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# U-shaped Channels

Cooling plate with flat channels

Since R2022b

Libraries:
Simscape / Battery / Thermal

## Description

The U-shaped Channels block models a battery cooling plate with flat channels. Use the `buildBattery` function to create a Simscape model of a battery and connect it to either end of the cooling plate. To learn how to connect a cooling plate block to a battery, see Connect Battery Block to Cooling Plate Block Automatically.

Typically, a cooling plate comprises two stamped flat plates joined together. The stamped portion of the plate forms a channel in which the fluid can flow. The U-shaped Channels block models the flat material of the plate by using one or more Thermal Mass blocks and the fluid-flow through the cooling channels by using Pipe (TL) blocks. The number of Pipe (TL) blocks and their connection to the plate depend on the discretization. For more information on the implementation of the Pipe (TL) block and its equations, see the Pipe (TL) documentation page.

The thermal masses of the cooling plate exchange heat with each other through heat conduction by using this equation:

where T is the temperature, K is the plate thermal conductivity, and A and x depend on the plate thickness and on the number of partitions and directions, x or y.

The fluid carries the heat away, or heats the battery pack, through these thermal masses. A thermal mass that is not connected to a pipe can only add or remove heat from a battery based on the heat conduction parameters that you specify.

### Cooling Plate Discretization

The Number of partitions in X direction and Number of partitions in Y direction parameters control the discretization of the cooling plate.

If you set the Number of partitions in X direction and Number of partitions in Y direction parameters to 1, the cooling plate is a lumped mass with a single thermal mass value. The software calculates this thermal mass from the value of the parameters in the Plate Material section. In this example, the value of the Number of flat channel partitions parameter is equal to 3 and the Select channel orientation direction parameter is set to `Channels along X axis`.

The software then places the Pipe (TL) blocks along the X-axis and connects them to the cooling plate. During the simulation, the cooling plate has one temperature value at each time step. Consequently, each cell of the battery pack connected to this cooling plate measures the same plate temperature value.

To increase the model fidelity, change the value of the Number of partitions in X direction to 2. The software now divides the cooling plate along the X dimension in two regions. Each region comprises a separate thermal mass. Since the X direction is also the direction of the coolant channels, the software discretizes the cooling pipes as well. With this configuration, each region of the cooling plate connects to four different Pipe (TL) blocks. During the simulation, the cooling plate has two different temperature values, one for each region of the plate.

To increase the model fidelity even further, change the value of the Number of partitions in Y direction to 3. The software discretizes the cooling plate along the Y dimension in three regions. The total number of regions in the cooling plate is now six. Each region of the plate then connects to a different Pipe (TL) block, with some regions connecting to multiple cooling channels. During the simulation, this cooling plate has six different temperature values at each time step. Consequently, the cells of the battery pack connected to this plate measure a temperature value that depends on the position of the cells.

For more information about cooling plates and their connection to battery blocks, see Connect Cooling Plate to Battery Blocks.

## Ports

### Output

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Temperature of the cooling plate, in Kelvin.

Temperature change of the fluid, in Kelvin.

Pressure drop of the fluid, in Pascal.

### Conserving

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Thermal fluid conserving port associated with the fluid that comes in the cooling plate.

Thermal fluid conserving port associated with the fluid that comes out of the cooling plate.

Thermal conserving port associated with the surface 1 of the cooling plate. This port connects the array of thermal nodes between the cooling plate and battery pack or module.

Thermal conserving port associated with the surface 2 of the cooling plate. This port connects the array of thermal nodes between the cooling plate and battery pack or module.

## Parameters

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### Interface

Option to choose the connectivity of the battery.

Number of battery thermal nodes on surface 1 of the cooling plate.

When manually connecting this cooling plate to a battery, you can obtain this information by querying the `ThermalNodes` property of the battery object associated with the battery block you are connecting this block to. The `ThermalNodes` property includes information such as the number of nodes, the 2-D location of nodes, and the dimensions of nodes.

