11454

# Heat Transfer between a Bar and a Fluid Reservoir: A Coupled PDE-ODE Model

Consider a thin bar of length with initial temperature . The right end and the sides of the bar are insulated. For times , the left end is connected to a well-mixed insulated reservoir at an initial temperature . This Demonstration determines the transient temperature of the bar and the reservoir.
We use the following dimensionless variables:
is the dimensionless temperature,
is the dimensionless space coordinate,
is dimensionless time.
Here are the dimensionless equations describing the system.
For the bar:
,
with
,
and
.
For the reservoir:
,
with
.
Here and are the temperatures of the bar and reservoir,
is a mass-heat capacity ratio,
and represent the mass and heat capacities of the reservoir and the bar respectively.
The coupled system of one partial and one ordinary differential equation is solved using the built-in Mathematica function NDSolve. The temperatures of the bar and the reservoir are shown for different values of the mass heat capacity ratio and dimensionless time .

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.
 © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS
 Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX Download or upgrade to Mathematica Player 7EX I already have Mathematica Player or Mathematica 7+