Purchase Solution

Partial Differential Equations (Dirichlet Boundary Condition; Separation of Variables)

Not what you're looking for?

Ask Custom Question

Consider a thin rod of heat-conducting material with length L. Suppose that the rod is initially heated to a temperature of T uniformly throughout the tod, and is dropped into a bucket of ice water at t = 0. Suppose that the rod is everywhere insulated, except for its left end (x = 0), which is expoosed to the ice water.

(a) Write down the system of equations that describes this scenario. (You can use Dirichlet boundary condition for the left end of the rod.)

(b) Find the temperature of the rod using seperation of variables.

(c) At any given time, which part of the rod will be the warmest? Estimate when the maximum temperature of the rod will be less than 1% of T.

Purchase this Solution

Solution Summary

A PDE is investigated. The solution is detailed and well presented.

Purchase this Solution


Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.