Heating Length Research Articles

Insight view on the CFD simulation of magneto-hydrodynamics natural convection in wavy enclosure with trapezoidal heater and circular cylinder

The present work examines numerically using a finite element scheme the magnetic field on natural convection within I-shaped wavy-walled enclosure filled by a nanofluid and porous medium. The porous medium had been modeled by the Darcy–Brinkman model while a single phase model treats the nanofluid. The thermal equilibrium model had been applied between the nanofluid and porous medium under steady-state conditions. The enclosure contains a trapezoidal heater attached to its bottom wall with an internal heated circular cylinder immersed in the enclosure. The two wavy walls are kept at a cold temperature, while the rest walls are insulated. The influence of the Rayleigh number , Darcy number , Hartmann number , nanofluid loading , magnetic field inclination angle , trapezoidal heater length , location of the trapezoidal heater , and position of the circular cylinder on fluid flow and heat transfer have been discussed deeply. It is obtained that the Nusselt number increases as the Rayleigh number, Darcy number, magnetic field angle increase, and the Hartmann number decreases. Also, for better heat transfer it is obtained that the center location gives the highest value at . Also, the location of the trapezoidal heater in the right region at reveals the best location in terms of heat transfer improvement.

Development of a new technique of waste heat recovery in cement plants based on Stirling engine technology

Cement plants are one of the most energy consuming industries in which a large amount of heat energy is lost into the atmosphere causing the increase of environmental issues and leading to the rise of cement production energy cost. Recently, waste heat recovery systems such as steam and Rankine cycles have received much attention by researchers and industrial sectors for power production application to enhance the system efficiency. However, the existing waste heat recovery systems present different drawbacks. This paper proposes, for the first time, a new technique of recovering cement plants waste heat based on Stirling engine technology. The modelling of a Gamma type Stirling engine was conducted for recovering the waste heat released from the clinker cooling process. Furthermore, the non-ideal adiabatic model was used for engine designing in MATLAB software. For model validation step, the results obtained from the present study have been compared with experimental data of Lewis Research Center in the National Aeronautics and Space Administration and previous numerical models. The comparison findings have shown a high accuracy of the current model. The effect of several geometrical and physical specifications on Stirling engine performances was studied to obtain the best engine design. The results showed that maximum efficiency can be achieved by increasing the regenerator porosity up to 79 % and by decreasing the regenerator length to 0.015 m. A matrix wire diameter of 50 μm has been found as an optimum value regarding the high output power generated and acceptable heat input required. The parametric analysis of heat exchangers geometries has revealed that the increase of the heater and cooler tube lengths reduces the engine performances. However, the rise of heater and cooler tube inner diameters could enhance the power and efficiency. Furthermore, it was found that the variation of phase angle has an important influence on Stirling engine outputs, thus the consideration of 90 degree as phase angle is more suitable for engine design which will be able to produce 1641.36 W with a thermal efficiency of 21.29 %. Additionally, it was concluded that the augmentation of pressure and rotational speed increases the engine power. Finally, it was shown that the rise of working gas mass enhances the engine output power but increases the heat input requirement. This work demonstrates the potential of using Stirling engine technology for cement plants waste heat recovery applications and highlights its ability to produce high output performances.

Effect of geometrical and operating parameters on performance of a rectangular two-phase natural circulation loop

Natural Circulation Loops (NCLs) find application in a wide range of engineering devices and it is often necessary to predict and ensure the performance of such loops under various operating conditions. In this paper analytical expressions are presented in non-dimensional form for steady-state mass flow rate in typical rectangular, two-phase natural circulation loops having Vertical-Heater Vertical-Cooler (VHVC) and Vertical-Heater Horizontal-Cooler (VHHC) configurations. The normalized loop mass flow rates are expressed in terms of several geometrical and operating variables such as, normalized heat input, density ratio, volume/diameter of heater and cooler sections, aspect ratio of loop, inlet subcooling, fractional length of heater and cooler sections, two-phase friction multiplier and the loss coefficient at heater inlet. The analytical mass flow rate expressions are first validated using published data for various loops and shown to reasonably capture the gravity and friction dominated regimes in two-phase pipe flow. Parametric studies are then conducted to elucidate the effect of key variables on steady-state loop mass flow rates. For the chosen geometrical configuration of the loops, the possibility of existence of multiple steady-state solutions is checked for the entire range of values used in this study for each variable. The discussions in this paper are limited to explaining the influence of individual variables by comparing with a base case analysis.

