How to Calculate Temperature Distribution in a Composite Cylinder?

In summary, the problem involves finding the temperature at any given time inside a cylinder with three sections made of different materials. The cylinder is subjected to a heat source at the top and a heat sink at the bottom, and the overall heat transfer coefficient, power supplied to the heater, length, diameter, and cross-sectional area are known. The equations involved are the 3D heat conduction equation and the formula for equivalent thermal resistance. To solve the problem, a coordinate system must be chosen and the boundary conditions must be written in that system before solving the equations.
  • #1
Tezzador
2
0

Homework Statement



I have a cylinder that's made up of three sections, brass, stainless steel, brass. There's a heat source at the top and a heat sink at the bottom. I know the overall heat transfer coefficient, power supplied to the heater, length, diameter, cross-sectional area of the cylinder. I also know the temperature of the heat sink, heat source and the average surface temperature. How do I go about it roughly?

Homework Equations



q" = -k * (dT/dx)

q = A * q" = (k/L) * A * (TL - TR)

L/Keq = L1/k1 + L2/k2 + L3/k3

The Attempt at a Solution



Can't figure it out.
 
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  • #2
Hi Tezzador, welcome to PF!:smile:

What exactly is the question asking you to find?

Assuming you are asked to find the temperature at any given time everywhere inside the cylinder, you'll need to solve the 3D heat conduction equation, subject to the boundary conditions you are given. Start by choosing a coordinate system (I recommend cylindrical coordinates for obvious reasons!)...write your boundary conditions (temperature of the heat sink/source and average surface temp) and your heat conduction equation in that coordinate system, and then solve away!
 

FAQ: How to Calculate Temperature Distribution in a Composite Cylinder?

What is heat transfer via conduction?

Heat transfer via conduction is the transfer of thermal energy between two objects in direct contact with each other. This transfer occurs due to the difference in temperature between the two objects, with heat flowing from the warmer object to the cooler one.

How does conduction differ from convection and radiation?

Conduction differs from convection and radiation as it does not require the movement of matter or the use of electromagnetic waves to transfer heat. Instead, heat transfer via conduction occurs through direct contact between two objects.

What are some examples of heat transfer via conduction?

Some examples of heat transfer via conduction include touching a hot stove, holding a cold drink, or cooking food in a pot on a stove. These all involve the transfer of heat through direct contact between objects.

How does the rate of heat transfer via conduction change with different materials?

The rate of heat transfer via conduction depends on the thermal conductivity of the materials involved. Materials with higher thermal conductivity, such as metals, transfer heat more quickly than materials with lower thermal conductivity, such as wood or plastic.

How do we measure heat transfer via conduction?

The rate of heat transfer via conduction can be measured using the thermal conductivity of the materials involved and the temperature difference between them. The thermal conductivity is a material property that describes how easily heat can flow through a material.

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