Non-Uniform Temperature Distributions

EXPORTS

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Non-Uniform Temperature Distributions

Overview

A temperature distribution property allows for non-uniform temperature distributions over a surface. You can access it via the Temperature Distribution tab in the Define|Apply Properties dialog. The surface shapes compatible with this feature are rectangular (A plane with a rectangular boundary), circular (A plane with a circular boundary), and cylindrical (The curved side of a cylinder, with each end perpendicular to the cylinder’s axis). The distribution information is stored in an ASCII file, and can be defined by: a two dimensional array of points along the surface, with bilinear interpolation between the given points; or a polynomial expression, up to the fifth order, with user-defined coefficients.

Distribution Types

There are three possible shapes – rectangular, circular, and cylindrical – and two ways to define temperature values along the surfaces – interpolating temperatures between defined points, or using a set of equations to relate the temperature. This makes for six types of non-uniform temperature distributions, which are listed in the table below.

TABLE 7.6. Types of temperature distributions

Type Description

0Rectangular region, with interpolated points

1Rectangular region, with polynomial distribution

2Circular region, with interpolated points

3Circular region, with polynomial distribution

4Cylindrical region, with interpolated points

5Cylindrical region, with polynomial distribution

Rectangular Coordinates

Rectangular surfaces are defined by an X and Y coordinate system. It is easiest to talk about a three-dimensional vector space in order to visualize the arrangement of the axes. The origin of the system is one of the vertices of the rectangular surface. The Z-axis is through the origin, outward from the object and normal to the given surface. The X and Y axes are along the two edges of the rectangle adjacent to the origin, selected by following the rules for a right-handed coordinate system. This situation is illustrated below:

TracePro 5.0 User’s Manual

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Technical Reference

You can cycle the origin between the four vertices using the Next Point button, on the Temperature Distribution tab under Apply Properties. The four possible axial systems are shown below:

TracePro calculates all these vectors automatically once you define the origin.

Circular Coordinates

Circular surfaces are defined by an R and θ polar coordinate system. The origin of the system is the center of the circular surface. You must set the X-axis as the axis from which the angle θ is measured, in a counter-clockwise direction, as shown below:

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Non-Uniform Temperature Distributions

Cylindrical Coordinates

Cylindrical surfaces are defined by a Z and θ coordinate system. The origin of the system is the center of the cylinder on which the surface is set. The Z-axis is set to be the central axis of the cylinder.

You can reverse the direction of the Z-Axis by pressing the Flip Local Z button, on the Temperature Distribution tab under Apply Properties. The θ coordinate is best visualized when viewing a cross-section of the cylinder. Set the X-axis as the axis from which θ is measured, in the same way as for Circular Coordinates. The two main differences between circular coordinates and cylindrical, when viewed in this way, are that: for the slice of the cylinder, the origin is the portion of the Z-axis cutting through the given cross-section; and that R is always set as the radius of the cylinder because we need to be on the cylinder’s surface.

TracePro 5.0 User’s Manual

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