Search results for: Conduction Heat Transfer

Authors: Mansour A. Al Qubeissi

Abstract:

The current paper presents a numerical approach in solving the conjugate heat transfer problems. A heat conduction code is coupled internally with a computational fluid dynamics solver for developing a couple conjugate heat transfer solver. Methodology of treating non-matching meshes at interface has also been proposed. The validation results of 1D and 2D cases for the developed conjugate heat transfer code have shown close agreement with the solutions given by analysis.

Keywords: Computational Fluid Dynamics, Conjugate Heat transfer, Heat Conduction, Heat Transfer

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Authors: D. Zabala, N. Sánchez, J. Pinto

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A transient heat transfer mathematical model for the prediction of temperature distribution in the car body during primer baking has been developed by considering the thermal radiation and convection in the furnace chamber and transient heat conduction governing equations in the car framework. The car cockpit is considered like a structure with six flat plates, four vertical plates representing the car doors and the rear and front panels. The other two flat plates are the car roof and floor. The transient heat conduction in each flat plate is modeled by the lumped capacitance method. Comparison with the experimental data shows that the heat transfer model works well for the prediction of thermal behavior of the car body in the curing furnace, with deviations below 5%.

Keywords: Transient heat transfer, car body, lumpedcapacitance, primer baking.

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Authors: Yu-Ching Yang, Haw-Long Lee, Win-Jin Chang

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The present work numerically analyzes the transient heat transfer in the absorber plates of a flat-plate solar collector based on the dual-phase-lag (DPL) heat conduction model. An efficient numerical scheme involving the hybrid application of the Laplace transform and control volume methods is used to solve the linear hyperbolic heat conduction equation. This work also examines the effect of different medium parameters on the behavior of heat transfer. Results show that, while the heat-flux phase lag induces thermal waves in the medium, the temperature-gradient phase lag smoothens the thermal waves by promoting non-Fourier diffusion-like conduction into the medium.

Keywords: Absorber plates, dual-phase-lag, non-Fourier, solar collector.

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Authors: U. Prasopchingchana

Abstract:

The temperature distribution and the heat transfer rates through a multi-layer door of a furnace were investigated. The inside of the door was in contact with hot air and the other side of the door was in contact with room air. Radiation heat transfer from the walls of the furnace to the door and the door to the surrounding area was included in the problem. This work is a two dimensional steady state problem. The Churchill and Chu correlation was used to find local convection heat transfer coefficients at the surfaces of the furnace door. The thermophysical properties of air were the functions of the temperatures. Polynomial curve fitting for the fluid properties were carried out. Finite difference method was used to discretize for conduction heat transfer within the furnace door. The Gauss-Seidel Iteration was employed to compute the temperature distribution in the door. The temperature distribution in the horizontal mid plane of the furnace door in a two dimensional problem agrees with the one dimensional problem. The local convection heat transfer coefficients at the inside and outside surfaces of the furnace door are exhibited.

Keywords: Conduction, heat transfer, multi-layer door, natural convection

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Authors: Te Wen Tu, Sen Yung Lee

Abstract:

An alternative approach is proposed to develop the analytic solution for one dimensional heat conduction with one mixed type boundary condition and general time-dependent heat transfer coefficient. In this study, the physic meaning of the solution procedure is revealed. It is shown that the shifting function takes the physic meaning of the reciprocal of Biot function in the initial time. Numerical results show the accuracy of this study. Comparing with those given in the existing literature, the difference is less than 0.3%.

Keywords: Analytic solution, heat transfer coefficient, shifting function method, time-dependent boundary condition.

