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Heating long pipes
Analysis and Mathematical Physics ( IF 1.4 ) Pub Date : 2021-01-08 , DOI: 10.1007/s13324-020-00474-0
Dimitrios Betsakos , Alexander Yu. Solynin

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 \([-a, a]\).



中文翻译:

加热长管

在本文中,我们研究了沿其表面某些区域受热的\({{mathbb {R}} ^ 3 \)中长管上热量的稳态分布。特别是,我们证明,如果管道\(P = \ {(x,y,z):\,x ^ 2 + y ^ 2 <1 \} \)沿其表面带\(B(a )= \ {(x,y,z):\,x ^ 2 + y ^ 2 = 1,-a <z <a \} \)\(a> 0 \),则其交叉点处的温度对于区间c ([-a,a] \)中的所有c,截面\(D_c = \ {{x,y,z)\ in P:\,z = c \} \)沿径向方向增加。

更新日期:2021-01-10
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