| Summary: | In a real solid there are different types of defects. During sudden cooling, near cracks, there can appear high thermal stresses. In this paper, the time-fractional heat conduction equation is studied in an infinite space with an external circular crack with the interior radius <i>R</i> in the case of axial symmetry. The surfaces of a crack are exposed to the constant heat flux loading in a circular ring <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo><</mo><mi>r</mi><mo><</mo><mi>ρ</mi></mrow></semantics></math></inline-formula>. The stress intensity factor is calculated as a function of the order of time-derivative, time, and the size of a circular ring and is presented graphically.
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