Results 1 to 2 of 2

Math Help - Newton's law of cooling with multiple containers system of DE's

  1. #1
    Newbie
    Joined
    Mar 2012
    From
    Valdosta, GA
    Posts
    1

    Angry Newton's law of cooling with multiple containers system of DE's

    I've been trying to figure out how to solve the following problem:


    "A metal bar is placed in a container (call it container A) which is inside of a much larger container (call it container B), whose temperature can be assumed to be constant. Find the function for the temperature of the metal bar at time t."


    First, I represent the temperature of container A as x(t) and the metal bar as y(t). The constant temperature of container B is TB. I assume that the temperature of the bar is proportional to the temperature of container A but the temperature of container A is proportional to both TB and the temperature of the bar. Then


    dx/dt = k1(TB - x) + k2(y - x) and
    dy/dt = k3(x - y)


    I was told that I need to make a substitution to solve this, but I can't seem to take this DE down to two variables. Any help would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Mar 2009
    Posts
    31

    Re: Newton's law of cooling with multiple containers system of DE's

    Try doing
    \frac{\frac{dx}{dt}}{\frac{dy}{dt}}
    So you get:
    \frac{dx}{dy}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Newton's Law of Cooling
    Posted in the Business Math Forum
    Replies: 2
    Last Post: March 12th 2012, 12:02 PM
  2. Newton's law of cooling.
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 11th 2010, 07:01 PM
  3. Newton's Law of Cooling
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 15th 2009, 01:07 PM
  4. Newton's Law of Cooling
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 8th 2009, 06:30 PM
  5. Newton's Law of Cooling
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: February 3rd 2009, 03:58 PM

Search Tags


/mathhelpforum @mathhelpforum