Heating Length Research Articles

Numerical study of natural convection in a cavity with discrete heat sources

Natural convection heat transfer in a cavity has always attracted researchers interest because of its numerous applications in engineering, e.g. , cooling of electronic parts, thermal insulators, buildings ventilation systems, solar collectors, and nuclear reactors. In general, due to favorable factors, such as process simplicity, cost-effectiveness, low noise, and the possibility of recovery, the process of natural convection has many uses in various industrial applications. In this study, a square cavity with air inside is considered. Three heaters are situated at the bottom wall, the top wall is maintained at a constant cold temperature, and the two side walls are insulated. The lattice Boltzmann method is used for simulation, and the overall goals are to optimize the installation location and heater length and also investigating the effects of the amplitude and oscillation period of heat flux fluctuation. The results indicate that increasing the difference between amplitudes and oscillation periods of heat flux in heaters causes the flow within the cavity to stabilize more quickly and also increases temperature oscillation due to larger amplitudes and periods. Also, in the cavity with three heaters, the average temperature of the middle heater remains unchanged relative to the case of constant heat flux. This research can be used in the design of an appropriate cooling system for electronic components to ensure effective and safe operational conditions.

Numerical investigation of natural convection of [formula omitted]-water nanofluid in a wavy cavity with conductive inner block using Buongiorno’s two-phase model

By employing the finite element method, thermophoresis and Brownian diffusion are studied numerically relating to the natural convection in a wavy cavity that is filled with an Al2O3-water nanofluid possessing a central heat-conducting solid block that is influenced by the local heater located on the bottom wall. An isothermal condition is established in the two wavy vertical walls, while adiabatic condition is for the top horizontal wall. Partial heating is applied to the bottom of the horizontal wall, while the remaining part remains in the adiabatic condition. Empirical correlations are employed for the thermal conductivity and dynamic viscosity of the nanofluid. The number of oscillations (1⩽N≤4), Rayleigh number (103⩽Ra≤106), nanoparticles volume fraction (0⩽ϕ≤0.04) and dimensionless length of the bottom heater (0.2⩽H⩽0.8) govern the parameters in this study. The grid independency test, as well as experimental and numerical data from other published works, was employed to validate the developed computational code comprehensively. Based on the obtained results, it was found that the heat transfer inside the cavity is enhanced by introducing nanoparticles as well as a selection of optimal number of oscillations.

Hybrid lattice Boltzmann-TVD simulation of natural convection of nanofluids in a partially heated square cavity using Buongiorno’s model

In this paper, the Buongiorno’s two-phase model is adopted to study natural convection in a partially heated enclosure filled with nanofluids having temperature-dependent properties. In order to solve the governing equations, a hybrid lattice Boltzmann (LB) and total variation diminishing (TVD) scheme is proposed, in which the traditional LB method is employed to handle the flow and temperature fields, while the volume fraction equation is solved by a TVD method due to the fact that the corresponding equation is a type of convection-dominated equation. Additionally, to improve the computational efficiency, the proposed algorithm is executed on the Graphics Processing Unit (GPU) by using “Compute Unified Device Architecture (CUDA)” programming. The effect of several parameters, such as Rayleigh number, nanoparticle diameter, temperature difference between the sidewalls, heating location and heater length on heat transfer rate and nanoparticle distribution are analyzed. It is observed that at low Rayleigh numbers, the heat transfer enhancement increases in nanoparticle volume fraction, while at high Rayleigh numbers, there exists an optimal volume fraction at which the heat transfer performance has a peak. Moreover, the average Nusselt number and the heat transfer enhancement are found to decrease with increasing heater length.

Fluid-structure interaction in natural convection heat transfer in an oblique cavity with a flexible oscillating fin and partial heating

Unsteady natural convection in a differentially heated oblique cavity with a flexible oscillating heat-conducting fin mounted on the bottom adiabatic wall is studied numerically by using the finite element method. The right inclined wall is kept at a constant low temperature, while the left one is adiabatic with a local isothermal heater, the fin is heated isothermally from the basis. The heat-conducting elastic fin is located in the central part of the bottom adiabatic wall. The Galerkin weighted residual finite element method with the aid of the Arbitrary Lagrangian-Eulerian (ALE) procedure is used in the numerical analysis. The developed computational code was validated comprehensively using a grid independency test, and numerical data of other authors. The governing parameters of this study are the dimensionless time (10-8⩽t≤3.5), thermal conductivity ratio between the heat-conducting fin and working medium (1⩽Kr≤1000), non-dimensional Young’s modulus (109⩽E≤1012), oscillating amplitude (0.01⩽A⩽0.1), left wall heater length (0.1⩽H≤0.9), and the inclination angle of tilted walls (-45⩽ϕ⩽45). The obtained results revealed an essential effect of the flexible oscillating heat-conducting fin on the fluid flow and heat transfer inside the oblique cavity.