Radiative and heat generation effects on MHD mixed convection of non-Newtonian nanofluids in lid-driven inclined odd-shaped porous cavity containing obstacle using local thermal non-equilibrium condition

The present work examines the local thermal non-equilibrium condition (LTNEM) on the mixed convection of non-Newtonian nanofluids in a lid-driven inclined odd-shaped porous cavity involving obstacles. The SIMPLE algorithm in the finite volume method (FVM) is adopted to handle the present physical problem. The impacts of pertinent physical parameters such as length/location of heaters, thermal radiation, heat generation parameter, Hartmann number, and microrotation parameter on the streamlines, isotherms of a fluid, isotherms of a solid, and iso-microrotations as well as the local Nusselt number, and average Nusselt number are investigated. The major achieved numerical results indicated the importance of the heater length and location on the improvement of the heat transport in fluid/solid phases within an odd-shaped cavity. Expanding enhances the values of local Nusselt number in a fluid phase and lowers the values of the mean Nusselt number . The heat generation parameter improves the isotherms, , and . The thermal radiation parameter acting effectively in enhancing isotherms of a solid phase and local Nusselt number in a solid phase .

Performance estimation of Triangular Solar air heater roughened absorber surface: An experimental and simulation modeling

The roughness on the absorber surface can increase the performance of a triangular solar air heater. This paper reveals a comparative study of smooth and rough absorber surfaces with V ribs to improve triangular solar air heater performance. The absorber plate coated with graphene nanoparticles doped into the black paint in both cases. The investigation incorporated rib roughness parameter as P/e = 1.4 for the arrangement and investigated at different parameters of the solar intensity. The roughness effect on friction factor and heat transfer characteristics has been investigated numerically and experimentally. A three-dimensional simulation is conceded out using Ansys 14.5 software and k-ε, RNG turbulence model to solve the governing equation in turbulence case. Using MATLAB optimizable Gaussian process regression (GPR) analysis, create an energy and exergy efficiency analysis prediction model. The experimental results indicate an average 4.93% thermal efficiency increase, and average exergy efficiency increases by 4.41 % to compare smooth plates. The simulation result shows temperature variation inside the duct, which is reduced through the length of the solar air heater. Compared to Reynolds number changes and relative roughness pitch (P/e), V-shaped rib roughness significantly impacts friction factor and heat transfer characteristics. We conclude that better outcomes are obtained after investigating triangular duct designs absorber surface roughness patterns.

Evaluation of convection flow and entropy generation in a wavy cubical container with nanofluid and embedded cylinder

Abstract This work examines steady convection heat transfer and entropy generation in a wavy cubical container with Al2O3–water nanofluid and the solid cylinder. An isothermal embedded heater of finite width is located within the left vertical surface center of the container. All surfaces are insulated, except that the right wavy surface is kept cold, and the left wall is partially heated. The Boussinesq approximation is assumed, and three-dimensional simulations of governing equations have been applied to utilize the Galerkin weighted residual finite-element approach. Numerical results for the three-dimensional patterns of nanofluid flow, iso-temperature surfaces, and isentropic lines are given. The local Nusselt number adjacent to the left and interface surfaces within the container and solid cylinder and Bejan number have been examined for different values of the Rayleigh number, nanoparticle volume fraction, number of undulations and heater length, and cylinder radius. The results indicate that the optimal local heat transfer between the solid cylinder and container declines with the increased cylinder radius, which yields an imperfect nanofluid flow circulation.

