# Temperature Propagation in a Thin Steel Rod

Temperature Propagation in a Thin Steel Rod

The temperature contour problem =-h(u-) has been recast for a "long" stainless steel 316 rod with lateral heat exchange, under the initial distributions (K) (Gaussian distribution represented by bar00 on the Demonstration chart) and (K) (represented by bar01, likewise). The factors and encode information related to the conduction and diffusion coefficients of the rod, under the parametrization =, =/, while labels the environment temperature. Particular values of m (length) and inch (perimeter) were chosen. Boundaries and environment temperatures are kept uniform and controllable in range with a maximum value of 473 K at both extremes, while the transient regime is mapped on real time for the first four hours. Factor is adjusted for an effective distribution of the external field localized around the rod's center with 10% deviation.

u

t

2

a

u

xx

u

0

u(x,0)=(12

πϵ

)-4ϵ

2

x

e

u(x,0)=300+(273-300)sin(πx/l)

a

h

c

1

h

l/ac

2

2

l

2

a

u

0

l=1

p=1