Design and dispatch optimization of a solid-oxide fuel cell assembly for unconventional oil and gas production

This paper presents design and dispatch optimization models of a solid-oxide fuel cell (SOFC) assembly for unconventional oil and gas production. Fuel cells are galvanic cells which electrochemically convert hydrocarbon-based fuels to electricity. The Geothermic Fuel Cell (GFC) concept involves utilizing heat from fuel cells during electricity generation to provide thermal energy required to pyrolyze kerogen into a mixture of oil, hydrocarbon gas and carbon-rich shale coke. We formulate a continuous, non-convex nonlinear program (NLP) in A Mathematical Programming Language (AMPL) to analyze the techno-economic characteristics of the GFC system. The problem is separated into a design model $$({{\mathcal {D}}})$$ and a dispatch model $$({{\mathcal {O}}})$$ . The GFC design problem determines the size and configuration of a single heater well. Specifically, we optimize the heater length and number of SOFC stacks in each assembly such that the maximum volume of oil shale is heated per well. Using the resulting design from $$({{\mathcal {D}}})$$ , the dispatch model $$({{\mathcal {O}}})$$ determines daily GFC operating conditions through variation in electric current, fuel utilization, and stoics of excess air. We optimize the system operating costs and the combined-heat-and-power efficiency, subject to geology heating demands, auxiliary component electric power demands and GFC system performance characteristics. Solutions to the design and dispatch problems are obtained using the IPOPT and KNITRO solvers. A case study shows that the optimal well-head cost of oil and gas produced using the GFC technology is about $39 bbl $$^{-1}$$ , which is comparable to that from other unconventional crude oil extraction techniques. The optimal dispatch strategy results in a maximum heating efficiency of 43% and a combined-heat-and-power efficiency of 79%. The Geothermic Fuel Cell’s performance is better than current in situ upgrading technologies that rely on electricity supplied from the grid at generation-and-transmission efficiencies near 33%.

Theoretical and experimental studies of heat transfer characteristics of a single-phase natural circulation mini-loop with end heat exchangers

In the present work, the heat transfer and fluid flow characteristics of a single-phase natural circulation loop (SPNCL) with both the heating and the cooling ends are theoretically and experimentally studied. Distilled water is chosen as the working fluid circulating in a rectangular loop that the top and bottom sides are respectively cooled and heated by 245 mm tube-in-tube heat exchangers. The height and diameter of the mini-loop are 250 mm and 4 mm, respectively. Both analytical and experimental results are obtained by varying the heating fluid temperatures from 30 °C to 60 °C but fixing cooling fluid temperature of 10 °C. Based on the experimental data, a Nu ∼ Re correlation is obtained and applied into the one-dimensional mathematical model. A good agreement between the experimental and theoretical results with a new correlation can be observed. Experimental results show that stable flow can be reached for the cases with different Th. The start-up time of natural circulation from quiescent state shortens with the increase of Th. The Reynolds number and heat transfer rate at steady state are proportional to the heating fluid temperature Th. Based on the proposed mathematical model, an optimal ratio of the heater length to the loop height can be reached when the total length and diameter of the mini-loop keep constants.

Natural convective heat transfer of Ag-water nanofluid flow inside enclosure with center heater and bottom heat source

A numerical study on natural convective heat transfer inside an enclosure with center heater using nanofluid has been carried out. The effect of different length of center heater on the flow and temperature fields is analysed for different Rayleigh numbers. Results are displayed in terms of streamlines, isotherms, mid height velocity profile and average Nusselt number. The numerical results reveal heat transfer increases with increasing heater length at both vertical and horizontal positions for increasing values of Rayleigh numbers. In particular, a higher increase in heat transfer is obtained with heater situated with vertical position of maximum length. Also it is obtained that enhancement of heat transfer is high for Ag - water nanofluid than CuO -water and Al2O3 -water nanofluids.

