations on laser forming process of mono layer sheet metals have been done, any experiments have not been conducted around bi- layer sheets. In this paper, laser forming process of bi-layer Al/SiC work pieces under Gaussian and Uniform heat distribution has been studied. Elastic- plastic temperature dependent material properties are considered. Also, the boundary condition is applied as free heat convection. The results of numerical simulations revealed that the amount of bending angle in Uniform heat flux distribution is always further than Gaussian distribution. In addition, temperature distribution diagram in Uniform heat flux is almost 5% further than Gaussian form, and the maximum temperature in the work piece is 6% larger. For validation of numerical analyses, experimental tests are done by an Nd: YAG laser on bi-layer Fe/Al sheets. The amounts of bending angles are so close to the results of simulation. The average of the bending angle is almost derived 0.0038 Degree/ Watt in these experimental tests.

Thermal cooling enhancement techniques for electronic components

Due to highly effective thermal spreaders, the vapor chambers have been widely applied on the electronic cooling. An effective thermal spreader can achieve more uniform heat flux distribution and thus enhance heat dissipation of heat sinks. This work investigates the thermal performance characteristics plate-fin vapor chamber. Parametric studies including different operating operation of CPU, coolant types, working fluids, filled ratios, flow direction of coolants, heat sink configurations, and the effect of the relevant parameters on the cooling performance in terms of the thermal resistance was considered and discussed. The results showed that the relevant parameters have a significant influence on the thermal resistance of the vapor chamber.

Numerical investigation on uniformity of heat flux for semi-gray surfaces inside a solar cavity receiver

Solar cavity receiver is quite often utilized in the solar tower power system. It is a photo-thermal conversion component, which absorbs solar radiation energy and heats the working fluid. The safety and thermal efficiency of solar cavity receiver can directly affect the efficiency of the entire power system. In this paper, a modified combined method is proposed to simulate the thermal performance of a saturated water/steam solar cavity receiver. Compared with the combined method presented previously, this modified one can describe the whole steady process of the receiver and accurately estimate the steady-state efficiency and the mass flow rate of the generated steam in the boiling tubes. Under the given boundary condition of incident solar flux, the modified method is adopted to find an optimized distribution of absorptivity in the solar wavelength band for the absorber surfaces in order to improve the uniformity of surface heat flux distribution. The simulation results show that the uniformity of surface heat flux is improved effectively and the maximum mean square deviation of the external tube temperature drops from 32.4°C to 23.6°C after optimizing. Based on the relatively uniform heat flux distribution, the effect of thermal emissivity of the absorber surfaces on the thermal performance of the cavity receiver is further investigated. Being different from those of parabolic trough and external cylindrical receivers, both the radiative and the convective heat loss of the present cavity receiver decrease with increasing thermal emissivity, which improves the receiver’s efficiency. These results can provide a useful reference for the design and selection of surface coatings for the cavity receivers.

