Transient Cooling of a Sphere in Space

1970 ◽  
Vol 92 (1) ◽  
pp. 180-182 ◽  
Author(s):  
D. L. Ayers
Keyword(s):  
Temperature Distribution ◽  
Finite Difference ◽  
Nonlinear Problem ◽  
Solid Sphere ◽  
Temperature History ◽  
Graphical Form ◽  
Transient Temperature ◽  
Uniform Temperature ◽  
Transient Temperature Distribution ◽  
Wide Range

A method is presented for determining the transient temperature distribution of a solid sphere cooling in space. The sphere is assumed initially to be at a uniform temperature and then instantaneously subjected to the radiation sink of space at time zero. This nonlinear problem was solved by using finite-difference computing techniques. Results are presented in dimensionless graphical form over a wide range of variables. This facilitates calculation of the transient temperature history at several points in the sphere.

The Transient Temperature Distribution in a Slab Subject to Thermal Radiation

1965 ◽  
Vol 87 (1) ◽  
pp. 117-130 ◽  
Author(s):  
R. D. Zerkle ◽  
J. Edward Sunderland
Keyword(s):  
Temperature Distribution ◽  
Thermal Radiation ◽  
Radiant Heat ◽  
Analog Computer ◽  
Graphical Form ◽  
Transient Temperature ◽  
Transient Temperature Distribution ◽  
Temperature Distributions ◽  
Approximate Analytical Solutions ◽  
Wide Range

The transient, one-dimensional temperature distribution is determined for a slab, insulated on one face, and subjected to thermal radiation at the other face. The slab is initially at a uniform temperature and is assumed to be homogeneous, isotropic, and opaque; the physical properties are assumed to be independent of temperature. Transient temperature distributions for both heating and cooling situations are obtained by means of a thermal-electrical analog computer. A diode limiter circuit is used to simulate the nonlinear radiant heat flux. The transient temperature distributions are presented in a dimensionless, graphical form for a wide range of variables. Approximate analytical solutions are also given which complement and extend the solution charts over ranges of parameters not covered in the charts.

Constant Temperature at the Surface of an Initially Uniform Temperature, Variable Conductivity Half Space

1971 ◽  
Vol 93 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Leonard Y. Cooper
Keyword(s):  
Temperature Distribution ◽  
Half Space ◽  
Constant Temperature ◽  
Analytic Solutions ◽  
Numerical Results ◽  
Transient Temperature ◽  
Uniform Temperature ◽  
Transient Temperature Distribution ◽  
Temperature Variable ◽  
Variable Conductivity

The transient temperature distribution resulting from a constant and uniform temperature being imposed on the surface of an initially uniform temperature, variable conductivity half space is studied. Various solution expansion ideas are discussed. These are utilized in the solution of an example problem, and the resulting approximate analytic solutions representations are compared to exact numerical results. One of these approximations is found to be superior to the others, and, in fact, it is shown to yield useful results over a range of variables where the nonlinearities of the problem are significant.

Thermal Engineering Analysis of Rubber Vulcanization and Tread Temperatures During Severe Sliding of a Tire

1999 ◽  
Vol 27 (1) ◽  
pp. 22-47 ◽  
Author(s):  
H. Sakai ◽  
K. Araki
Keyword(s):  
Temperature Distribution ◽  
Chemical Reaction ◽  
Sliding Friction ◽  
Rolling Resistance ◽  
Temperature History ◽  
Thermal Engineering ◽  
Transient Temperature ◽  
Engineering Analysis ◽  
Transient Temperature Distribution ◽  
Heating And Cooling

Abstract Tire skid marks at the scene of an accident are often used as evidence and are a very important phenomenon. However, the mechanism of this complex phenomenon has not yet been fully examined. Tires are manufactured by a chemical reaction in which rubber molecules are combined into a network structure during a process called vulcanization, in which the tire is heated in a mold. The transient temperature distribution is important in determining the state of vulcanization, but the analysis is very difficult. We treat the tire tread as a rubber slab to estimate the temperature history during heating and cooling. Then we calculate the vulcanization index using Arrhenius's equation, assuming that the rate of chemical reaction approximately doubles as the temperature increases by 10° C. Finally, we calculate the transient temperature distribution of the tread due to the heat generated by internal friction (rolling resistance of the tire), and the heat generated by sliding friction under conditions of severe cornering and braking. We investigate a criterion for modeling the occurrence of tire skid marks, assuming that skid marks are caused by exceeding the softening temperatures of the rubber and asphalt.