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Authors: Ashok K. Satapathy, Prerana Nashine

Abstract:

Radiative heat transfer in participating medium was carried out using the finite volume method. The radiative transfer equations are formulated for absorbing and anisotropically scattering and emitting medium. The solution strategy is discussed and the conditions for computational stability are conferred. The equations have been solved for transient radiative medium and transient radiation incorporated with transient conduction. Results have been obtained for irradiation and corresponding heat fluxes for both the cases. The solutions can be used to conclude incident energy and surface heat flux. Transient solutions were obtained for a slab of heat conducting in slab and by thermal radiation. The effect of heat conduction during the transient phase is to partially equalize the internal temperature distribution. The solution procedure provides accurate temperature distributions in these regions. A finite volume procedure with variable space and time increments is used to solve the transient radiation equation. The medium in the enclosure absorbs, emits, and anisotropically scatters radiative energy. The incident radiations and the radiative heat fluxes are presented in graphical forms. The phase function anisotropy plays a significant role in the radiation heat transfer when the boundary condition is non-symmetric.

Keywords: Participating media, finite volume method, radiation coupled with conduction, heat transfer.

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Authors: Raoudha Chaabane, Faouzi Askri, Sassi Ben Nasrallah

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Simultaneous transient conduction and radiation heat transfer with heat generation is investigated. Analysis is carried out for both steady and unsteady situations. two-dimensional gray cylindrical enclosure with an absorbing, emitting, and isotropically scattering medium is considered. Enclosure boundaries are assumed at specified temperatures. The heat generation rate is considered uniform and constant throughout the medium. The lattice Boltzmann method (LBM) was used to solve the energy equation of a transient conduction-radiation heat transfer problem. The control volume finite element method (CVFEM) was used to compute the radiative information. To study the compatibility of the LBM for the energy equation and the CVFEM for the radiative transfer equation, transient conduction and radiation heat transfer problems in 2-D cylindrical geometries were considered. In order to establish the suitability of the LBM, the energy equation of the present problem was also solved using the the finite difference method (FDM) of the computational fluid dynamics. The CVFEM used in the radiative heat transfer was employed to compute the radiative information required for the solution of the energy equation using the LBM or the FDM (of the CFD). To study the compatibility and suitability of the LBM for the solution of energy equation and the CVFEM for the radiative information, results were analyzed for the effects of various parameters such as the boundary emissivity. The results of the LBMCVFEM combination were found to be in excellent agreement with the FDM-CVFEM combination. The number of iterations and the steady state temperature in both of the combinations were found comparable. Results are found for situations with and without heat generation. Heat generation is found to have significant bearing on temperature distribution.

Keywords: heat generation, cylindrical coordinates; RTE;transient; coupled conduction radiation; heat transfer; CVFEM; LBM

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Authors: Yew Mun Hung, Ching Sze Lim, Tiew Wei Ting, Ningqun Guo

Abstract:

The effect of streamwise conduction on the thermal characteristics of forced convection for nanofluidic flow in rectangular microchannel heat sinks under isothermal wall has been investigated. By applying the fin approach, models with and without streamwise conduction term in the energy equation were developed for hydrodynamically and thermally fully-developed flow. These two models were solved to obtain closed form analytical solutions for the nanofluid and solid wall temperature distributions and the analysis emphasized details of the variations induced by the streamwise conduction on the nanofluid heat transport characteristics. The effects of the Peclet number, nanoparticle volume fraction, thermal conductivity ratio on the thermal characteristics of forced convection in microchannel heat sinks are analyzed. Due to the anomalous increase in the effective thermal conductivity of nanofluid compared to its base fluid, the effect of streamwise conduction is expected to be more significant. This study reveals the significance of the effect of streamwise conduction under certain conditions of which the streamwise conduction should not be neglected in the forced convective heat transfer analysis of microchannel heat sinks.

Keywords: fin approach, microchannel heat sink, nanofluid, streamwise conduction

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Authors: Tao Nie, Weiqiang Liu

Abstract:

In order to obtain an accurate result of the heat transfer of the rib in the internal cooling Rectangular channel, using separation of variables, analytical solutions of three dimensional steady-state heat conduction in rectangular ribs are given by solving three dimensional steady-state function of the rectangular ribs. Therefore, we can get solution of three dimensional temperature field in the rib. Based on the solution, we can get how the Bi number affected on heat transfer. Furthermore, comparisons of the analytical and numerical results indicate agreement on temperature field in the rib.

