Two-Dimensional Transient Temperature Distribution in Cylindrical Bodies With Pulsating Time and Space-Dependent Boundary Conditions

1974 ◽  
Vol 96 (3) ◽  
pp. 300-306 ◽  
Author(s):  
J. A. Copley ◽  
W. C. Thomas
Keyword(s):  
Heat Flux ◽  
Boundary Conditions ◽  
Analytical Techniques ◽  
Transient Temperature ◽  
Two Dimensional ◽  
Transient Temperature Distribution ◽  
Gun Barrel ◽  
External Cooling ◽  
Periodic Heat ◽  
Good Agreement

The two-dimensional conduction equation is solved for a hollow cylinder subjected to a series of heat flux pulses on the inner boundary. The periodic heat flux is represented by an exponentially decreasing pulse with a spatial distribution of peak magnitude. The analytical techniques and representation of the boundary conditions apply to different situations involving pulsating boundary conditions. An application to the gun barrel heating problem is given. Calculated bore surface and internal temperature histories are in good agreement with experimental data. During the actual firing time in rapidly-firing guns, results show that external cooling is generally ineffective for controlling barrel bore surface temperature.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

Modeling of Mixed Convection Between Vertical Parallel Plates in Electric Equipment Immersed in High-Pr Liquids

2019 ◽  
Vol 11 (5) ◽  
Author(s):  
Thomas B. Gradinger ◽  
T. Laneryd
Keyword(s):  
Heat Flux ◽  
Reynolds Number ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Parallel Plates ◽  
One Dimensional ◽  
Electric Equipment

Natural-convection cooling with oil or other fluids of high Prandtl number plays an important role in many technical applications such as transformers or other electric equipment. For design and optimization, one-dimensional (1D) flow models are of great value. A standard configuration in such models is flow between vertical parallel plates. Accurate modeling of heat transfer, buoyancy, and pressure drop for this configuration is therefore of high importance but gets challenging as the influence of buoyancy rises. For increasing ratio of Grashof to Reynolds number, the accuracy of one-dimensional models based on the locally forced-flow assumption drops. In the present work, buoyancy corrections for use in one-dimensional models are developed and verified. Based on two-dimensional (2D) simulations of buoyant flow using finite-element solver COMSOL Multiphysics, corrections are derived for the local Nusselt number, the local friction coefficient, and a parameter relating velocity-weighted and volumetric mean temperature. The corrections are expressed in terms of the ratio of local Grashof to Reynolds number and a normalized distance from the channel inlet, both readily available in a one-dimensional model. The corrections universally apply to constant wall temperature, constant wall heat flux, and mixed boundary conditions. The developed correlations are tested against two-dimensional simulations for a case of mixed boundary conditions and are found to yield high accuracy in temperature, wall heat flux, and wall shear stress. An application example of a natural-convection loop with two finned heat exchangers shows the influence on mass-flow rate and top-to-bottom temperature difference.

Transient temperature distribution in insulated pavements—predictions vs. observations

1970 ◽  
Vol 7 (3) ◽  
pp. 275-284 ◽  
Author(s):  
D. M. Ho ◽  
M. E. Harr ◽  
G. A. Leonards
Keyword(s):  
Transient Temperature ◽  
Site Conditions ◽  
Two Dimensional ◽  
Ambient Conditions ◽  
Layered Systems ◽  
Temperature Variations ◽  
Finite Difference Technique ◽  
Transient Temperature Distribution ◽  
Temperature Distributions ◽  
Number Of Layers

Based on a finite difference technique, computer programs have been developed whereby temperature variations in layered systems as a function of position and time may be computed under conditions of both one- and two-dimensional heat flow by conduction. No limitations are imposed on the number of layers, or on the form of the initial and boundary temperature conditions. Variations in thermal properties of the materials with temperature and location, and the non-linear relation between amount of water frozen as a function of temperature, are directly taken into account. Comparison of predictions with actual measurements demonstrate that accurate forecasts of temperature distributions as a function of time can be made when prevailing ambient conditions are known. Even if the site conditions can be evaluated only approximately sufficiently reliable predictions can be made for design purposes.

