Cylinders Heisler charts

The Heisler charts discussed above may be used to obtain the temperature distribution in the infinite plate of thickness 2L, in the long cylinder, or in the sphere. When a wall whose height and depth dimensions are not large compared with the thickness or a cylinder whose length is not large compared with its diameter is encountered, additional space coordinates are necessary to specify the temperature, the above charts no longer apply, and we are forced to seek another method of solution. Fortunately, it is possible to combine the solutions... 

To solve this problem we combine the solutions from the Heisler charts for an infinite cylinder and an infinite plate in accordance with the combination shown in Fig. 4-18/ For the infinite-plate problem... 

The transient temperature charts in Figs. 4-15, 4-16, and 4-17 for a large plane wall, long cylinder, and sphere were presented by M. P. Heisler in 1947 and are called Heisler charts. They were supplemented in 1961 with transient heal transfer charts by II. Grober. There are three charts associated with each geometry the first chart is to determine the temperature Tj at the center of the... 

The diffusion coefficients in solids are typically very low (on the order of 10 to 10" mVs), and thus the diffusion process usually affects a thin layer at the surface. A solid can conveniently be treated as a semi-infinite medium during transient mass diffusion regardless of its size and shape when the penetration depth is small relative to the thickness of the solid. When this is not the case, solutions for one dimensional transient mass diffusion through a plane wall, cylinder, and sphere can be obtained from the solution.s of analogous heat conduction problems using the Heisler charts or one term solutions pieseiited in Chapter 4. 

Heisler charts Aset of graphical plots used to determine the time taken for thermal penetration by heat conduction into a soUd body by heating or cooling at its surface. The plots are prepared for standard geometric shapes such as slabs, cylinders, and spheres with the Fourier number on the x-axis and a dimensionless temperature on the y-axis. The lines represent the reciprocal of the Biot number. They are named after M. P. Heisler, who com -piled them in 1947. 

Temperatures at off-centre locations within the solid body can then be obtained from a further series of charts given by Heisler (Figures 9.17-9.19) which link the desired temperature to the centre-temperature as a function of Biot number, with location within the particle as parameter (that is the distance x from the centre plane in the slab or radius in the cylinder or sphere). Additional charts are given by Heisler for the quantity of heat transferred from the particle in a given time in terms of the initial heat content of the particle. 

The basic solutions for the plate and the cylinder can be used to obtain solutions within rectangular plates, cuboids, and finite circular cylinders. The equations and the initial and boundary conditions are well known [4,11, 23, 28, 29, 38, 49, 56, 80, 87]. The solutions presented below follow the recent review of Yovanovich [151]. The Heisler [36] cooling charts for dimensionless temperature are obtained from the series solution ... 

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