Study on thermo-optic Mech-Zehnder switches with buried heater by image charge method

In this paper, the analytical solution for temperature change and switching power of the thermo-optic switches with buried heater is achieved by Image Charge Method, and the influence of different structure parameters on the switching power, such as the offset distance away from the heater to the cladding oxide layer surface, the heater width and length, the thickness of cladding and buried oxide layer is studied in detail. Results show that the analytical solution of Image Charge Method is a convenient way of less computational time-consuming to solve temperature field of thermo-optic switches with buried heater, meanwhile, higher heat efficiency and lower switching power can be obtained with narrower, buried heater of the thermo-optic switches, which may provide guides in thermo-optic switches’ designs and their applications.

Observation of departure from nucleate boiling under flow using optical visualization and IR thermometry

Departure from nucleate boiling (DNB) is a limiting phenomenon in the safety of nuclear reactors. Several mechanistic models have been suggested for predicting the critical heat flux at the DNB. However, existing experiments could not fully reveal the underlying phenomena of mechanistic models. In this study, we closely examined the phenomenon of rewetting failure of a dry patch during DNB to provide a deeper understanding of the mechanism of DNB occurrence and to assist in subsequent mechanistic modeling. Specifically, we utilized the total reflection technique and IR thermometry to obtain the synchronized side-view, total reflection view, temperature, and heat flux profile images at the DNB. We established a water flow loop under atmospheric pressure with a vertical rectangular test section comprising an ITO heater coated on a sapphire substrate. The ITO heater was 10 mm wide and 120 mm long. The long length of the ITO heater enabled the development of elongated bubbles upstream of the DNB location. A series of tests were conducted under various flow rates. Slug flow was observed in all tests conducted. An alternate passage of elongated bubbles and water slugs led to expansion and shrinkage of the dry patches. At the DNB, the dry patch size continued to increase, but the developing pattern was dependent on the flow rate. The peripheral temperature of the dry patches at the DNB was found to be ∼150°C.

OPTIMIZATION OF STATIONARY AND TRANSITIONAL OPERATING MODES OF THE ELECTRICAL COMPLEX IN METAL PROCESSING LINE

In the electrical complex “induction heater - deforming equipment”, the limiting performance of the complex is the induction heating unit. In this regard, an important task of increasing the effi ciency of the processing complex is to optimize both the design and operating parameters of the induction heating unit. It is shown that the main design parameter infl uencing the energy characteristics of the complex is the length of the heating system. When optimizing the total length of the heater, an iterative model of the process of induction heating of ferromagnetic billets is used. The power distribution algorithm along the length of a two-section heater is a piecewise continuous function. Optimization of the heater length according to the proposed method made it possible to reduce the heater length from 2.8 m to 2.1 m, i.e. by 25%. To search for eff ective control algorithms for non-stationary modes, a refi ned electrothermal model is proposed in the work. It takes into account the nonlinear dependence of the distribution of the power of the sources of internal heat release on the temperature distribution in the metal of the workpieces along the radial and axial coordinates. The problem of fi nding the optimal control of transient modes of a two-section induction heater of methodical action is formulated and solved. The results obtained provide a minimum of energy consumption for heating billets in transient modes under conditions of technological and energy constraints. Variants of starting the heater at various initial temperature states of the load are considered. The results of a comparative analysis of the eff ectiveness of the obtained control algorithms are presented. The structure of the power supply and control system of the induction heating complex is proposed.