scholarly journals Group method analysis of two-dimensional plate in heat flux

2003 ◽  
Vol 2003 (22) ◽  
pp. 1369-1382
Author(s):  
Mina B. Abd-el-Malek ◽  
Fayez H. Michael ◽  
Samy M. A. El-Mansi
Keyword(s):  
Differential Equation ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Linear Ordinary Differential Equation ◽  
Group Method ◽  
Theoretic Approach ◽  
Polynomial Functions ◽  
Two Dimensional ◽  
General Shape ◽  
Method Analysis

The group transformation theoretic approach is applied to present an analytic study of the temperature distribution in a triangular plate,Ω, placed in the field of heat flux, along one boundary, in a form of polynomial functions of any degree “n.” The Laplace's equation has been reduced to second-order linear ordinary differential equation with an appropriate boundary conditions. Exact solution has been obtained for general shape ofΩand different boundary conditions.

Polynomial Based Elasticity Solutions of Beams and their Numerical Validation: A Review

2011 ◽  
Vol 311-313 ◽  
pp. 2315-2321
Author(s):  
Sebin Jose ◽  
Sunil Bhat
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Two Dimensional ◽  
Element Analysis ◽  
Stress Problem ◽  
Elasticity Solutions ◽  
Harmonic Equation ◽  
Complex Cases ◽  
Good Agreement

Solution of two-dimensional stress problem is reduced to integration of bi-harmonic equation[1].A polynomial is chosen as Airy’s stress function.Constants of the polynomial[2] are found by fulfilling the boundary conditions. Stress solutions are obtained from.The paper presents polynomial based stress solutions of beams for complex cases involving offset loads and other combinations with offset loads.The results are compared with those obtained from finite element analysis[3] and conventional methods.The results are in good agreement with each other.

Transient Heat Transfer in a Partially Cooled Cylindrical Rod

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Lawrence Agbezuge
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Finite Difference ◽  
Spent Nuclear Fuel ◽  
Numerical Technique ◽  
Analytical Techniques ◽  
Transient Temperature ◽  
Finite Element Software ◽  
Transient Temperature Distribution ◽  
Nuclear Fuel Rods

Finite element and finite difference solutions are obtained for transient temperature distribution in a partially cooled cylindrical rod that generates heat at a uniform rate. A portion of the rod is immersed in a coolant reservoir that is maintained at constant temperature, and the exposed portion of the rod is cooled by convective heat transfer. Because thermal conductivity of the rod is temperature dependent, the governing partial differential equation is nonlinear. The analytical techniques utilized in solving the problem could be applied to analyzing the cooling of spent nuclear fuel rods. The finite difference method used to solve the problem utilizes an implicit formulation of the governing equation, and a numerical technique for handling the nonlinear terms. Validation of the numerical solution is obtained by comparing the results at a specified time against those generated by a commercial finite element software package. The computer model for the problem was used to estimate heat generation rates that could initiate meltdown of a fuel rod.

Numerical Analysis of Transient Temperature Distribution Inside a Current Transformer

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Jie Cui ◽  
Mahesh Nadkarni ◽  
Satish M. Mahajan ◽  
Diego M. Robalino
Keyword(s):  
Temperature Distribution ◽  
Numerical Analysis ◽  
Performance Monitoring ◽  
Electrical Energy ◽  
Current Transformer ◽  
Transient Temperature ◽  
Transient Temperature Distribution ◽  
And Performance ◽  
A Current ◽  
Good Agreement

Current transformer (CT) is a device that transfers the electrical energy from one circuit to another through a shared magnetic field. In a CT, heat is generated in the core, tank wall, and primary and secondary windings. The performance of a CT is well indicated by the temperature distribution inside it. In this study, numerical analysis was performed to predict the temperature distribution inside the CT at every instant under different load conditions. It was found that the numerical results obtained were in good agreement with the experimental measurements. Thus, it was concluded that the numerical method can be a useful tool in CT design and performance monitoring.

Sign in / Sign up

Export Citation Format

Share Document