The effect of substrate conduction on boiling data on pin-fin heat sinks

Heat-transfer experiments for a copper heat sink containing pin-fins with a cross section of 1 mm by 1 mm and a height of 1 mm have been reported previously. The pin-fins were manufactured on a 5 mm thick, 50 mm square base plate in a square, in-line arrangement with a pitch of 2 mm. Data were produced while boiling R113 and water at atmospheric pressure.The heat sink was heated from below through a 5 mm thick aluminium wall by an electrical heating method that is normally associated with the uniform heat flux boundary condition. However, variations in the heat-transfer coefficient and the liquid subcooling interacted with the high thermal conductivity of the aluminium and copper materials to produce a near isothermal wall boundary condition. Thus, heat conduction effects had to be taken into account when determining the heat-flux distribution required in the analysis of the data. Many experiments like these have used the uniform heat-flux assumption to analyse the data. The discrepancies produced from this approach are explored.Single-phase flows across a pin-fin surface produce a reasonably uniform distribution of heat-transfer coefficient. However, the liquid temperature increases as it moves across the heat sink. This produces a non-uniform heat flux distribution at the solid–fluid interface. The uniform heat-flux assumption is shown to lead to errors of ±17% in the estimation of the heat-transfer coefficient.The original boiling flow experiments found that the water data were confined and that the majority of the R113 data were not. The confined and unconfined data are processed with the thermal conduction in the walls taken into account and by assuming a uniform heat flux at the solid–fluid interface. The uniform heat-flux distribution analysis for unconfined flows shows errors in the heat-transfer coefficient to be typically ±17%. Confined flows produce smaller errors, typically ±12%, close to the onset of nucleation. However, these damp out as the distance from the onset increases.The effect of test-section design is investigated by repeating the analyses with smaller wall thickness and lower wall thermal conductivities. Lower wall thermal conductivity is shown to produce a uniform heat flux distribution at the expense of reduced extended surface effectiveness. Thinner substrate thicknesses are found to give limited improvements.These analyses demonstrate that an applied uniform heat flux to the heat sink base will not result in a uniform heat flux at the solid–liquid interface.

Influence of circumferential solar heat flux distribution on the heat transfer coefficients of linear Fresnel collector absorber tubes

The absorber tubes of solar thermal collectors have enormous influence on the performance of the solar collector systems. In this numerical study, the influence of circumferential uniform and non-uniform solar heat flux distributions on the internal and overall heat transfer coefficients of the absorber tubes of a linear Fresnel solar collector was investigated. A 3D steady-state numerical simulation was implemented based on ANSYS Fluent code version 14. The non-uniform solar heat flux distribution was modelled as a sinusoidal function of the concentrated solar heat flux incident on the circumference of the absorber tube. The k–ε model was employed to simulate the turbulent flow of the heat transfer fluid through the absorber tube. The tube-wall heat conduction and the convective and irradiative heat losses to the surroundings were also considered in the model. The average internal and overall heat transfer coefficients were determined for the sinusoidal circumferential non-uniform heat flux distribution span of 160°, 180°, 200° and 240°, and the 360° span of circumferential uniform heat flux for 10m long absorber tubes of different inner diameters and wall thicknesses with thermal conductivity of 16.27W/mK between the Reynolds number range of 4000 and 210,000 based on the inlet temperature. The results showed that the average internal heat transfer coefficients for the 360° span of circumferential uniform heat flux with different concentration ratios on absorber tubes of the same inner diameters, wall thicknesses and thermal conductivity were approximately the same, but the average overall heat transfer coefficient increased with the increase in the concentration ratios of the uniform heat flux incident on the tubes. Also, the average internal heat transfer coefficient for the absorber tube with a 360° span of uniform heat flux was approximately the same as that of the absorber tubes with the sinusoidal circumferential non-uniform heat flux span of 160°, 180°, 200° and 240° for the heat flux of the same concentration ratio, but the average overall heat transfer coefficient for the uniform heat flux case was higher than that of the non-uniform flux distributions. The average axial local internal heat transfer coefficient for the 360° span of uniform heat flux distribution on a 10m long absorber tube was slightly higher than that of the 160°, 200° and 240° span of non-uniform flux distributions at the Reynolds number of 4000. The average internal and overall heat transfer coefficients for four absorber tubes of different inner diameters and wall thicknesses and thermal conductivity of 16.27W/mK with 200° span of circumferential non-uniform flux were found to increase with the decrease in the inner-wall diameter of the absorber tubes. The numerical results showed good agreement with the Nusselt number experimental correlations for fully developed turbulent flow available in the literature.