Buoyancy Induced Convection From Biheaters in a Cavity: A Numerical Study

A computational study of natural convection from biheaters of finite thickness and finite conductivity placed on a finite thickness and a finite conductive bottom plate of a cavity is performed under constant heat input condition. Cavity is cooled by the sidewalls, while the top and backside of the bottom plate are insulated. Streamline, isotherms, and local heat flux distribution of the sidewalls are discussed. Base Grashof number is chosen as 2.5 × 106. Biheater maintains a nondimensional distance of 0.4 between them. The left heater is placed at a nondimensional distance of 0.2 from the left wall. Heater length ratio is varied from 0.4 to 1.7, while heater strength ratio is varied from 0.25 to 7.0. Optimum operating temperature condition is found from the analysis.

MHD mixed convective heat transfer in a lid-driven enclosure filled with Ag-water nanofluid with center heater

The MHD mixed convection inside enclosure with center heater is numerically investigated. The oppositely moving side walls of the enclosure are maintained at constant cold temperature whereas a constant heat source is considered in the bottom wall. The remaining parts of the bottom and top walls are kept adiabatic. The finite volume method and SIMPLE algorithm with power-law scheme is used to solve the governing equations. The present study is concerned with effect of pertinent parameters such as length of heater (Γ = 0.25, 0.50 and 0.75), Richardson number (Ri = 0.01, 1.0 and 100), Hartmann number (Ha = 0, 25 and 50) and solid volume fraction of nanoparticles on the fluid flow and heat transfer performance of the enclosure. Results are presented with streamlines, isotherms, velocity profiles and average Nusselt numbers. It is observed that heat transfer rate increases as heater length and Grashof number increases whereas heat transfer decrease is found for increasing magnetic field effect. The enhancement rate in heat transfer by increasing the solid volume fraction of nanoparticles is also obtained.

팬히터의 입구 온도 및 공기 유입량에 따른 출구측 유속의 변화

This study was carried out to analyze the change of temperature and flow velocity at the exit side of the fan heater cover according to the change of the inlet temperature and the air flow rates for the production of the electric fan heater for aircraft. The analyses were performed with the commercial software, ANSYS 17.0. The CAD model was applied as follows; (1) Parts before the Coupler were eliminated. (2) The corner shape of the Heater was fixed so that it is rounded off. (3) The model was quartered. Its inside volume was meshed using a tetrahedral element. Though a couple of layer element should be meshed to express the boundary layer and to enhance the analytical accuracy, there is no layer mesh on the wall. In the analysis, the temperature increment was less than 274 K. Therefore, the most crucial reason about that is that the length of heater is too short to transfer heat energy to the air. Hence, it is strongly recommended that the length of the heater elongates or its specific surface area increases.

Role of curvature of walls (concave/convex) for intensification of thermal processing with optimal exergy loss during natural convection of fluids

Based on its potential to develop more sustainable and energy efficient systems, process intensification is on increasing importance in various processing industries. The process intensification vs efficiency is carried out for natural convection in square enclosure and curved (concave/convex) wall enclosures via heatlines and entropy generation analysis for the development of sustainable process equipment design. As the selection of an optimal cavity is the main objective for the increase in efficiency, a comparative study has been carried out among the enclosures with equal dimensionless area (= unity) and equal heater length (= 1 unit). Two heating strategies are considered such as (a) case 1: hot bottom wall (b) case 2: hot left wall. Numerical simulations have been carried out for various values of Prandtl (Pr) and Rayleigh (Ra) numbers. Heatline trajectories illustrate that convex cavities with case 1 or case 2 may be chosen based on higher thermal mixing for various Ra. On the other hand, based on higher entropy savings with higher wall heat transfer rates, concave cavities with case 1 or case 2 are preferred. Overall, economic design of the cavity must consider the enhanced thermal mixing vs savings of entropy generation or exergy loss.

An approach to combine the second-order and third-order analysis methods for optimization of a Stirling engine

Second-order and third-order models are the two main methods for Stirling cycle analysis. A second-order one has relatively reliable accuracy without detailed cyclic information, while a third-order one provides relatively comprehensive operational information with uncertainty. In this work, a third-order model, Sage, is tried to be improved by a second-order model, Improved Simple Analytical Model, and 100 W β-type Stirling engine is used as a modelling prototype engine. As suggested by Improved Simple Analytical Model, the gap of the piston seal and the empirical multiplier for heat transfer of cooler in Sage should be adjusted. This is accomplished by combining these two models so that the effects of seal leakage loss, gas spring hysteresis loss, and piston friction loss could be considered in an improved Sage. The improved Sage indicates that the overall relative errors for the indicated power output and the thermal efficiency are reduced by over 30 percentage points and 20 percentage points, respectively. Pressure–volume diagrams provided by the improved Sage are much closer to the experimental ones, and the pattern similarities of pressure–volume diagrams increase from 78.6–81.4% to 80.8–85.0%. Performance simulation of the Stirling engine is carried out by the improved Sage and the results show that regenerator takes a major role in improving the performance of the 100 W β-type Stirling engine. Lengths of regenerator, heater and cooler are optimized for the maximum indicated power output and the maximum thermal efficiency respectively, and the optimized values are increased by 15.9% and 25.2%, respectively.