Keywords: variable separation method, analytical solution, rib, heat transfer

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Authors: A. Ashok, K.Satapathy, B. Prerana Nashine

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The objective of this research work is to investigate for one dimensional transient radiative transfer equations with conduction using finite volume method. Within the infrastructure of finite-volume, we obtain the conservative discretization of the terms in order to preserve the overall conservative property of finitevolume schemes. Coupling of conductive and radiative equation resulting in fluxes is governed by the magnitude of emissivity, extinction coefficient, and temperature of the medium as well as geometry of the problem. The problem under consideration has been solved, for a slab dominating radiation coupled with transient conduction based on finite volume method. The boundary conditions are also chosen so as to give a good model of the discretized form of radiation transfer equation. The important feature of the present method is flexibility in specifying the control angles in the FVM, while keeping the simplicity in the solution procedure. Effects of various model parameters are examined on the distributions of temperature, radiative and conductive heat fluxes and incident radiation energy etc. The finite volume method is considered to effectively evaluate the propagation of radiation intensity through a participating medium.

Keywords: Radiative transfer equation, finite volume method, conduction, transient radiation.

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Authors: Dalvir Singh, Somnath Chattopadhyaya

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During welding or flame cutting of metals, the prediction of heat affected zone (HAZ) is critical. There is need to develop a simple mathematical model to calculate the temperature variation in HAZ and derivative analysis can be used for this purpose. This study presents analytical solution for heat transfer through conduction in mild steel plate. The homogeneous and nonhomogeneous boundary conditions are single variables. The full field analytical solutions of temperature measurement, subjected to local heating source, are derived first by method of separation of variables followed with the experimental visualization using infrared imaging. Based on the present work, it is suggested that appropriate heat input characteristics controls the temperature distribution in and around HAZ.

Keywords: Conduction Heat Transfer, Heat Affected Zone (HAZ), Infra-Red Imaging, Numerical Method, Orthogonal Function, Plasma Arc Cutting, Separation of Variables, Temperature Measurement.

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Authors: A. Kargar, A. Kianifar, H. Mohammadiun

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Two-dimensional heat conduction within a composed solid material with a constant internal heat generation has been investigated numerically in a sector of the rotor a generator. The heat transfer between two adjacent materials is assumed to be purely conduction. Boundary conditions are assumed to be forced convection on the fluid side and adiabatic on symmetry lines. The control volume method is applied for the diffusion energy equation. Physical coordinates are transformed to the general curvilinear coordinates. Then by using a line-by-line method, the temperature distribution in a sector of the rotor has been determined. Finally, the results are normalized and the effect of cooling fluid on the maximum temperature of insulation is investigated.

Keywords: general curvilinear coordinates , jacobian, controlvolume.

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Authors: Imen Mejri, Ahmed Mahmoudi, Mohamed A. Abbassi, Ahmed Omri

Abstract:

Thermal radiation plays a very important role in the heat transfer combination through the various components of the SOFC fuel cell operating at high temperatures. Lattice Boltzmann method is used for treating conduction-radiation heat transfer in the electrolyte. The thermal radiation heat transfer is coupled to the overall energy conservation equations through the divergence of the local radiative flux. The equation of energy in one dimension is numerically resolved by using the Lattice Boltzmann method. A computing program (FORTRAN) is developed locally for this purpose in order to obtain fields of temperature in every element of the cell. The parameters investigated are: functioning temperature, cell voltages and electrolyte thickness. The results show that the radiation effect increases with increasing the electrolyte thickness, also increases with increasing the functioning temperature and decreases with the increase of the voltage of the cell.

Keywords: SOFC, lattice Boltzmann method, conduction, radiation, planar medium.