Multi-objective optimum design of porous triangular chamber using RSM

The present research enlightens the study of natural convection in an isosceles triangular shaped chamber heated from below and cooled from the sides filled with porous media. The study is conducted due to the wide use of this subject in nature and thermal industrial systems, such as in a valley. Natural convection in a chamber is numerically simulated in two dimensions using the Finite Volume Method. A wide range of Rayleigh numbers (Ra) from 102 to 5 × 103 is examined for various inclination angles (θ), heater lengths (Lh) and heater locations (Ph). It is found that the plumelike patterns for the isotherms occur at Ra = 2.5 × 103, with two rotating large vortices breaking into multi smaller vortices as the length of the heater is increased. Additionally, for an inclination angle of 0°, the Nusselt number records a higher value nearly 26% compared to θ = 180° at the highest Ra. Finally, Response Surface Methodology (RSM) is used to show that porosity (ε), aspect ratio (L/H), and Ra have a major effect on hydrothermal efficiency, which is almost equal to 1.27 at the minimum porosity (ε), the maximum values of aspect ratio (L/H) and Ra with higher desirability. This study offers a novel approach to designing an isosceles porous triangular-shaped chamber as well as practical advice.

Magnetohydrodynamic Effect on Thermal Transport by Silver Nanofluid Flow in Enclosure with Central and Lower Heat Sources

A numerical investigation into the magneto-convection heat transfer performance of Ag-based nanofluid (i.e., silver nanoparticles dispersed in fluid) filled square enclosure containing a thin central heater and a lower heated wall section is performed. The analysis focuses particularly on the effects of the magnetic field strength, central heater orientation and length, lower heated wall section length, Rayleigh number, and Ag nanoparticle volume fraction on the average Nusselt number along the cool, vertical sidewalls of the enclosure. It is found that the heat transfer performance improves as the lengths of the central heater and lower heated wall section increase. Also, the average Nusselt number increases given a vertical orientation of the central heater. Regardless of the heater orientation, the heat transfer performance decreases with increasing magnetic field strength. As Ag nanoparticle volume fraction increases, the average Nusselt number increases with increasing values of Rayleigh number. Finally, the heat transfer performance improves for increasing nanoparticle volume fraction (0.00, 0.03, 0.06, 0.09) at high Rayleigh numbers of 106 and 107.

Experimental study of transition to instability in a Rijke tube with axially distributed heat source

Self-excited thermoacoustic oscillations are favorable in thermoacoustic engines, but unwanted in many combustion systems due to the detrimental outcomes, including the structure vibration and overloaded thermal flux to combustor wall. To explore some proper methods to modify thermoacoustic oscillations, understanding the mechanism of thermoacoustic instability is needed. In the present work, the transition to instability in a Rijke-type thermoacoustic system with axially distributed heat source is explored experimentally. A silicon/ceramic tube is used as the acoustic resonator, and the distributed heat source is designed by wounding electric wires over two ceramic rings. The influences of the characteristics of heat source (including heating power, heater length and heater location), mass flow rate, and tube materials on the nonlinear dynamic behaviors and stability boundaries of the Rijke-type thermoacoustic system are systematically evaluated. Large-amplitude limit cycle is observed, and subcritical and supercritical bifurcations are present in the thermoacoustic system. For the system with fixed mass flow rates, the critical heat power for transition to instability is found to be approximately linearly proportional to the heater length, while the strength of pressure oscillations responds nonlinearly. In addition, the system with a thin heater is more prone to undergo subcritical bifurcation. As for the influence of the mass flow rate, it has also been found that increasing the mass flow rate would enhance the nonlinearity of the coupling between the unsteady heat release rate and acoustic waves, which leads to a high possibility of occurrence of subcritical bifurcation. For all the heater length studied, there is an optimal mass flow rate where the critical heat power for the transition to instability is minimal. Last, the results show that the thermoacoustic system with ceramic tube has a narrower stability region at small air flow rate and is more prone to subcritical bifurcation than the silicon tube.

Two-dimensional lattice Boltzmann method to study the influence of nucleation distance on heat flux during bubble coalescence

The lattice Boltzmann method studied the merging of double bubbles under different spacings in pool boiling. This paper analyzes the influence of bubble nucleation distance on heat transfer performance. According to the difference of nucleation distance within the scope of this article, the impact of bubble coalescence on bubble departure frequency can be divided into three regions: promotion, inhibitive, and promotion. The dynamic behavior of the bubble is linked with the heat flux, the heat flux evolution characteristics of different bubble separation distances are analyzed. The optimal nucleation distances were found to exist to achieve the maximum thermal transfer performance. The optimal distance is correlated with environmental factors such as superheat, heater length, and gravity. The main reason affecting the optimal separation distance is the bubble diameter. The larger the bubble leaves the diameter, the larger the optimal separation distance.

