TY - JOUR

T1 - Heating long pipes

AU - Betsakos, Dimitrios

AU - Solynin, Alexander

N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.

PY - 2021/1/8

Y1 - 2021/1/8

N2 - In this paper, we study the steady-state distribution of heat on long pipes in R3 heated along some regions of their surfaces. In particular, we prove that, if the pipe P={(x,y,z):x2+y2<1} is heated along its surface belt B(a)={(x,y,z):x2+y2=1,-a 0 , then the temperature in its cross-sections Dc={(x,y,z)∈P:z=c} is increasing in the radial direction for all c in the interval [- a, a].

AB - In this paper, we study the steady-state distribution of heat on long pipes in R3 heated along some regions of their surfaces. In particular, we prove that, if the pipe P={(x,y,z):x2+y2<1} is heated along its surface belt B(a)={(x,y,z):x2+y2=1,-a 0 , then the temperature in its cross-sections Dc={(x,y,z)∈P:z=c} is increasing in the radial direction for all c in the interval [- a, a].

U2 - 10.1007/s13324-020-00474-0

DO - 10.1007/s13324-020-00474-0

M3 - Article

SN - 1664-2368

SP - Paper No. 40, 35 pp.

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

ER -