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In numerical heat transfer, the model validation problem with respect to epistemic uncertainty, where only a small amount of experimental information is available, has been recognized as a challenging issue. To overcome the drawback of traditional probabilistic methods in dealing with limited data, this paper proposes a novel model validation approach by using evidence theory. First, the evidence variables are adopted to characterize the uncertain input parameters, where the focal elements are expressed as mutually connected intervals with basic probability assignment (BPA). In the subsequent process of predicting response focal elements, an interval collocation analysis method with small computational cost is presented. By combining the response BPAs in both experimental measurements and numerical predictions, a new parameter calibration method is then developed to further improve the accuracy of computational model. Meanwhile, an evidence-theory-based model validation metric is defined to test the model credibility. Eventually, the famous Sandia thermal challenge problem is utilized to verify the feasibility of presented model validation method in engineering application. [ABSTRACT FROM AUTHOR]

In this paper, a numerical model describing the heat transfer and air flow inside and outside the casing of the permanent magnet brushless direct current (PM BLDC) motor is presented. In the model, a conjugate heat transfer including the heat conduction with heat sources in windings, magnets, bearings, natural and forced convection and radiation phenomena within internal and external air domain were analysed. The complex geometrical model included windings, a magnet circuit, a rotor with neodymium magnets, a PCB electronic plate, plastic covers, internal air between solid parts as well as a portion of the external air. The validation process of the developed model was realised on the basis of the velocity and temperature fields. The experimental data were recorded by 7 constant temperature anemometers at 4 levels above the motor housing, Laser Doppler Anemometry sensors in two axes inside the rear portion of the motor and 25 thermocouples fixed inside and outside the motor. The experimental and numerical tests were performed for 4 motor loadings and 3 rotational speeds. The average temperature error for the internal point was of 9 K, while that of the external points was of 2 K. The velocity field was very well predicted close to the housing wall in terms of horizontal and vertical components. A slightly worse agreement was found for the vertical component, especially in the vicinity of the shaft. The results were consistent for all the considered motor loadings and rotational speeds. [ABSTRACT FROM AUTHOR]

The convection onset in a evaporation thermal model of a solute/solvent solution is numerically studied. The transient nature of the diffusion temperature profile requires to control the perturbations which will lead to the transition to a convective flow. Contrary to previous papers, we adopted here a perturbation mode, which is physical and experimentally reproducible, by accounting for a heat transfer at the lateral walls. Based on the Péclet number evaluated in the core flow field only, the critical viscosities and the corresponding times for the transition between a diffusion and convection regimes were calculated as a function of the fluid layer thickness, the aspect ratio and the convective heat transfer coefficient. The study of the spatio-temporal diagrams allowed us to characterize the way the convection propagates in the fluid domain as well as the evolution of the mean cell size and wavenumber. [ABSTRACT FROM AUTHOR]

The present paper presents fluid flow and mixed convective heat transfer characteristics past a semi-circular cylinder at incidence with a tandem square cylinder in cross flow. Using air ( Pr = 0.71 ) as an operating medium, numerical simulations are performed for the range of Reynolds numbers, 10 ≤ Re ≤ 45 and incidence angles, 0 0 ≤ α ≤ 180 0 . The effect of thermal buoyancy is brought about by varying the Richardson number in the range 0 ≤ R i ≤ 2 . The mathematical model is firstly validated with the experimental and numerical results from the literature and found to be in good agreement. The steady separated flow is observed to become unsteady periodic under the superimposed thermal buoyancy. Furthermore, apart from thermal buoyancy effect, angle of incidence is found to play a pivotal role in bringing hydrodynamic instabilities and thereby vortex shedding for such steady mixed convective flows. Functional dependence of drag ( C D ) , lift ( C L ) , and moment ( C M ) coefficients on the combined influence of α and R i , is explored and analysed in detail. Additionally, other global quantities, such as local and average Nusselt number distribution, Strouhal number ( S t ) are determined with respect to the various ranges of parameters considered in the present investigation. [ABSTRACT FROM AUTHOR]

