Radially Polarized and Magnetized Rotating Cylinders Under Thermal Loading

2012 ◽  
Author(s):  
A. H. Akbarzadeh ◽  
Z. T. Chen
Keyword(s):  
Boundary Condition ◽  
Thermal Loading ◽  
Thermal Boundary Condition ◽  
Inertial Effects ◽  
Exact Form ◽  
Decoupling Method ◽  
Thermal Boundary Conditions ◽  
Mechanical Boundary Condition ◽  
Steady State Heat ◽  
Radially Polarized

Analytical solutions are acquired for radially polarized and magnetized rotating magnetoelectroelastic hollow and solid cylinders. The cylinders are orthotropic and infinitely long and are subjected to a combination of thermal, magnetic, electric, and mechanical loadings. The symmetric and steady state heat conduction equation is solved based on a general form of thermal boundary conditions to give the temperature distribution along the radial direction of cylinders. The governing ordinary differential equations in terms of displacement, electric potential, and magnetic potential with considering the thermal and inertial effects are obtained and solved in an exact form using the straightforward successive decoupling method. Numerical results are illustrated to reveal influences of thermal boundary condition, angular velocity, aspect ratio, and magneto-electro-mechanical boundary condition on the multiphysical responses of the rotating hollow and solid cylinders. The results are validated with those available in the literature.

Heat Transfer Prediction With Unknown Thermal Boundary Conditions Using Physics-Informed Neural Networks

2020 ◽  
Author(s):  
Shengze Cai ◽  
Zhicheng Wang ◽  
Chryssostomos Chryssostomidis ◽  
George Em Karniadakis
Keyword(s):  
Heat Transfer ◽  
Neural Networks ◽  
Boundary Condition ◽  
Boundary Conditions ◽  
Thermal Boundary Condition ◽  
Temperature Measurements ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Thermal Boundary Conditions ◽  
Energy Equations

Abstract Simulating convective heat transfer using traditional numerical methods requires explicit definition of thermal boundary conditions on all boundaries of the domain, which is almost impossible to fulfill in real applications. Here, we address this ill-posed problem using machine learning techniques by assuming that we have some extra measurements of the temperature at a few locations in the domain, not necessarily located on the boundaries with the unknown thermal boundary condition. In particular, we employ physics-informed neural networks (PINNs) to represent the velocity and temperature fields while simultaneously enforce the Navier-Stokes and energy equations at random points in the domain. In PINNs, all differential operators are computed using automatic differentiation, hence avoiding discretization in either space or time. The loss function is composed of multiple terms, including the mismatch in the velocity and temperature data, the boundary and initial conditions, as well as the residuals of the Navier-Stokes and energy equations. Here, we develop a data-driven strategy based on PINNs to infer the temperature field in the prototypical problem of convective heat transfer in flow past a cylinder. We assume that we have just a couple of temperature measurements on the cylinder surface and a couple more temperature measurements in the wake region, but the thermal boundary condition on the cylinder surface is totally unknown. Upon training the PINN, we can discover the unknown boundary condition while simultaneously infer the temperature field everywhere in the domain with less than 5% error in the Nusselt number prediction. In order to assess the performance of PINN, we carried out a high fidelity simulation of the same heat transfer problem (with known thermal boundary conditions) by using the high-order spectral/hp-element method (SEM), and quantitatively evaluated the accuracy of PINN’s prediction with respect to SEM. We also propose a method to adaptively select the location of sensors in order to minimize the number of required temperature measurements while increasing the accuracy of the inference in heat transfer.

