Isogeometric Analysis of Heat Transfer in Fluids

2011 ◽  
Vol 105-107 ◽  
pp. 2174-2178
Author(s):  
Wen Lei Zhang ◽  
Rong Mo ◽  
Neng Wan ◽  
Qin Zhang
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Numerical Simulation ◽  
Partial Differential Equation ◽  
Integral Equation ◽  
Isogeometric Analysis ◽  
Two Dimensions ◽  
Programming Algorithm ◽  
Nurbs Basis Function ◽  
Numerical Formulation

This paper is devoted to the numerical simulation of heat transfer in fluids. We develop a numerical formulation based on isogeometric analysis that permits straightforward construction of higher order smooth NURBS approximation. Firstly, we introduce the partial differential equation (PDE) which servers as basis for the whole paper. Then, we introduce Lagrange multiplier method to deal with essentional boundary contions accroding to the nature of NURBS basis function. After getting the Equivalent integral equation, the isogeometric solving format is established based on the idea of isoparametric which is the necessary fundamentals of Isogeometric Analysis. We also discuss the programming algorithm of isogeometric analysis based on Matlab. Finally, a numerical example in two dimensions is presented that illustrate the effectiveness and robustness of our approach.

scholarly journals The study of the numerical diffusion in computational calculation

2020 ◽  
Vol 310 ◽  
pp. 00039
Author(s):  
Kamila Kotrasova ◽  
Vladimira Michalcova
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Numerical Simulation ◽  
Continuity Equation ◽  
Cfd Simulation ◽  
Flow Process ◽  
Ansys Fluent ◽  
Numerical Diffusion ◽  
Mesh Density ◽  
Computational Calculation

The numerical simulation of flow process and heat transfer phenomena demands the solution of continuous differential equation and energy-conservation equations coupled with the continuity equation. The choosing of computation parameters in numerical simulation of computation domain have influence on accuracy of obtained results. The choose parameters, as mesh density, mesh type and computation procedures, for the numerical diffusion of computation domain were analysed and compared. The CFD simulation in ANSYS – Fluent was used for numerical simulation of 3D stational temperature flow of the computation domain.

Invariance, Conservation Laws, and Exact Solutions of the Nonlinear Cylindrical Fin Equation

2014 ◽  
Vol 69 (5-6) ◽  
pp. 195-198 ◽  
Author(s):  
Saeed M. Ali ◽  
Ashfaque H. Bokhari ◽  
Fiazuddin D. Zaman ◽  
Abdul H. Kara
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Exchange ◽  
Thermal Diffusivity ◽  
Conservation Laws ◽  
Cylindrical Shape ◽  
Method Of Multipliers ◽  
Double Reduction ◽  
Temperature Dependent

Fins are heat exchange surfaces which are used widely in industry. The partial differential equation arising from heat transfer in a fin of cylindrical shape with temperature dependent thermal diffusivity are studied. The method of multipliers and invariance of the differential equations is employed to obtain conservation laws and perform double reduction.

Numerical Simulation of Orientation Distribution on Fibers Suspensions in Planar Extensional Field

2013 ◽  
Vol 395-396 ◽  
pp. 1174-1178
Author(s):  
Pei Fang Luo ◽  
Zan Huang
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Fiber Orientation ◽  
Extensional Flow ◽  
Orientation Distribution ◽  
Specific Form ◽  
Fiber Orientation Distribution ◽  
Planar Extensional Flow

A mathematical model of evolution process is adopted to simulate orientation distribution of fibers suspensions in planar extensional flow, i.e., specific form of Fokker-Plank partial differential equation and Jeffery equation. The analytical solution of differential equation on forecast fiber orientation distribution is deduced.

scholarly journals A Numerical Well-Balanced Scheme for One-Dimensional Heat Transfer in Longitudinal Triangular Fins

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
I. Rusagara ◽  
C. Harley
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Nonlinear Partial Differential Equation ◽  
Transfer Coefficients ◽  
Partial Differential ◽  
One Dimensional ◽  
Heat Transfer Coefficients ◽  
Highly Nonlinear ◽  
Triangular Fin

The temperature profile for fins with temperature-dependent thermal conductivity and heat transfer coefficients will be considered. Assuming such forms for these coefficients leads to a highly nonlinear partial differential equation (PDE) which cannot easily be solved analytically. We establish a numerical balance rule which can assist in getting a well-balanced numerical scheme. When coupled with the zero-flux condition, this scheme can be used to solve this nonlinear partial differential equation (PDE) modelling the temperature distribution in a one-dimensional longitudinal triangular fin without requiring any additional assumptions or simplifications of the fin profile.