The ammonothermal crystal growth technique is one of the most effective methods used for growing Gallium Nitride (GaN) crystals in terms of the final product quality and manufacturing efficiency. Popular applications of GaN crystals include light emitting diodes (LEDs) and high-frequency electronic devices. A laterally-heated cylindrical enclosure with a top to bottom temperature gradient is considered in this study to investigate the fluid mechanics and heat transfer in an ammonothermal crystal growth reactor. Three-dimensional (3D) large eddy simulations (LES) results of natural convection in a laterally heated cylindrical reactor, using the commercial computational fluid dynamics (CFD) software, ANSYS FLUENT, are presented in this paper for a Rayleigh number ( R a ) of 8.8 × 10 6 . The R a is defined based on a length scale that is equal to the ratio of volume to the lateral area of the cylinder ( R / 2 ). In addition, an experiment of a geometrically- and dynamically-similar geometry is developed, and particle image velocimetry (PIV)-based flow visualizations are carried out for the purpose of validating the numerical model. Comparisons between experiments and numerical simulations showed that flow patterns were qualitatively similar, and Fourier transforms of velocity magnitudes at selected points in the domain matched reasonably well. An added interesting observation in the simulation was the existence of temperature inversion, which has potential implications on the choice of mineralizer (acidic/basic). [ABSTRACT FROM AUTHOR]

This study numerically examines three-dimensional natural convection of air induced by temperature difference between a cold outer cubic enclosure and a hot inner cylinder. Simulations have been carried out for Rayleigh numbers ranging from 10 3 to 10 7 and a titled angle of the enclosure varying from 0° to 90°. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by finite volume method. The effects of cylinder inclination and Rayleigh number on fluid flow and heat transfer are presented. The distribution of isocontours of temperature, components of velocity and streamtraces eventually reaches a steady state for Rayleigh numbers ranging from 10 3 to 10 7 for titled inclination of 90°. However, for the remaining inclinations, Rayleigh numbers must be in the range 10 3 –10 6 to avoid unsteady state which is manifested by the subdivision of the area, containing the maximum local heat transfer rate, into three parts for a Rayleigh number equal to 10 7 and an inclination of 90°. We mention that instability study is not included in the present paper which is solely devoted to three dimensional calculations. Results indicate also that optimal average heat transfer rate is obtained for Rayleigh number set to 10 6 and an inclination of 90° for both cases of the inner cylinder and lateral walls of cubical enclosure. [ABSTRACT FROM AUTHOR]

In this paper, a numerical investigation is presented to study Buongiorno's mathematical model for hydromagnetic free convection flow in an isosceles triangular cavity filled with nanofluid. The inclined walls of the cavity are maintained at constant cold temperature whereas various combinations of the thermal boundary conditions at the bottom heated wall are considered. The cavity is permeated by an inclined uniform magnetic field and the effects of Brownian motion and thermophoresis are incorporated into the nanofluid model. The Galerkin weighted residual finite element method has been employed to solve the governing partial differential equations after converting them into a non-dimensional form using a suitable transformation of variables. In the numerical simulations, alumina-water based nanofluid has been taken into account. Comparisons with previously published work are performed and excellent agreement is obtained. The effects of various parameters such as Hartmann number, Rayleigh number and inclined magnetic field angle on streamlines, isotherms and isoconcentrations have been displayed graphically. The heat transfer augmentation for various combination of model parameters as well as various thermal boundary conditions have been done in light of the average Nusselt number from the bottom heated wall. The results show that the heat transfer rate can be decreased with the increasing values of the Hartmann number and inclination angle of the magnetic field but it can be increased by increasing the Rayleigh number and by reducing the diameter of the nanoparticles. The obtained numerical results also indicate that the variable thermal boundary conditions have significant effects on the flow and thermal fields. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical study on the optimization of key material parameters of multilayer clothing assemblies for thermal comfort in cold climate. A mathematical model of heat and moisture transfer through a multilayer clothing assembly is established. The existence and uniqueness of the solution of the model are verified by using the fixed point theorem. The model predicts the optimum thicknesses and porosities of the two internal layers of the clothing assembly, with which the thermal comfort index will fall within the required intervals with the greatest probability. This study is significant for the optimum design of multilayer clothing assembly for thermal comfort. [ABSTRACT FROM AUTHOR]

In this paper, a distributed parameter model for tubular reactor in the ethylene cracking furnace based on 3-D temperature reconstruction is developed. The mathematical model was formulated to predict the distributions of the heat flux and the tube temperature while considering a non-uniform distribution of the surface heat transfer and the ethylene pyrolysis process. The results show that the heat flux distribution on the tubular reactor has four high heat flux zones, and the tube temperature reaches a maximum of 1088 °C. The value of the maximum tube temperature decreases compared with the value of the maximum heat flux due to the heat exchange coefficient of pyrolysis gas increasing slowly in the bend region. The tube temperature distribution was validated by using a spectrometer system and the errors between three major product yields at the tube outlet obtained by the proposed model and in-situ measured values were within 5%. This distributed parameter model can be used as a guide for ethylene cracking furnace operators and as a tool for design. [ABSTRACT FROM AUTHOR]