Applications of Transient Conduction

Thermal Capacitance in Heat Transfer Analysis –Lesson 3

2

Stent Cooling in Different Quenchants

• A stent is used in a medical procedure to open blocked blood vessels‐ The stent, a tiny tube, is inserted into the artery to restore blood flow

‐ They are made of either metal or plastic

‐ A commonly used material for stents is Nitinol (Ni – Ti Alloy)

• The manufacturing process includes annealing followed by quenching to achieve a specific shape and properties‐ The annealing process holds the stent at high temperature for a specified

time

‐ The quenching process rapidly cools the stent

• Controlling the cooling rate is very important to tailor material properties‐ Too slow cooling can allow thermodynamics forces to change the

microstructure of the metal and weaken it

‐ Too fast cooling can cause brittleness, temperature-induced stresses and cracks

3

Stent Cooling – Problem Description

• Starting with a stent model that has been annealed, we want to understand the factors involved in quenching it using transient thermal analysis

‐ The stent has been annealed at 400 ℃ and it needs to be cooled down to room temperature at 20 ℃

‐ For the quenching process, two approaches are used – quenching in water or forced air

‐ The difference between these two quenchants is the convection film coefficient

• The goal of this simulation is to:

‐ Understand the process of heat transfer and its time-dependence

‐ Understand the factors affecting the rate of heat transfer

‐ Learn how to expedite simulation by using cyclic symmetry

4

Stent Cooling - Materials

• Here, the stent material is isotropic and has constant thermal conductivity‐ To model different quenchants, different convection film coefficients are used in each case

Water Cooling: Convection Film Coefficient = 0.002 W/mm2 ℃

Nitinol:Density = 6450 kg/m3

Thermal Conductivity = 18 W/(m ℃) Specific Heat = 200 J/(kg ℃)

Forced Air Cooling:Convection Film Coefficient = 0.0003 W/mm2 ℃

5

Stent Cooling – Boundary Conditions

In this simulation, the following boundary conditions are applied:

• Initial temperature = 400 ℃

• A cyclic boundary condition is imposed on one quarter of the stent geometry to speed up simulation time

• The following convection boundary conditions are applied to all stent faces except cyclic boundaries:‐ Ambient temperature = 20 ℃

‐ For quenching in water: convection film coefficient is 0.002 W/mm2℃

‐ For quenching in forced air : convection film coefficient is 0.0003 W/mm2 ℃

6

Stent Cooling – Results and Discussion

Let us analyze the results of this simulation at 0.09 s time

• For water cooling the maximum temperature is around 49 ℃

• For forced air cooling the maximum temperature is around 234 ℃

7

Stent Cooling – Results and Discussion

Comparing the temperature graph for both quenchants:

For a given stent size, water cooling is almost 4 times faster than forced air cooling

• For water cooling it takes around 0.25 s to cool down to 20 ℃

• For forced air cooling it takes almost 1 s to cool down to 20 ℃

Water Cooling Forced Air Cooling

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Tem

pera

ture

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Time [s]

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Tem

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8

An Electric Iron

An electric iron consists of a heating element/coil which converts electrical energy to heat energy:

• When switched on, heat energy from the heating element is conducted to the adjacent bodies

• The heated metal base of the electric iron conducts heat to the item to be ironed

• The handle is made of insulating material; it will not be modeled for analysis as we do not expect a large temperature change in the handle

9

An Electric Iron

Let’s conduct a transient thermal analysis of a simple electric iron model

• The iron is at an initial temperature of 22 ℃

• The heat energy is generated in the heating element and then transferred to the other bodies through conduction

• Parts of the iron are modeled as one geometry and are assumed to have perfect contact without leaks, meaning that the heat is purely transferred by conduction in the materials

• The outside surface of the iron keeps transferring heat to the environment by convection

22 °C

10

An Electric Iron: Boundary Conditions

In the simulation, the boundary condition for the problem is simplified as follows:

• Internal heat generation applied to the heating element

• Convection boundary condition for all the outside surfaces

Internal heat generation being

applied to the heating element

Convection boundary condition applied

to the outer faces

Convection will be discussed in later sections of this course. Here we can consider convection to be a

boundary condition to dissipate heat from a surface.

11

An Electric Iron: Material Properties

In this simulation, materials are all isotropic and have constant material properties (density ρ, thermal conductivity k, specific heat c).

Part ρ (kg/m3) k (W/m. 0C) C (J/kg.0C)

PBT Plastic 1340 0.28 1450

ABS Plastic 1040 0.258 1720

Nickel 8900 90 444

Structural Steel 7850 60.5 434

Handle

(ABS Plastic)

Heating

Element

(Nickel)

Middle Layer

(Structural

Steel)

Body

(PBT Plastic)

Metal Base

(Structural Steel)

12

An Electric Iron: Results and Discussion

Let’s have a look at the results from this simulation.

• At the start, after 1 second, the temperature starts increasing around the heating element. After 100 seconds, the temperature rises to ~ 200 ℃.

13

An Electric Iron: Results and Discussion (cont.)

• A change in temperature of the bodies is seen with respect to time, which was not seen in the steady-state analysis.

• You can try to model the handle and see the temperature in the insulating material of the handle.

• In the graph below, the temperature is rising continuously over 100 seconds. In the real world, an electric iron has a thermostat that cuts off the circuit to avoid further heating after reaching a certain temperature. You can also let the electric iron cool to room temperature and see how much time it takes to do so. This can be done by defining an additional step consisting of a large time period without internal heat generation to see when the temperature cools down to room temperature.

Maximum

Average

Minimum