DNB heat flux on inner side of a vertical pipe in forced flow of liquid hydrogen and liquid nitrogen

Heat transfer from inner side of a heated vertical pipe to liquid hydrogen flowing upward was measured at the pressures of 0.4, 0.7 and 1.1 MPa for wide ranges of flow rate and liquid temperature. Nine test heaters with different inner diameters of 3, 4, 6 and 9 mm and the lengths of 50, 100, 150, 200, 250 and 300 mm were used. The DNB (departure from nucleate boiling) heat fluxes in forced flow of liquid hydrogen were measured for various subcoolings and flow velocities at pressures of 0.4, 0.7 and 1.1 MPa. Effect of L/d (ratio of heater length to diameter) was clarified for the range of L/d⩽50. A new correlation of DNB heat flux was presented based on a simple model and the experimental data. Similar experiments were performed for liquid nitrogen at pressures of 0.5 MPa and 1.0 MPa by using the same experimental system and some of the test heaters. It was confirmed that the new correlation can describe not only the hydrogen data, but also the data of liquid nitrogen.

Modeling and PSO optimization of Humidifier-Dehumidifier desalination

The aim of this study is modeling a solar-air heater humidification-dehumidification unit with applying particle swarm optimization to find out the maximum gained output ratio with respect to the mass flow rate of water and air entering humidifier, mass flow rate of cooling water entering dehumidifier, width and length of solar air heater and terminal temperature difference (TTD) of dehumidifier representing temperature difference of inlet cooling water and saturated air to dehumidifier as its decision variable. A sensitivity analysis, furthermore, is performed to distinguish the effect of operating parameters including mass flow rate and streams’ temperature. The results showed that the optimum productivity decreases by decreasing the ratio of mass flow rate of water entering humidifier to air ones.Article History: Received: July 12th 2017; Revised: December 15th 2017; Accepted: 2nd February 2018; Available onlineHow to Cite This Article: Afshar, M.A., Naseri, A., Bidi, M., Ahmadi, M.H. and Hadiyanto, H. (2018) Modeling and PSO Optimization of Humidifier-Dehumidifier Desalination. International Journal of Renewable Energy Development, 7(1),59-64.https://doi.org/10.14710/ijred.7.1.59-64

Simulation of natural convection of nanofluids in a square enclosure embedded with bottom discrete heater

The present work aims at studying natural convection of nanofluids in a square enclosure embedded with a discrete heater at the bottom. The numerical simulations are performed using commercial software ‘STAR CMM+’ based on finite volume technique. Firstly, the results from the simulations are validated against the published results. Subsequently, numerical simulations have been carried out for predicting the flow and heat transfer characteristics of different water based nanofluids (Al2O3, Cu, TiO2) at wide range of Rayleigh numbers, volume fractions, position of the heater and heater length. Results are presented in the form of streamline plots, isotherm contours and plots of average Nusselt numbers. It has been found that the average Nusselt number increases with increasing Rayleigh number, volume fraction and heater length. Further, the effect of heater position on the flow and temperature fields for different nanofluids are discussed. However, Nusselt number was observed to be sensitive to the position of the heater.

Lattice-Boltzmann modeling of natural convection in a cavity with a heated plate inside

In the present work, Lattice Boltzmann Method (LBM) is used to analyze the natural convection flow and heat transfer in a square cavity with an inside thin heater. The vertical walls of the cavity are adiabatic, while its horizontal ones are maintained at constant temperature. The square cavity contains a thin vertical heated plate, with the temperature. The present problem is governed by the Rayleigh number, the heater length, the heater location, and the Prandtl number,. The results of the study show that the position and the length of the heated plate alter significantly the temperature distribution, the flow field and the heat transfer in the cavity.