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Authors: F. Rezaie Moghaddam, J. Amani, T. Rezaie Moghaddam

Abstract:

Many computational techniques were applied to solution of heat conduction problem. Those techniques were the finite difference (FD), finite element (FE) and recently meshless methods. FE is commonly used in solution of equation of heat conduction problem based on the summation of stiffness matrix of elements and the solution of the final system of equations. Because of summation process of finite element, convergence rate was decreased. Hence in the present paper Cellular Automata (CA) approach is presented for the solution of heat conduction problem. Each cell considered as a fixed point in a regular grid lead to the solution of a system of equations is substituted by discrete systems of equations with small dimensions. Results show that CA can be used for solution of heat conduction problem.

Keywords: Heat conduction, Cellular automata, convergencerate, discrete system.

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Authors: D Bhargavi, J. Sharath Kumar Reddy

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The present investigation has been undertaken to assess the effect of viscous dissipation and axial conduction on forced convection heat transfer in the entrance region of a parallel plate channel with the porous insert attached to both walls of the channel. The flow field is unidirectional. Flow in the porous region corresponds to Darcy-Brinkman model and the clear fluid region to that of plane Poiseuille flow. The effects of the parameters Darcy number, Da, Peclet number, Pe, Brinkman number, Br and a porous fraction γ_p on the local heat transfer coefficient are analyzed graphically. Effects of viscous dissipation employing the Darcy model and the clear fluid compatible model have been studied.

Keywords: Porous material, channel partially filled with a porous material, axial conduction, viscous dissipation.

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Authors: Ahmed Mahmoudi, Imen Mejri, Mohamed A. Abbassi, Ahmed Omri

Abstract:

In this paper, the 1-D conduction-radiation problem is solved by the lattice Boltzmann method. The effects of various parameters such as the scattering albedo, the conduction–radiation parameter and the wall emissivity are studied. In order to check on the accuracy of the numerical technique employed for the solution of the considered problem, the present numerical code was validated with the published study. The found results are in good agreement with those published

Keywords: Conduction, lattice Boltzmann method, planar medium, radiation.

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Authors: O. Afshar

Abstract:

A solar receiver is designed for operation under extremely uneven heat flux distribution, cyclic weather, and cloud transient cycle conditions, which can include large thermal stress and even receiver failure. In this study, the effect of different oil velocity on convection coefficient factor and impact of wind velocity on local Nusselt number by Finite Volume Method will be analyzed. This study is organized to give an overview of the numerical modeling using a MATLAB software, as an accurate, time efficient and economical way of analyzing the heat transfer trends over stationary receiver tube for different Reynolds number. The results reveal when oil velocity is below 0.33m/s, the value of convection coefficient is negligible at low temperature. The numerical graphs indicate that when oil velocity increases up to 1.2 m/s, heat convection coefficient increases significantly. In fact, a reduction in oil velocity causes a reduction in heat conduction through the glass envelope. In addition, the different local Nusselt number is reduced when the wind blows toward the concave side of the collector and it has a significant effect on heat losses reduction through the glass envelope.

Keywords: Receiver tube, heat convection, heat conduction, Nusselt number.

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Authors: Zhang Lei, Liu Min, Liu Botao

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In order to improve the simulation effects of space cold black environment, this paper described a rectangular channel plate heat sink. By using fluid mechanics theory and finite element method, the internal fluid flow and heat transfer in heat sink was numerically simulated to analyze the impact of channel structural on fluid flow and heat transfer. The result showed that heat sink temperature uniformity is well, and the impact of channel structural on the heat sink temperature uniformity is not significant. The channel depth and spacing are important factors which affect the fluid flow and heat transfer in the heat sink. The two factors of heat transfer and resistance need to be considered comprehensively to determine the optimal flow structure parameters.