Optimal heliostat aiming strategy for uniform distribution of heat flux on the receiver of a solar power tower plant

Temperature distribution on the receiver surface of a solar power tower plant is of great importance. High temperature gradients may lead to local hot spots and consequently failure of the receiver. The temperature distribution can be controlled by defining several aiming points on the receiver surface and adjusting the heliostats accordingly. In this paper, a new optimization algorithm which works based on the principles of genetic algorithm is developed to find the optimal flux distribution on the receiver surface. The objective is to minimize the standard deviation of the flux density distribution by changing the aiming points of individual heliostats. Flux distribution of each heliostat is found by using the HFLCAL model [1], which is validated against experimental data. The results show that after employing the new algorithm the maximum flux density is reduced by an order of magnitude. The effects of number of aiming points and size of the aiming surface on the flux density distribution are investigated in detail.

Manifold microchannel heat sink design using optimization under uncertainty

A three-dimensional numerical model is developed and validated to study the effect of geometric parameters such as microchannel depth and width, manifold depth, and manifold inlet and outlet lengths on the performance of a manifold microchannel (MMC) heat sink. The manifold arrangement used to distribute the flow through alternating inlet and outlet pairs greatly reduces the pressure drop incurred in conventional fluid supply arrangements due to its shorter flow paths, while simultaneously enhancing the heat transfer coefficient by limiting the growth of thermal boundary layers. The computational analysis is performed on a simple unit-cell model to obtain an optimized design for uniform thermal boundary conditions, as well as on a porous-medium model to obtain a complete system-level analysis of multiple microchannels across one manifold. The porous-medium approach can be further modified to analyze the performance under asymmetrical heating conditions. Along with conventional deterministic optimization, a probabilistic optimization study is performed to identify the optimal geometric design parameters that maximize heat transfer coefficient while minimizing pressure drop for an MMC heat sink. In the presence of uncertainties in the geometric and operating parameters of the system, this probabilistic optimization approach yields a design that is robust and reliable, in addition to being optimal. Such an optimization analysis provides a quantitative estimate of the allowable uncertainty in input parameters for acceptable uncertainties in the relevant output parameters. The approach also yields information such as the local and global sensitivities which are used to identify microchannel width and manifold inlet length as the critical input parameters to which the outputs are most sensitive. The deterministic analysis shows that the heat transfer performance of the MMC heat sink is optimal at a manifold inlet to outlet length ratio of 3. A comparison between the deterministic and probabilistic optimization approaches is presented for the unit-cell model. A probabilistic optimization study is performed for the porous-medium model and the results thus obtained are compared with those of the unit-cell model for a uniform heat flux distribution.

Ray-Thermal Sequential Coupled Heat Transfer ANALYSIS of Porous Media Receiver for Solar Dish Collector

For the sake of reflecting the concentrated heat flux distribution boundary condition as genuine as possible during simulation, the sequential coupled optical-thermal heat transfer analysis is introduced for porous media receiver. During the sequential coupled numerical analysis, the non-uniform heat flux distribution on the fluid entrance surface of porous media receiver is obtained by Monte-Carlo ray tracing method. Finite element method (FEM) is adopted to solve energy equation using the calculated heat flux distribution as the third boundary condition. The dimensionless temperature distribution comparisons between uniform and non-uniform heat flux distribution boundary conditions, various porosities, and different solar dish concentrator tracking errors are investigated in this research.

Experimental study on flow boiling heat transfer of multiport tubes with R245fa and R1234ze(E)

The upward flow boiling experiments were carried out in a flat aluminum extruded multiport tube, which is composed of 7 parallel rectangular channels (1.1 mm × 2.1 mm) with hydraulic diameter of 1.4 mm. Two refrigerants, R245fa and R1234ze, the latter a recent environmentally safe refrigerant proposed as a potential replacement for R134a, were tested. A new hot water heating technique that accounts for either uniform or non-uniform local heat flux distribution along the channel was developed to obtain and reduce the data. Effects of heat flux, mass flux, vapor quality, and saturation temperature on flow boiling heat transfer in multiport tubes were considered. Finally, the experimental results were compared with some well-known correlations to evaluate the capabilities of existing prediction methods. The analysis shows that the three-zone model for slug flows works well for that subset of test results, utilizing the apparent surface roughness in place of the dryout thickness in the model, as has been previously done for silicon, stainless steel and copper microchannels with measured surface roughnesses.