scholarly journals Analytic transient solutions of a cylindrical heat equation

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2617-2628
Author(s):  
K.Y. Kung ◽  
Man-Feng Gong ◽  
H.M. Srivastava ◽  
Shy-Der Lin
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Conduction ◽  
Heat Equation ◽  
Heat Conduction Equation ◽  
Separation Of Variables ◽  
Transient Heat Conduction ◽  
Transient Temperature ◽  
Transient Solutions

The principles of superposition and separation of variables are used here in order to investigate the analytical solutions of a certain transient heat conduction equation. The structure of the transient temperature appropriations and the heat-transfer distributions are summed up for a straight mix of the results by means of the Fourier-Bessel arrangement of the exponential type for the investigated partial differential equation.

scholarly journals A boundary integral equation method for the numerical solution of a second order elliptic equation with variable coefficients

1980 ◽  
Vol 22 (2) ◽  
pp. 218-228 ◽  
Author(s):  
D. L. Clements
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Integral Equation ◽  
Elliptic Partial Differential Equation ◽  
Integral Equation Method ◽  
Variable Coefficients ◽  
Boundary Integral ◽  
Second Order ◽  
Order Elliptic Equation ◽  
Second Order Elliptic Equation

AbstractA method is derived for the solution of boundary value problems governed by a second-order elliptic partial differential equation with variable coefficients. The method is obtained by expressing the solution to a particular problem in terms of an integral taken round the boundary of the region under consideration.

A Two-Temperature Model of the Regenerative Solid-Vapor Heat Pump

1994 ◽  
Vol 116 (4) ◽  
pp. 297-304 ◽  
Author(s):  
T. A. Fuller ◽  
W. J. Wepfer ◽  
S. V. Shelton ◽  
M. W. Ellis
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Pump ◽  
Flow Direction ◽  
Time And Space ◽  
Partial Differential ◽  
Thermodynamic Performance ◽  
Heat Regeneration ◽  
Two Temperature

A thermally driven heat pump using a solid/vapor adsorption/desorption compression process is thermodynamically analyzed. Heat regeneration between the two adsorbent beds is accomplished through the use of a circulating heat transfer (HX) fluid. Effective heat regeneration and system performance requires that steep thermal profiles or waves be established in the beds along the path of the HX-fluid flow direction. Previous studies by Shelton, Wepfer, and Miles have used square and ramp profiles to approximate the temperature profiles in the adsorbent beds, which, in turn, enable the thermodynamic performance of the heat pump to be computed. In this study, an integrated heat transfer and thermodynamic model is described. The beds are modeled using a two-temperature approach. A partial differential equation for the lumped adsorbent bed and tube is developed to represent the bed temperature as a function of time and space (along the flow direction), while a second partial differential equation is developed for the heat transfer fluid to represent the fluid temperature as a function of time and space (along the flow direction). The resulting differential equations are nonlinear due to pressure and temperature-dependent coefficients. Energy and mass balances are made at each time step to compute the bed pressure, mass, adsorption level, and energy changes that occur during the adsorption and desorption process. Using these results, the thermodynamic performance of the heat pump is calculated. Results showing the heat pump’s performance and capacity as a function of the four major dimensionless groups, DR, Pe, Bi, and KAr, are presented.

scholarly journals Modelling heat transfer in heterogeneous media using fractional calculus

2013 ◽  
Vol 371 (1990) ◽  
pp. 20120146 ◽  
Author(s):  
Dominik Sierociuk ◽  
Andrzej Dzieliński ◽  
Grzegorz Sarwas ◽  
Ivo Petras ◽  
Igor Podlubny ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Flux ◽  
Transfer Function ◽  
Transfer Process ◽  
Heterogeneous Media ◽  
Heat Transfer Process ◽  
Order Partial Differential Equation ◽  
Partial Differential

This paper presents the results of modelling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in a solid material (beam) can be described by an integer order partial differential equation. However, in heterogeneous media, it can be described by a sub- or hyperdiffusion equation which results in a fractional order partial differential equation. Taking into consideration that part of the heat flux is dispersed into the neighbouring environment we additionally modify the main relation between heat flux and the temperature, and we obtain in this case the heat transfer equation in a new form. This leads to the transfer function that describes the dependency between the heat flux at the beginning of the beam and the temperature at a given distance. This article also presents the experimental results of modelling real plant in the frequency domain based on the obtained transfer function.

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