Heat Equation : Temperature Distribution on a Brass Rod

9. The temperature distribution u(x, t) in a 2-m long brass rod is governed by the problem
......

(a) Determine the solution for u(x, t).
(b) Compute the temperature at the midpoint of the rod at the end of 1 hour.
(c) Compute the time it will take for the temperature at that point to diminish to 5° C.
(d) Compute the time it will take for the temperature at that point to diminish to 1°C.

Please see the attached file for the fully formatted problems.

Consider the following problem; it can be interpreted as modeling the temperaturedistribution along a rod of length 1 with temperature decreasing along every point of the rod at a rate of bx (x the distance from the left endpoint, b a constant) while a heat source increases at each point the temperature by a rate proportional t

See attached file.
A clock driven by a brassrod pendulum loses time when the rod expands as the temperature rises. Find the error in one day.
A pendulum clock is driven by a brassrod of length Lo= 1.6 meters, pivoted at one end.
The pendulum beats perfect time when the temperature is to= 21 degrees Celsius.
If the

A brass ring of diameter 10.00 cm at 20.0 degrees C is heated and slipped over an aluminum rod of diameter 10.01 cm at 20 degrees C.
Assuming the average coefficients of linear expansion are constant,
a) to what temperature must the combination be cooled to separate the two metals?
Is that temperature attainable?
b)

(Please see the attachment for detailed problem description)
Distinguish between reversible and irreversible processes in thermodynamics. Describe the circumstances under which a) dQ = Tds and dW = -PdV.
A long cylinderical rod of radius R is attached to a source of heat at one end and its surroundings are at temperature

The heat transfer in a semi-infinite rod can be described by the following PARTIAL differential equation:
∂u/∂t = (c^2)∂^2u/∂x^2
where t is the time, x distance from the beginning of the rod and c is the material constant. Function
u(t,x) represents the temperature at the given time t and p

The base of a 2 cm X 3 cm X 20 cm long rectangular rod is kept at 175 degrees Celsius by electrically generated heat. This is known as a straight fin or longitudinal fin. The ambient air surrounding this fin is at 28 degrees Celsius and h=10 W/m^2-C. There is negligible heat loss at the tip of the rod.
1. What is the tempe

An artificial satellite in space has a panel attached to it with dimensions 20m X 25m X 3m. The panel is made of Carbon steel with a carbon content of 1.5%. In the temperature range of interest, the value of the thermal conductivity is k = 36 W/(m-°C). The panel has an artificial heating source applied to it causing it to ha

8. HeatEquation with Circular Symmetry. Assume that the temperature is circularly symmetric:
u u(r,t), where r^2 x^2 | y^2. Consider any circular annulus a ≤ r ≤ b.
a) Show that the total heat energy is r π f^b_a cpurdr.
b) Show that the flow of heat energy per unit time out of the annulus at r b is: (see attachment