Abstract
Abstract
A numerical approach employing finite element methodology is utilized to analyze the thermal behavior of a three-dimensional multilayer sphere composed of copper, single-wall, and multi-wall carbon nanotubes. The study investigates the external heat flux, temperatures within the three spherical layers, and their associated contours. Notably, this research diverges from prior studies by opting for copper, single-wall, and multiwall carbon nanotubes instead of generic metallic layers. Graphs are generated to illustrate the relationships between various effects and profiles. Analysis of temperature contours and distributions under non-uniform heat flux reveals that temperatures are more concentrated towards the center when the initial temperature is non-zero compared to scenarios where the inner surface starts at zero temperature. Temperature contours at t = 2, 5, 7, 9, 11, 13, 15, 27, 35, and 45 s with non-zero initial temperature are calculated. For non-zero initial temperature contours are drawn for t = 2, 45 s temperature contours are drawn. Temperature in radial azimuthal and tangential directions for t = 1, 1.5, 2, 2.5, 3 s and steady state are drawn. The initial temperature of the ith surface is kept at
f
i
(
r
,
θ
,
ϕ
)
,
where
r
o
≤
r
≤
r
3
,
0
≤
θ
≤
π
,
0
≤
ϕ
≤
2
π
.
It has been concluded that for zero initial temperatures after 45 s, the temperature is at
0.005
K
and Temperature contours for non-zero inner layer temperature t = 5 s shows
10.7
K
.