Dimension of the battery thermal nodes on surface 1 of the cooling plate.

When manually connecting this cooling plate to a battery, you can obtain this information by querying the `ThermalNodes` property of the battery object associated with the battery block you are connecting this block to. The `ThermalNodes` property includes information such as the number of nodes, the 2-D location of nodes, and the dimensions of nodes.

Coordinates of the battery thermal nodes on surface 1 of the cooling plate.

When manually connecting this cooling plate to a battery, you can obtain this information by querying the `ThermalNodes` property of the battery object associated with the battery block you are connecting this block to. The `ThermalNodes` property includes information such as the number of nodes, the 2-D location of nodes, and the dimensions of nodes.

Number of battery thermal nodes on surface 2 of the cooling plate.

When manually connecting this cooling plate to a battery, you can obtain this information by querying the `ThermalNodes` property of the battery object associated with the battery block you are connecting this block to. The `ThermalNodes` property includes information such as the number of nodes, the 2-D location of nodes, and the dimensions of nodes.

#### Dependencies

To enable this parameter, set Battery Connectivity to ```Double sided```.

Dimension of the battery thermal nodes on surface 2 of the cooling plate.

When manually connecting this cooling plate to a battery, you can obtain this information by querying the `ThermalNodes` property of the battery object associated with the battery block you are connecting this block to. The `ThermalNodes` property includes information such as the number of nodes, the 2-D location of nodes, and the dimensions of nodes.

#### Dependencies

To enable this parameter, set Battery Connectivity to ```Double sided```.

Coordinates of the battery thermal nodes on surface 2 of the cooling plate.

When manually connecting this cooling plate to a battery, you can obtain this information by querying the `ThermalNodes` property of the battery object associated with the battery block you are connecting this block to. The `ThermalNodes` property includes information such as the number of nodes, the 2-D location of nodes, and the dimensions of nodes.

#### Dependencies

To enable this parameter, set Battery Connectivity to ```Double sided```.

Number of partitions in the X dimension for the cooling plate. This parameter affects the level of fidelity of the cooling plate.

Number of partitions in the Y dimension for cooling plate. This parameter affects the level of fidelity of the cooling plate.

### Plate Material

Thickness of the material of the cooling plate.

Thermal conductivity of the material of the cooling plate.

Density of the material of the cooling plate.

Specific heat of the material of the cooling plate.

Temperature of the cooling plate and of the coolant fluid at the start of simulation.

### Fluid Properties

Reynolds number above which flow begins to transition from laminar to turbulent. This number equals the maximum Reynolds number corresponding to fully developed laminar flow.

Reynolds number below which flow begins to transition from turbulent to laminar. This number equals to the minimum Reynolds number corresponding to fully developed turbulent flow.

The value of this parameter must be greater than the value of the Reynolds number upper limit for laminar flow parameter.

Ratio of convective to conductive heat transfer in the laminar flow regime. Its value depends on the pipe cross-sectional geometry and pipe wall thermal boundary conditions, such as constant temperature or constant heat flux. Typical value is 3.66, for a circular cross section with constant wall temperature.

Combined length of all local resistances present in the pipe. Local resistances include bends, fittings, armatures, and pipe inlets and outlets. The effect of the local resistances is to increase the effective length of the pipe segment. This length is added to the geometrical pipe length only for friction calculations. The liquid volume inside the pipe depends only on the pipe geometrical length.

Dimensionless factor that encodes the effect of pipe cross-sectional geometry on the viscous friction losses in the laminar flow regime. Typical values are 64 for a circular cross section, 57 for a square cross section, 62 for a rectangular cross section with an aspect ratio of 2, and 96 for a thin annular cross section.

### Design

Number of the partitions of the flat channels.

Option to choose the axis direction of the channel orientation. You can place the channels along the X axis or the Y axis. This figure shows the coolant channels for a cooling plate with 3 channels in both the X direction and the Y direction.

Thickness of the coolant channel.

Width of the partition.

Roughness of the coolant channel.

## Version History

Introduced in R2022b