Keywords: heat transfer, heat sink, numerical simulation

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Authors: M. Kito, M. Takezaki, T. Shakouchi, K. Tsujimoto, T. Ando

Abstract:

Impinging jets are widely used in industrial cooling systems for their high heat transfer characteristics at stagnation points. However, the heat transfer characteristics are low in the downstream direction. In order to improve the heat transfer coefficient further downstream, investigations introducing ribs on jet-cooled flat plates have been conducted. Most studies regarding the heat-transfer enhancement using a rib-roughened wall have dealt with the rib pitch. In this paper, we focused on the rib spacing and demonstrated that the rib spacing must be more than 6 times the nozzle width to improve heat transfer at Reynolds number Re=5.0×103 because it is necessary to have enough space to allow reattachment of flow behind the first rib.

Keywords: Forced convection, heat transfer, impinging jet cooling, rib roughened wall

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Authors: Jaehyug Lee, Tae-Ho Song

Abstract:

Vacuum Insulation Panel (VIP) can achieve very low thermal conductivity by evacuating its inner space. Heat transfer in the core materials of highly-evacuated VIP occurs by conduction through the solid structure and radiation through the pore. The effect of various scattering modes in combined conduction-radiation in VIP is investigated through numerical analysis. The discrete ordinates interpolation method (DOIM) incorporated with the commercial code FLUENT® is employed. It is found that backward scattering is more effective in reducing the total heat transfer while isotropic scattering is almost identical with pure absorbing/emitting case of the same optical thickness. For a purely scattering medium, the results agrees well with additive solution with diffusion approximation, while a modified term is added in the effect of optical thickness to backward scattering is employed. For other scattering phase functions, it is also confirmed that backwardly scattering phase function gives a lower effective thermal conductivity. Thus the materials with backward scattering properties, with radiation shields are desirable to lower the thermal conductivity of VIPs.

Keywords: Combined conduction and radiation, discrete ordinates interpolation method, scattering phase function, vacuum insulation panel.

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Authors: Shen-Kuei Du, Jen-Chieh Chang, Chia-Hong Kao, Tzu-Chen Hung, Chii-Ray Lin

Abstract:

This study experimentally investigates the heat transfer effects of forced convection and natural convection under different substrate openings design. A computational fluid dynamics (CFD) model was established and implemented to verify and explain the experimental results and heat transfer behavior. It is found that different opening position will destroy the growth of the boundary layer on substrates to alter the cooling ability for both forced under low Reynolds number and natural convection. Nevertheless, having too many opening may reduce heat conduction and affect the overall heat transfer performance. This study provides future researchers with a guideline on designing and electronic package manufacturing.

Keywords: electronic cooling, experiment, opening concept, CFD.

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Authors: Jeong Hyun Kim, Gyo Woo Lee

Abstract:

In this study, heat release performances of the three extruded-type heat sinks can be used in inverter for solar power generation were evaluated. Numbers of fins in the heat sinks (namely E-38, E-47 and E-76) were 38, 47 and 76, respectively. Heat transfer areas of them were 1.8, 1.9 and 2.8m². The heat release performances of E-38, E-47 and E-76 heat sinks were measured as 79.6, 81.6 and 83.2%, respectively. The results of heat release performance show that the larger amount of heat transfer area the higher heat release rate. While on the other, in this experiment, variations of mass flow rates caused by different cross sectional areas of the three heat sinks may not be the major parameter of the heat release. Despite the 47.4% increment of heat transfer area of E-76 heat sink than that of E-47 one, its heat release rate was higher by only 2.0%; this suggests that its heat transfer area need to be optimized.

Keywords: Solar Inverter, Heat Sink, Forced Convection, Heat Transfer, Performance Evaluation.

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Authors: A. Amiri Delouei

Abstract:

In the current study, two-dimensional unsteady heat conduction in a functionally graded cylinder is studied analytically. The temperature distribution is in radial and longitudinal directions. Heat conduction coefficients are considered a power function of radius both in radial and longitudinal directions. The proposed solution can exactly satisfy the boundary conditions. Analytical unsteady temperature distribution for different parameters of functionally graded cylinder is investigated. The achieved exact solution is useful for thermal stress analysis of functionally graded cylinders. Regarding the analytical approach, this solution can be used to understand the concepts of heat conduction in functionally graded materials.