Natural convection in triangular fin‐shaped cavity with partially heated base using nanofluid

AbstractComputational analysis of convective heat transfer characteristics of Al2O3–Cu‐water hybrid nanofluid inside a triangular fin‐shaped cavity is performed. A heater of different lengths is attached to the base wall while the other walls are kept cold. The governing equations are modeled and transformed into dimensionless forms by utilizing dimensionless variables. For further investigation of the problem obtained, dimensionless coupled partial differential equations with appropriate boundary conditions are solved numerically using Galerkin Finite element method. A grid dependency test is carried out to check the efficiency and accuracy of the proposed numerical method. Impact of heater length, nanoparticle volume fraction and Rayleigh number on the dimensionless velocity, temperature, streamlines, isotherms, local and average Nusselt number is investigated through graphical analysis. It is demonstrated that the local and average Nusselt numbers increase with Rayleigh number and solid volume fraction of both nanoparticles. It is important to note that the results of this investigation are useful for cooling systems in various thermal devices, building structures, and electronic components.

Hydromagnetic natural convection in a wavy-walled enclosure equipped with hybrid nanofluid and heat generating cylinder

Flow and heat transfer components of buoyancy driven convection in a hybrid nanofluid filled wavy-walled cavity are numerically investigated in this study. A cylindrical heat generating blockage is placed at the center of the cavity. The cavity is partially heated from its bottom wall and cooled from wavy-walls while the remaining walls are adiabatic. The cavity is permeated by a transverse magnetic field. Thermal conductivity model of hybrid nanofluid is developed comprising Brownian motions of different nanoparticles. The non dimensional governing equations are solved by implementing finite element method. Obtained results demonstrate the intensification of fluid flow circulation for increasing Rayleigh number and heater length. The heat transfer rate is expeditiously augmented for increase in Rayleigh number and hybrid nanoparticles volume fraction but reverse trend is observed for higher Hartmann number. The flow circulation and temperature distribution are influenced with the presence of heat generating cylinder and roughness of the cavity walls. In addition, strength of fluid motion becomes higher for wavy cavity containing heat generating obstacle compared to smooth cavity without blockage. Maximum heat transfer is ensured at lower heater length and radius of the heat generating cylinder. Heat transfer rate also increases with the roughness of the cavity.

Numerical investigation of steady state characteristics and stability of supercritical water natural circulation loop of a heater and cooler arrangements

The present paper studies the thermal-hydraulic behaviour of the rectangular supercritical natural circulation loop (SCNCL) using numerical model of one dimensional. Then the results of this model is confirmed with experimental and benchmark results. Variations with several geometric parameters like loop diameter, riser length, and heater length and operating conditions like heater inlet enthalpy, pressure, friction factor, and inlet and exit loss coefficient on steady-state performance are investigated for various orientations like HHHC, HHVC, VHVC and VHHC of the heater and cooler. The chances of existing static instability (Ledinegg excursion) has been investigated, which reveals that it can arise only in a low inlet enthalpy condition, far from the suggested various orientations of heater and cooler.

Experimental Study of Critical Heat Flux During Pool Boiling on Mini Tubes: Effect of Subcooling, Orientation, and Dimensions

Pool boiling is cost-effective, simple and prevalent amongst all available cooling schemes. The lack of quantitative data, qualitative theories and explanations in the area of critical heat flux (CHF) in mini tubes makes it an interesting domain of research. This paper discusses the effect of heater length, diameter, orientation and subcooling on CHF. There is the scarcity of literature that considers all the effects altogether. This paper analyses the effect of all the parameters together in a single study. SS304 mini tubes of 2.5- and 1.2-mm diameters with various lengths are used as a heater in horizontal and vertical orientations. The water pool is kept at 30, 50, 75 °C and saturation temperature. The study is performed at atmospheric pressure. It has been observed that with the increase in pool temperature, the magnitude of CHF decreases. The shortest length has a higher magnitude of CHF corresponding to a given pool temperature. The values of CHF decrease with an increase in tube diameter. The CHF value is higher for horizontal as compared to vertical orientation. An empirical correlation, including the effect of subcooling, orientation and tube dimensions is derived from the CHF data. The experimental data is presented in a tabulated form to contribute to pool boiling CHF databank.

