# OS-T: 1090: Linear Transient Heat Transfer Analysis of an Extended Surface Heat Transfer Fin

This tutorial outlines the procedure to perform a linear transient heat transfer analysis on a steel extended-surface heat transfer fin attached to the outer surface of a system generating heat flux (Example: IC engine). The extended surface heat transfer fin analyzed in this tutorial is one of many from an array of such fins connected to the system.

The fins draw heat away from the outer surface of the system and dissipate it to the surrounding air. The process of heat transfer out of the fin depends upon the flow of air around the fin (Free or forced convection). In the current tutorial, the focus is on transient heat transfer through heat flux loading and free convection dissipation.

An extended surface heat transfer fin made of steel is illustrated in Figure 1. To meet certain structural design requirements, the fin is bent at 90° at approximately a quarter of its length.

^{2}is applied to the face connected to the outer surface of the system. An ambient temperature of 25°C is assumed and all material properties are assumed to remain constant with temperature and time. Free (Natural) convection is assumed over the entire surface of the material, wherein heat transfer between the surface of the fin and the surrounding air occurs due to a complex mechanism of density differences as a result of temperature gradients.

- The latest version of HyperMesh, HyperView and OptiStruct software installations. Transient heat transfer analysis is available only in HyperMesh version-12.0.110, HyperView version-12.0.110 and OptiStruct version-12.0.202 and later.
- The heat_transfer_fin.fem solver deck is available from the optistruct.zip file. Refer to Access the Model Files.

Linear transient heat transfer analysis can be used to calculate the temperature distribution in a system with respect to time. The applied thermal loads can either be time-dependent or time-invariant; transient thermal analysis is used to capture the thermal behavior of a system over a specific period in time.

- $$\left[C\right]$$
- Heat capacity matrix
- $$\left[K\right]$$
- Conductivity matrix
- $$\left[H\right]$$
- Boundary convection matrix due to free convection
- $$\left\{\stackrel{.}{T}\right\}$$
- Temperature derivative with respect to time
- $$\left\{\stackrel{.}{T}\right\}$$
- Unknown nodal temperature
- $$\left\{p\right\}$$
- Thermal loading vector

The differential equation (Equation 1) is solved to find nodal temperature $$\left\{\stackrel{.}{T}\right\}$$ at the specified time steps. The difference between Equation 1 and the steady-state heat transfer equation is the term, $$\left[C\right]\left\{\stackrel{.}{T}\right\}$$ that captures the transient nature of the analysis.

Steady-state heat transfer analysis, generally, is sufficient for a wide variety of applications. However, in situations where the system properties vary significantly over time the transient nature of heat transfer must be considered. Some examples are the relatively slow heating up of airplane gas turbine compressor disks compared to the turbine casing leading to aerodynamic issues during takeoff or the analysis of the time taken for the onset of frostbite in fingers or toes.

## Launch HyperMesh and Set the OptiStruct User Profile

## Import the Model

## Set Up the Model

### Create Thermal Material and Property

### Link Thermal Material and Property to the Structure

### Create Transient Heat Transfer Analysis Time Steps

### Create Transient Heat Transfer Analysis Initial Conditions

## Apply Ambient Temperature Boundary Conditions

Ambient temperature thermal boundary conditions is applied on the model by creating specific load collectors for each. The ambient temperature is controlled using an SPCD entry, as this will allow an ambient temperature variation over time to help mimic such physical requirements (if any).

### Create a Time-variant Ambient Temperature

Checkpoint

## Apply Heat Flux Load

Ambient temperature thermal boundary conditions have been assigned to the model and heat flux
load from the outer surface of the engine (to which the fin is attached) is applied
on the model. A time-varying heat flux load of 0 to 0.1 W/mm^{2} from 0 to
500 seconds is used for the analysis of this fin. This load is applied on the model
by creating specific load collectors for the corresponding
TLOAD1, QBDY1 and TABLED1
entries similar to the procedure used for the ambient temperature SPCD
definition.

### Create a Time-variant Linearly Increasing Heat Flux Load

Checkpoint

The QBDY1 flux load and its corresponding table are linked to the previously created TLOAD1 entry.

## Add Free Convection

Free convection is assigned in a similar manner to the procedure used for the creation of the conduction interface. Free convection is, however, automatically assigned to all heat transfer subcases and the PCONV and CONV entries should refer to the material, steel, and the ambient temperature. The ambient temperature calculates the amount of heat transferred through free convection.

### Create Surface Elements for Free Convection

### Combine TLOAD1 Entries into a DLOAD Entry

### Create a Transient Heat Transfer Load Step

## Submit the Job

## View Results

Checkpoint

In Figure 26, this is the grid point temperature plot after
500 seconds. The system is input a linearly increasing heat flux from 0 to 0.1
W/mm^{2} from 0 to 500 seconds respectively. Therefore, a physical
correlation can be the effect of starting an IC engine to full capacity wherein
the flux transmitted to the outer surface linearly increases with time. Note
that the flux patterns in actuality may be different and may fluctuate based on
the duration of the power cycles. The maximum temperature of 81.3°C predictably
occurs at the elements closest to the heat flux loading site and the minimum
temperature of 29.5°C occurs at elements farthest from the heat source.