Heat transfer enhancement due to properly managing the distribution of the heat flux: Exact solutions

This work seeks for the maximum possible heat transfer enhancement in laminar channel flow due to properly distributing the heat flux over the boundaries. The considered heat flux distributions are (A) Periodic step, (B) Periodic sinusoidal (C) Linear, and the (D) Exponential distribution. All of these distributions have the same average heat flux value. Appropriate dimensionless governing energy equations are solved using various complex analysis methods. Different energy performance factors computed to completely characterize the problem. Comparisons with numerical solutions are performed and excellent agreement is obtained. Various correlations are identified. A parametric study of all involved parameters is presented graphically. It is found that the maximum heating source excess temperature for case (D) is at most 22.4% lower than that with uniform heat flux distribution. The previous percentage changes to 18% and 10.7% for the cases (C) and (B), respectively. These results are capable of increasing heat flux by 21.35%, 15.98% and 10.22%, respectively, to attain the same maximum temperature of the uniform heat flux distribution. Finally, this work proves that properly managing the heat flux distribution can transfer additional noticeable heat under same maximum temperatures.

Numerical Analysis of an Inverse Boundary Design Problem of a 3-D Radiant Furnace with a 3-D Design Object

For the uniform thermal conditions, the present study investigates the constraints on the size of a 3-D design object (DO) that can be placed inside a 3-D radiant furnace. To cover a wide range of the dimensions of the DO, 29 models are considered. Radiation element method by ray emission model (REM2) is used to calculate the radiative information. The objective function is minimized using the micro-genetic algorithm (MGA). Estimated heat flux distributions on the DOs are compared with the desired uniform heat flux distribution. The suitability of a DO is decided on the basis of the maximum allowable deviation of the estimated heat flux. For a given power range of the panel heaters, study has also been made for different values of the desired uniform heat flux. For a realistic heating process for uniform thermal conditions, this study provides a guideline for a priori knowing the maximum possible size of a DO that can be processed inside a radiant furnace.

Effect of non-uniform heating on entropy generation for the laminar developing pipe flow of a high Prandtl number fluid

Non-uniform distribution of heat flux as a wall boundary condition is used for laminar developing pipe flow to find the optimum case in which minimum entropy is generated. Several cases are solved for the same amount of heat rate but with different heat flux distribution and entropy generation is determined for each one. It is shown that entropy generation in the cases with decreasing heat flux distribution is always more than the cases with the same amount of heat flux at sections but with increasing distribution. In addition, it is found that the generated entropy for the cases with decreasing heat flux distribution is always more than the case of uniform heat flux. It is also seen that the optimum case is not the case with uniform heat flux distribution and the least generated entropy is due to a case with increasing heat flux distribution.

Premixed flame impingement heat transfer with induced swirl

Experiments were performed to study the heat transfer characteristics of a swirling premixed flame impinging vertically normal to a horizontal plate. The effects of Reynolds number ( Re), equivalence ratio ( Ф) and nozzle-to-plate distance ( H) on the heat flux were examined. Comparisons were also made between the heat transfer behaviors of the swirling premixed flame (SPF) with a non-swirling premixed flame (PF) operating under the same conditions. Compared with the PF, the swirling flows in the SPF increase the entrainment of ambient air and induce a faster radial spreading rate of the flame jet. Therefore, the SPF provides a larger heating area and produces a more uniform radial heat flux distribution. For both the SPF and PF, the heat flux increases with Re due to the more complete combustion occurring at higher Re. For the SPF, the heat transfer increases with Ф, while it decreases with Ф for the PF because the stronger entrainment of ambient air in the SPF supports a more complete combustion. A smaller H is required for the maximum heat transfer to occur for the SPF.

