Modeling a steady state heat distribution in 2D
in Assignments
(10 pts)
For this problem, you're going to use our 2D Steady State Explorer to model the steady state distribution throughout a long, thin domain. You can get your personal version here.
Comments
With no external heat source this is what my bar looks like in a steady state. at the vertex denoted by (30,0) the heat is about .947 in the steady state
The temperature at the lower right end of the bar looks to be roughly 0.9467 in the steady state.
With $\kappa = 0$ and $f = 0$, the steady state temperature at the lower right corner of the bar is 0.84905.
The temperature in the lower right hand corner of the bar at steady state is roughly 0.91361.
Given the conditions of my problem with $\kappa=0$ and $f=0$ the temperature at the lower right hand corner of the bar at steady state is 0.75700.
With my unique conditions I formed a polygon where $\kappa=0$ and $f=0$, meaning there was no external heat source present and no signs of growth/decay. After reaching steady state the temperature in the lower right hand corner of the polygon was $u=0.87677$.
For my unique conditions, $\kappa = 0$ and $f = 0$. The three sides on the lower left, sticking out of the bar, are set to temperature zero. The side at the very top of the rectangle on the upper right is set to temperature 1. The remaining sides are insulated. At the steady state for the heat distribution, the temperature for the lower right corner of the bar is $u = 0.80488$.
The temperature in the lower right corner of the bar is $0.74727$.
For our conditions, $k=0$ and $f=0$, the steady-state of this polygon is shown above. The temperature in the lower right corner, at about $(31,1)$, is approximately $.96731.$
For my conditions, $k=0$ and $f=0$, the steady-state of my polygon is shown below. The temperature in the lower right hand corner $(28.69,0.93)$, is approximately $u=0.92895$.
For the condition $k = 0$ and $f = 0$, the steady-state temperature of the lower right corner of the bar is $0.89962.$
Based on my assigned parameters, the temperature in the lower right corner of the bar after reaching steady-state is 0.90877.
With zero source and the boundary conditions given in my problem, the temperature at the lower right corner of the bar is $0.91330$ temperature units.
Given my conditions, the temperature in the lower right hand corner is 0.90549
The steady-state temperature of the bar at the lower right corner is approximately $0.909$ [temperature units]
The temperature at the lower right corner of the bar is $0.89869$.
The temperature at the lower right corner is approximately 0.806 at a steady state.