Abstract
In this paper, we study the steady-state distribution of heat on long pipes in \({\mathbb {R}}^3\) heated along some regions of their surfaces. In particular, we prove that, if the pipe \(P=\{(x,y,z):\,x^2+y^2<1\}\) is heated along its surface belt \(B(a)=\{(x,y,z):\,x^2+y^2=1,-a<z<a\}\), \(a>0\), then the temperature in its cross-sections \(D_c=\{(x,y,z)\in P:\, z=c\}\) is increasing in the radial direction for all c in the interval \([-a, a]\).
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Betsakos, D., Solynin, A.Y. Heating long pipes. Anal.Math.Phys. 11, 40 (2021). https://doi.org/10.1007/s13324-020-00474-0
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DOI: https://doi.org/10.1007/s13324-020-00474-0