Nanofluid MHD combined convection in a porous chamber with various thermal sources

The impact of various sizes and positions of the heater in a nanofluid-saturated porous lid-driven chamber with a uniform Lorentz force is studied numerically. In this investigation, three different lengths of heater with higher temperature at six different locations along the left sidewall of the cavity are considered. Lower temperature is maintained at the right sidewall. Further, lower and moving upper horizontal walls and the rest of left wall are supposed to be thermally insulated. Based on the finite volume method, the system of nondimensional governing equations is solved by SIMPLE algorithm. The results conclude that the average Nusselt number is reduced with the enhancement of Richardson and Hartmann numbers. When the heater length is reduced from bottom to top, the heat transfer rate is increased for all the considered Richardson, Darcy and Hartmann numbers. In the lower permeability of the porous medium, the effect of solid volume fraction of nanofluid is more vulnerable. In the case of nanofluid, the steady state is reached quickly than the pure fluid.

Heat enhancement analysis in a differentially heated inclined square enclosure with water and ethylene glycol based Al2O3 nanofluid

This paper investigates the analysis of natural-convection heat enhancement in an inclined square enclosure when filled with water-based nanofluids with left edge wall undergoing heating with consistent heat flux while the right edge wall being cold and other remaining walls are kept adiabatic. The parameters used in this analysis include: solid fraction volume (range from 0-20%), length of the heaters (0.25 cm, 0.50 cm, and 1.0 cm from the left edge), and Rayleigh number (range from 104 to 106 ). The nanolayer thickness ratio was kept at a constant value of 1.0 throughout the analysis. The heat source is found at the center of the left wall. Polynomial differential quadrature equations have been adopted for this analysis for various angles range from 0-90?. As the Rayleigh numbers and particle volume fraction got the much-needed raise, the average count of the heat transfer rate improved too. The length of the heat flux heater has become more prominent parameter that has been affecting the calculated temperature and the flow fields. When the heat flux heater length is pushed to an increasing limit, the heat enhancement rate essentially starts to decline. This happens at the smaller inclination angle, though.

CONJUGATE NATURAL CONVECTION IN A POROUS ENCLOSURE SANDWICHED BY FINITE WALLS AND SUBJECTED TO CONVECTION COOLING CONDITION

Steady conjugate natural convection heat transfers in a two-dimensional enclosure filled with fluid saturated porous medium is studied numerically. The two vertical boundaries of the enclosure are kept isothermally at same temperature, the horizontal upper wall is adiabatic, and the horizontal lower wall is partially heated. The Darcy extended Brinkman Forcheimer model is used as the momentum equation and Ansys Fluent software is utilized to solve the governing equations. Rayleigh number (1.38 ≤ Ra ≤ 2.32), Darcy number (3.9 * 10-8), the ratio of conjugate wall thickness to its height (0.025 ≤ W ≤ 0.1), heater length to the bottom wall ratio (1/4 ≤  ≤ 3/4) and inclination angle (0°, 30° and 60°) are the main considered parameters. The presented results show the effect of these parameters on the heat transfer and fluid flow characteristics. These results include streamlines, isotherm patterns, and local and average Nusselt number for different values of the governing parameters. It is found that either increasing the Rayleigh number and the ratio of conjugate wall thickness to its height (d/H) or decreasing the ratio of heat source width to bottom wall (l/L), the average Nusselt number is increased. Also, it was observed that the average Nusselt number does not change substantially with inclination angle.