Thermal Contact Between Cylindrical Surfaces

Consider the problem of the steady heat flux in the complex plate with the width 0.5(dn-d1) and thermal conductivity coefficients ki and , whose first and last surfaces maintain temperatures t1 and tn+1 , and between the sheets with numbers m-1 and m+1, there is the thermal contact with specific resistance Rm (see figure).

 

The temperature change and thermal flux, normalized to the length of the cylinder, along the width of the complex plate, which consists of n sheets with widths h1, h2, ..., hn and thermal conductivity coefficients k1, k2,... kn, respectively, for each sheet are fi, i=1,2,..., n and are determined using the following formula:

Let all sheets, save two ones, are in the ideal thermal contact along the boundary surfaces, and put thermal resistance between sheets numbered m-1 and m+1; then the thermal flux will be uninterrupted at the transition from one area to the other and, in this case, it will be the same in any point (i.e.f1=f2=...=fn=fl ). The temperature change between the opposite surfaces of the entire complex plate will be equal to the sum of temperature changes in separate sheets:

Hence,
,

Assume the following initial data: number of sheets n=2 , diameters d1, d2, d3 of each sheet equal 350; 380; and 420 mm, respectively. Applied temperatures t1and t4 equal 473K and 273K respectively

Thermal conductivity coefficients are:

Thermal resistance of the contact (it is approximately equivalent to the thermal resistance of the cylindrical air layer with the width 0.05 mm and

Thus,

,
,


By calculation with the help of AutoFEM Analysis, we have obtained the following results (for the lower and upper sides of the contact, respectively):

Table 1*

Table 2*

 

 

*The results of numerical tests depend on the finite element mesh and may differ slightly from those given in the table.

 

Read more about AutoFEM Thermal Analysis

autofem.com

 

Return to contents