Keywords: Functionally graded materials, unsteady heat conduction, cylinder, Temperature distribution.

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Authors: Imane Khalil, Quinn Pratt

Abstract:

In a nuclear reactor, an array of fuel rods containing stacked uranium dioxide pellets clad with zircalloy is the heat source for a thermodynamic cycle of energy conversion from heat to electricity. After fuel is used in a nuclear reactor, the assemblies are stored underwater in a spent nuclear fuel pool at the nuclear power plant while heat generation and radioactive decay rates decrease before it is placed in packages for dry storage or transportation. A computational model of a Boiling Water Reactor spent fuel assembly is modeled using FLUENT, the computational fluid dynamics package. Heat transfer simulations were performed on the two-dimensional 9x9 spent fuel assembly to predict the maximum cladding temperature for different input to the FLUENT model. Uncertainty quantification is used to predict the heat transfer and the maximum temperature profile inside the assembly.

Keywords: Spent nuclear fuel, conduction, heat transfer, uncertainty quantification.

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Authors: Shima Soleimani, Steven Eckels

Abstract:

One area of special importance for the surface-level study of heat exchangers is tubes with internal micro-fins (< 0.5 mm tall). Micro-finned surfaces are a kind of extended solid surface in which energy is exchanged with water that acts as the source or sink of energy. Significant performance gains are possible for either shell, tube, or double pipe heat exchangers if the best surfaces are identified. The parametric studies of micro-finned tubes that have appeared in the literature left some key parameters unexplored. Specifically, they ignored three-dimensional (3D) micro-fin configurations, conduction heat transfer in the fins, and conduction in the solid surface below the micro-fins. Thus, this study aimed at implementing a parametric study of 3D micro-finned tubes that considered micro-fine height and discontinuity features. A 3D conductive and convective heat-transfer simulation through coupled solid and periodic fluid domains is applied in a commercial package, ANSYS Fluent 19.1. The simulation is steady-state with turbulent water flow cooling the inner wall of a tube with micro-fins. The simulation utilizes a constant and uniform temperature on the tube outer wall. Performance is mapped for 18 different simulation cases, including a smooth tube using a realizable k-ε turbulence model at a Reynolds number of 48,928. Results compared the performance of 3D tubes with results for the similar two-dimensional (2D) one. Results showed that the micro-fine height has a greater impact on performance factors than discontinuity features in 3D micro-fin tubes. A transformed 3D micro-fin tube can enhance heat transfer, and pressure drops up to 21% and 56% compared to a 2D one, respectfully.

Keywords: Three-dimensional micro-fin tube, heat transfer, friction factor, heat exchanger.

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Authors: Chen-Yu Wang, Tsung-Chien Chen, Ming-Hui Lee, Jen-Feng Huang

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In this paper, the innovative intelligent fuzzy weighted input estimation method (FWIEM) can be applied to the inverse heat transfer conduction problem (IHCP) to estimate the unknown time-varying heat flux efficiently as presented. The feasibility of this method can be verified by adopting the temperature measurement experiment. We would like to focus attention on the heat flux estimation to three kinds of samples (Copper, Iron and Steel/AISI 304) with the same 3mm thickness. The temperature measurements are then regarded as the inputs into the FWIEM to estimate the heat flux. The experiment results show that the proposed algorithm can estimate the unknown time-varying heat flux on-line.

Keywords: Fuzzy Weighted Input Estimation Method, IHCP andHeat Flux.

