Solution of the Heat Equation for a Couple in Bed with a Cat

t

0.01

δ

0.15

k

6

show cat

show couple

This Demonstration solves the heat equation for two people and a cat lying in bed. The model assumes that the couple are linear heat sources, that the cat is a point source, and that both are constant and of the same magnitude (even though cats are slightly warmer than humans). The bed has no heat flow at the borders (it is zero at all times) and extends over a square area of 2m by 2m. The people are placed at positions

x

1

=5

and

x

2

=1.5

, with a height of 1.7 m lying between

y

1

=0.15

and

y

2

=1.75

, and the cat is placed between the feet of the people. The plots show the temperature distribution as a function of time. Only

k

terms in the solution are considered, with a spatial discretization of width

δ

.