Study of buoyancy driven heat transport in silicone oils and in liquid nitrogen in view of cooling applications

Motivated by applications for cooling superconducting pellets with liquid nitrogen, we consider a source with a fixed heating rate per unit volume, immersed in a liquid pool and cooled through natural convection. In one recent experimental investigation (Dubois et al., 2016) carried on silicone oils and liquid nitrogen, we have demonstrated that the velocity field satisfies specific scaling laws with respect to the temperature increase in the liquid pool. In this work, we pursue the analysis by modeling the heat transfer in a parallelepiped enclosure for a steady laminar flow regime. The Navier-Stokes equations are solved using a finite volume approach to obtain the detailed three-dimensional flow and heat-transfer characteristics. A quantitative analysis of the velocity field over the temperature field shows that the experimental power laws are reproduced in simulations. Following Dubois and Berge (1978), a theoretical law originally introduced in the context of the classical Rayleigh-Bénard experiment is shown to be satisfied in the simulations over a wide range of Rayleigh numbers (Ra), assuming the definition of the characteristic convection length is adapted to the investigated geometry. Moreover, the simulations are shown to correctly reproduce the main features of the flow, including the characteristic convection length, for different heater lengths.

Unsteady natural convection with entropy generation in partially open triangular cavities with a local heat source

Purpose The main aim of this work is to perform a numerical analysis on natural convection with entropy generation in a partially open triangular cavity with a local heat source. Design/methodology/approach The unsteady governing dimensionless partial differential equations with corresponding initially and boundary conditions were numerically solved by the finite difference method of the second-order accuracy. The effects of dimensionless time is studied, and other governing parameters are Rayleigh number (Ra = 103 − 105), Prandtl number (Pr = 6.82), heater length (w/L = 0.2, 0.4 and 0.6) and distance of heater ratio (δ/L = 0.3). Findings An increase in the Rayleigh number leads to an increment of the fluid flow and heat transfer rates. Average Bejan number decreases with Ra as opposed to the average Nusselt number and average entropy generation. High values of Ra characterize a formation of long-duration oscillating behavior for the average Nusselt number and entropy generation. Originality/value The originality of this work is to analyze the entropy generation in natural convection in a one side open and partial heater-located cavity. This is a good application for electronical systems or building design.

Compact Si-based asymmetric MZI waveguide on SOI as a thermo-optical switch

A compact low power consuming asymmetric MZI based optical modulator with fast response time has been proposed on SOI platform. The geometrical and performance characteristics were analyzed in depth and optimized using coupled mode analysis and FDTD simulation tools, respectively. It was tested with and without implementation of thermo-optic (TO) effect. The device showed good frequency modulating characteristics when tested without the implementation of the TO effect. The fabricated device showed quality factor, Q ≈ 10,000, and this value is comparable to the Q of the device simulated with 25% transmission loss, showing FSR of 0.195 nm, FWHM ≈ 0.16 nm, and ER of 13 dB. With TO effect, it showed temperature sensitivity of 0.01 nm/°C and FSR of 0.19 nm. With the heater length of 4.18 mm, the device required 0.26 mW per π shift power with a switching voltage of 0.309 V, response time of 10 μ, and figure-of-merit of 2.6 mW μs. All of these characteristics make this device highly attractive for use in integrated Si photonics network as optical switch and wavelength modulator.

Influence of geometric parameters on thermalhydraulic characteristics of supercritical CO2 in natural circulation loop

Deterioration of mass flow rate in supercritical natural circulation loops, accompanied by rapid decline in the heat transfer coefficient, is a phenomenon reported both experimentally and theoretically in recent years. It is generally recognised as the consequence of fluid temperature crossing the pseudocritical limit throughout the loop and sets a practicable limit for loop operation. Present study investigates the dependence of such flow-induced deterioration on the associated geometric parameters, with an aim of identifying guidelines for a safer design. Accordingly a computational model of a rectangular loop, with source and sink in opposite horizontal arms, is developed and employed to explore the influence of geometric variables, including diameter, height, width, inclination, corner bends, and heating and cooling lengths and their orientations. Reduction in loop diameter and increase in adiabatic length in the horizontal arms are found to lead towards early initiation of deterioration, while the presence of an optimum loop height is envisaged. Length of heater is predicted to have minimal influence. However, a longer sink is found to be favorable, as that corresponds to a lower level of heat transfer coefficient for identical power supply. Positioning of the source and sink, and the specifications of the corner bends are also observed to impose trivial effect on the overall loop thermalhydraulics, apart from enforcing a pre-defined flow direction and minor centrifugal action respectively. Inclining the loop to vertical results in substantial reduction in the flow rate, owing to lower effective buoyancy, without significantly tampering the initiation of deterioration.