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Authors: P.Kumar

Abstract:

Fluids are used for heat transfer in many engineering equipments. Water, ethylene glycol and propylene glycol are some of the common heat transfer fluids. Over the years, in an attempt to reduce the size of the equipment and/or efficiency of the process, various techniques have been employed to improve the heat transfer rate of these fluids. Surface modification, use of inserts and increased fluid velocity are some examples of heat transfer enhancement techniques. Addition of milli or micro sized particles to the heat transfer fluid is another way of improving heat transfer rate. Though this looks simple, this method has practical problems such as high pressure loss, clogging and erosion of the material of construction. These problems can be overcome by using nanofluids, which is a dispersion of nanosized particles in a base fluid. Nanoparticles increase the thermal conductivity of the base fluid manifold which in turn increases the heat transfer rate. In this work, the heat transfer enhancement using aluminium oxide nanofluid has been studied by computational fluid dynamic modeling of the nanofluid flow adopting the single phase approach.

Keywords: Heat transfer intensification, nanofluid, CFD, friction factor

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Authors: Muzna Tariq, Ihtzaz Qamar

Abstract:

In most engineering cases, the working temperatures inside a combustion chamber are high enough that they lie beyond the operational range of thermocouples. Furthermore, design and manufacturing limitations restrict the use of internal thermocouples in many applications. Heat transfer inside a combustion chamber is caused due to interaction of the post-combustion hot fluid with the chamber wall. Heat transfer that involves an interaction between the fluid and solid is categorized as Conjugate Heat Transfer (CHT). Therefore, to satisfy the needs of CHT, CHT Analysis is performed by using ANSYS CFD tool to estimate theoretically precise thermocouple positions at the combustion chamber wall where excessive temperatures (beyond thermocouple range) can be avoided. In accordance with these Computational Fluid Dynamics (CFD) results, a combustion chamber is designed, and a prototype is manufactured with multiple thermocouple ports positioned at the specified distances so that the temperature of hot gases can be measured on the chamber wall where the temperatures do not exceed the thermocouple working range.

Keywords: Computational Fluid Dynamics, CFD, conduction, conjugate heat transfer, CHT, convection, fluid flow, thermocouples.

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Authors: Boris Golman, Wittaya Julklang

Abstract:

The heat and mass transfer was investigated during the falling rate period of spray drying of a slurry droplet. The effect of the porosity of crust layer formed from primary particles during liquid evaporation was studied numerically using the developed mathematical model which takes into account the heat and mass transfer in the core and crust regions, the movement of the evaporation interface, and the external heat and mass transfer between the drying air and the droplet surface. It was confirmed that the heat transfer through the crust layer was more intense in the case of the dense droplet than the loose one due to the enhanced thermal conduction resulting in the higher average droplet temperature. The mass transfer was facilitated in the crust layer of loose droplet owing to the large pore space available for diffusion of water vapor from the evaporation interface to the outer droplet surface. The longer drying time is required for the droplet of high porosity to reach the final moisture content than that for the dense one due to the larger amount of water to be evaporated during the falling rate.

Keywords: Spray Drying, Slurry Droplet, Heat and Mass Transfer, Crust Layer Porosity, Mathematical Modeling.

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Authors: A. M. Gheitaghy, H. Saffari, G. Q. Zhang

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Numerical approach based on the electrical simulation method is proposed to solve a nonlinear transient heat conduction problem with nonlinear boundary for a spherical body. This problem represents a strong nonlinearity in both the governing equation for temperature dependent thermal property and the boundary condition for combined convective and radiative cooling. By analysing the equivalent electrical model using the electrical circuit simulation program HSPICE, transient temperature and heat flux distributions at sphere can be obtained easily and fast. The solutions clearly illustrate the effect of the radiation-conduction parameter N_rc, the Biot number and the linear coefficient of temperature dependent conductivity and heat capacity. On comparing the results with corresponding numerical solutions, the accuracy and efficiency of this computational method is found to be good.

Keywords: Convective boundary, radiative boundary, electrical simulation method, nonlinear heat conduction, spherical coordinate.

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