Transient Temperature Distribution in Round and Slab-Type Loads Heated by Electric Induction

1971 ◽  
Vol 93 (1) ◽  
pp. 110-118 ◽  
Author(s):  
Robert J. Kasper
Keyword(s):  
Temperature Distribution ◽  
Initial Distribution ◽  
Transient Temperature ◽  
Uniform Temperature ◽  
Radiation Boundary Condition ◽  
Transient Temperature Distribution ◽  
Electric Induction ◽  
Induction Process ◽  
Steel Sections ◽  
Radiation Boundary

Equations are derived for the transient temperature distribution in a round or slab-type load with a radiation boundary condition, as required for a thermal analysis of large steel sections heated for forging, by electric induction. The load is assumed to be initially at a uniform temperature and then has heat generated in it by the induction process. Initial distribution curves of the derived transient corrections are compared with the steady-state induced thermal wave shapes that would exist at various heating frequencies if not dampened by the transient correction.

Transient Temperature Distribution in Partially Filled Rotating Horizontal Cylinders

1986 ◽  
Vol 53 (2) ◽  
pp. 436-439 ◽  
Author(s):  
J. J. Blech ◽  
I. Green ◽  
J. Kopelman
Keyword(s):  
Temperature Distribution ◽  
Viscous Fluid ◽  
Initial Conditions ◽  
Outer Boundary ◽  
Rotating Cylinder ◽  
Transient Temperature ◽  
Cylinder Surface ◽  
Uniform Temperature ◽  
Transient Temperature Distribution ◽  
Horizontal Cylinders

The transient temperature distribution in an infinitely long horizontal rotating cylinder which is partially filled by a viscous fluid is calculated. Thermal boundary and initial conditions are such that the fluid starts from a uniform temperature, and that the outer boundary (cylinder surface) is isothermal at a different temperature. Nondimensional analysis shows that the problem can be fully described by a properly defined Fourier modulus and a normalized bubble eccentricity.

A method of convergence for finite difference thermal stress computation in axially symmetrical bodies

1967 ◽  
Vol 2 (4) ◽  
pp. 332-340
Author(s):  
C L Chow ◽  
R Hoyle
Keyword(s):  
Thermal Stress ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Rate Of Convergence ◽  
Thermal Load ◽  
Turbine Rotor ◽  
Transient Temperature ◽  
Rapid Rate ◽  
Transient Temperature Distribution ◽  
Stress Computation

The most general axially symmetrical thermal load is one in which a transient temperature distribution, varying axially and radially, is applied to an axially symmetrical system with an irregular axial boundary. When the thermal stress equations are applied to such a system, using the conventional Gauss-Siedel or Liebmann method, severe oscillation has been experienced making convergence impossible to achieve. The authors present in this paper a method which not only converts a diverging solution but also yields a rapid rate of convergence. This method has been successfully applied to the problem of a steam turbine rotor.

Boundary Condition Design to Heat a Moving Object at Uniform Transient Temperature Using Inverse Formulation

2004 ◽  
Vol 126 (3) ◽  
pp. 619-626 ◽  
Author(s):  
Hakan Ertu¨rk ◽  
Ofodike A. Ezekoye ◽  
John R. Howell
Keyword(s):  
Boundary Condition ◽  
Temperature Distribution ◽  
Design Problem ◽  
Manufacturing Industry ◽  
Three Dimensional ◽  
Chemical Deposition ◽  
Iterative Solution ◽  
Conveyor Belt ◽  
Temperature History ◽  
Transient Temperature

The boundary condition design of a three-dimensional furnace that heats an object moving along a conveyor belt of an assembly line is considered. A furnace of this type can be used by the manufacturing industry for applications such as industrial baking, curing of paint, annealing or manufacturing through chemical deposition. The object that is to be heated moves along the furnace as it is heated following a specified temperature history. The spatial temperature distribution on the object is kept isothermal through the whole process. The temperature distribution of the heaters of the furnace should be changed as the object moves so that the specified temperature history can be satisfied. The design problem is transient where a series of inverse problems are solved. The process furnace considered is in the shape of a rectangular tunnel where the heaters are located on the top and the design object moves along the bottom. The inverse design approach is used for the solution, which is advantageous over a traditional trial-and-error solution where an iterative solution is required for every position as the object moves. The inverse formulation of the design problem is ill-posed and involves a set of Fredholm equations of the first kind. The use of advanced solvers that are able to regularize the resulting system is essential. These include the conjugate gradient method, the truncated singular value decomposition or Tikhonov regularization, rather than an ordinary solver, like Gauss-Seidel or Gauss elimination.

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