Laser Surface Hardening Considering Coupled Thermoelasticity

AbstractThermoelastic temperature, displacement and stress in heat transfer during laser surface hardening are solved in both Lagrangian formulation and Eulerian formulation. In the Eulerian formulation, the heat flux is fixed in space and the work-piece is moved through a control volume. In the case of uniform velocity and uniform heat flux distribution, the Eulerian formulation leads to a steady-state problem, while the Lagrangian formulation remains transient. In the Eulerian formulation, the reduction to a steady-state problem increases the computational efficiency. Also, in this study, an analytical solution is developed for an uncoupled transient heat conduction equation in which a plane slab is heated by a laser beam. The thermal results of the numerical models are compared with the results of the analytical model. A comparison of the results shows that numerical solutions in the case of uncoupled problem are in good agreement with the analytical solution.

The experimental study on flat plate heat pipe of magnetic working fluid

An effective thermal spreader can achieve uniform heat flux distribution and thus enhance heat dissipation of heat sinks. Flat plate heat pipe is one of the highly effective thermal spreaders. Magnetic fluid is liquid and can be moved by the force of magnetic field. Therefore, the magnetic fluid is suitable to be used as the working fluid of flat plate heat pipes which have a very small gap between evaporation and condensation surfaces. We prepared a disk-shaped wickless flat plate heat pipe, and the distance between evaporation and condensation surfaces is only 1 mm. From experimental study, the effect of heat flux and working fluid ratio on the performance of flat plate heat pipe is presented. Also we compared the experimental results between the performance of water and magnetic fluid as working fluids.

Numerical simulation and experimental verification of a flat two-phase thermosyphon

The flat two-phase thermosyphon is placed between the heat source and the heat sink, which can achieve the uniform heat flux distribution and improve the performance of heat sink. In this paper, a two-dimensional heat and mass transfer model for a disk-shaped flat two-phase thermosyphon is developed. By solving the equations of continuity, momentum and energy numerically, the vapor velocity and temperature distributions of the flat two-phase thermosyphon are obtained. An analysis is also carried out on the ability of flat two-phase thermosyphon to spread heat and remove hot spots. In order to observe boiling and condensation phenomena, a transparent flat two-phase thermosyphon is manufactured and studied experimentally. The experimental results are compared with numerical results, which verify the physical and mathematical model of the flat two-phase thermosyphon. In order to study the main factors affecting the axial thermal resistance of two-phase thermosyphon, the temperatures inside the flat two-phase thermosyphon are measured and analyzed.

The experimental and numerical investigation of a grooved vapor chamber

An effective thermal spreader can achieve more uniform heat flux distribution and thus enhance heat dissipation of heat sinks. Vapor chamber is one of highly effective thermal spreaders. In this paper, a novel grooved vapor chamber was designed. The grooved structure of the vapor chamber can improve its axial and radial heat transfer and also can form the capillary loop between condensation and evaporation surfaces. The effect of heat flux, filling amount and gravity to the performance of this vapor chamber is studied by experiment. From experiment, we also obtained the best filling amount of this grooved vapor chamber. By comparing the thermal resistance of a solid copper plate with that of the vapor chamber, it is suggested that the critical heat flux condition should be maintained to use vapor chamber as efficient thermal spreaders for electronics cooling. A two-dimensional heat and mass transfer model for the grooved vapor chamber is developed. The numerical simulation results show the thickness distribution of liquid film in the grooves is not uniform. The temperature and velocity field in vapor chamber are obtained. The thickness of the liquid film in groove is mainly influenced by pressure of vapor and liquid beside liquid–vapor interface. The thin liquid film in heat source region can enhance the performance of vapor chamber, but if the starting point of liquid film is backward beyond the heat source region, the vapor chamber will dry out easily. The optimal filling ratio should maintain steady thin liquid film in heat source region of vapor chamber. The vapor condenses on whole condensation surface, so that the condensation surface achieves great uniform temperature distribution. By comparing the experimental results with numerical simulation results, the reliability of the numerical model can be verified.