Spatial and Temporal Stabilities of Flow in a Natural Circulation Loop: Influences of Thermal Boundary Condition

2003 ◽  
Vol 125 (4) ◽  
pp. 612-623 ◽  
Author(s):  
Y. Y. Jiang ◽  
M. Shoji
Keyword(s):  
Boundary Condition ◽  
Multiple Scales ◽  
Natural Circulation ◽  
Three Dimensional ◽  
Thermal Boundary Condition ◽  
Circular Loop ◽  
Thermal Boundary Conditions ◽  
Natural Circulation Loop ◽  
Control Of Flow ◽  
Multiple Scales Analysis

In a natural circular loop, the thermal convection demonstrates various spatial patterns and temporal instabilities. Problem consists in determining them with respects to thermal boundary conditions. To this end a multiple scales analysis is applied which resembles the inherent characteristic of the pattern formation in the Rayleigh-Be´nard convection. A three-dimensional nonlinear model is proposed by incorporating the flow modes derived along the analysis. The differences of thermal boundary condition are reflected by a coefficient δ. For small δ, numerical solution to the model shows that only temporal instability exists and Lorenz chaos is possible, otherwise, for large values both spatial and temporal instabilities occur leading to cellular flow and intermittency chaos. The model predicted some additional phenomena opening for experimental observation. It seems significant that this study proposes an algorithm for the control of flow stability and distribution by varying the thermal boundary condition.

Effects of thermal boundary conditions on rotating Rayleigh-Bénard convection with implications on geophysical and astrophysical systems

2021 ◽  
Author(s):  
Janet Peifer ◽  
Onno Bokhove ◽  
Steve Tobias
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Biot Number ◽  
Thermal Flux ◽  
Thermal Boundary Condition ◽  
Actual Condition ◽  
Fixed Temperature ◽  
Thermal Boundary Conditions ◽  
Core Dynamics

<p>Rayleigh-Bénard convection (RBC) is a fluid phenomenon that has been studied for over a century because of its utility in simplifying very complex physical systems. Many geophysical and astrophysical systems, including planetary core dynamics and components of weather prediction, are modeled by including rotational forcing in classic RBC. Our understanding of these systems is confined by experimental and numerical limits, as well as theoretical assumptions. </p><p>The role of thermal boundary condition choice on experimental studies of geophysical and astrophysical systems has been often been overlooked, which could account for some lack of agreement between experimental and numerical models as well as the actual flows. The typical thermal boundary conditions prescribed at the top and the bottom of a convection system are fixed temperature conditions, despite few real geophysical systems being bounded with a fixed temperature. A constant heat flux is generally more applicable for real large-scale geophysical systems. However, when this condition is applied in numerical systems, the lack of fixed temperature can cause a temperature drift. In this study, we seek to minimize temperature drifting by applying a fixed temperature condition on one boundary and a fixed thermal flux on the other.</p><p>Experimental boundary conditions are also often assumed to be a fixed temperature. However, the actual condition is determined by the ratio of the height and thermal conductivity of the boundary material to that of the contained fluid, known as the Biot number. The relationship between the Biot number and thermal boundary condition behavior is defined by the Robin, or 'thin-lid', boundary condition such that low Biot number boundaries are essentially fixed thermal flux and high Biot number boundaries are essentially fixed temperature. </p><p>This study seeks to strengthen the link between numerical and experimental models and geophysical flows by investigating the effects of thermal boundary conditions and their relationship to real-world processes. Both fixed temperature and fixed flux boundary conditions are considered. In addition, the Robin boundary condition is studied at a range of Biot numbers spanning from fixed temperature to fixed flux, allowing intermediate conditions to be investigated. Each system is studied at increasingly rapid rotation rates, corresponding to decreasing Ekman numbers as low as Ek=10<sup>-5</sup> Heat transport is analyzed using the Nusselt number, Nu, and the form of the solution is described by the number of convection rolls and time-dependency. Further investigations will analyze Nu and fluid movement within a system with heterogeneous heat flux condition on the  sidewall boundary conditions, which is useful in the study of planetary core dynamics. The results of this study have implications for improvements in modeling geophysical systems both experimentally and numerically. </p>

Fuzzy Adaptive Regularization Method for Inverse Steady-State Heat Transfer Problem

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Kun Wang ◽  
Guangjun Wang
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Regularization Method ◽  
Thermal Boundary Condition ◽  
Transfer System ◽  
Steady State Heat ◽  
Heat Transfer System ◽  
Steady State Heat Transfer ◽  
Adaptive Ability ◽  
Fuzzy Adaptive

For the steady-state heat transfer process, a fuzzy adaptive regularization method (FARM) is proposed to estimate the distributed thermal boundary condition in heat transfer system. First, the relationship model between temperatures at measurement points and parameters to be estimated is established based on sensitivity matrix. The regularization term is introduced into the least-squares objective function, and then the distributed thermal boundary condition is estimated by optimizing the new objective function. A fuzzy inference mechanism is developed to ensure the adaptive ability of FARM in which the regularization parameter is updated based on the residual norm between calculated and measured temperatures at measurement points and the norm of inversion parameters. Taking the plate heat conduction system and fluid–solid conjugate heat transfer system as research objects, the effects of the parameter distribution, the number of measurement points, and measurement errors on the inversion results are discussed by numerical experiments, and comparison with the classical regularization method is also conducted. Results indicate that FARM exhibits a good adaptive ability.

Numerical Simulation of Human Thermal Comfort with Different Thermal Boundary Conditions in Buildings

2014 ◽  
Vol 522-524 ◽  
pp. 1707-1712 ◽  
Author(s):  
Qing Long Peng ◽  
Zhao Hui Qi ◽  
Xia Gan ◽  
Chao Li
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Boundary Condition ◽  
Thermal Comfort ◽  
Human Body ◽  
Thermal Boundary Condition ◽  
Human Thermal Comfort ◽  
The Third ◽  
Thermal Boundary Conditions ◽  
Body Heat

How to use numerical simulation method to analyze human body heat transfer and human thermal comfort is introduced in this paper systematically. Under the same working conditions, numerical simulation of human body heat transfer has been finished based on three thermal boundary conditions, and then the results are compared. The results show that the third thermal boundary condition is better than the first and the second one, which have some problems in simulation and are not good at reflecting the fact on thermal comfort of human body. The third thermal boundary condition which is made to adapt the surrounding flow field automatically can get a more accurate result on calculating the heat transfer of different parts on human body and reflect hot or cool feeling preferably, which proves that the method put forward in this article to research the human body comfort is feasible.

scholarly journals Darcy-Brinkman free convection about a wedge and a cone subjected to a mixed thermal boundary condition

1992 ◽  
Vol 15 (4) ◽  
pp. 789-794 ◽  
Author(s):  
G. Ramanaiah ◽  
V. Kumaran
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Porous Medium ◽  
Heat Transfer Coefficient ◽  
Free Convection ◽  
Transformation Group ◽  
Darcy Number ◽  
Thermal Boundary Condition ◽  
High Porosity

The Darcy-Brinkman free convection near a wedge and a cone in a porous medium with high porosity has been considered. The surfaces are subjected to a mixed thermal boundary condition characterized by a parameterm;m=0,1,∞correspond to the cases of prescribed temperature, prescribed heat flux and prescribed heat transfer coefficient respectively. It is shown that the solutions for differentmare dependent and a transformation group has been found, through which one can get solution for anymprovided solution for a particular value ofmis known. The effects of Darcy number on skin friction and rate of heat transfer are analyzed.

scholarly journals A new multifield finite element method in steady state heat analysis

2005 ◽  
Vol 9 (1) ◽  
pp. 111-130 ◽  
Author(s):  
Dubravka Mijuca ◽  
Ana Ziberna ◽  
Bojan Medjo
Keyword(s):  
Finite Element Method ◽  
Heat Flux ◽  
Finite Element ◽  
Thermal Loading ◽  
Mixed Finite Element ◽  
Finite Element Approach ◽  
Benchmark Tests ◽  
Element Approach ◽  
Steady State Heat ◽  
Solid Bodies

A new original primal-mixed finite element approach and related hexahedral finite element HC:T/q for the analysis of behavior of solid bodies under thermal loading is presented. The essential contributions of the present approach is the treatment of temperature and heat flux as fundamental variables that are simultaneously calculated, as well as capability to introduce initial and prescribed temperature and heal flux. In order to minimize accuracy error and enable introductions afflux constraints, the tensorial character of the present finite element equations is fully respected. The proposed finite element is subjected to some standard benchmark tests in order to test convergence of the results, which enlighten the effectiveness and reliability of the approach proposed.

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