Cross-Flow Heat Exchanger

This application simulates the fluid flow and heat transfer in a micro heat exchanger of cross-flow type made of stainless steel. Heat exchangers of this type are found in lab-on-chip devices in biotechnology and microreactors, for example for micro fuel cells. The application takes into account heat transferred through both convection and conduction. The geometry and material properties are taken from Ref. 1.

Model Definition

Figure 1 shows the heat exchanger’s geometry. Notice that the fluid channels have a square cross section rather than the circular cross section more commonly used in micro heat exchangers. A cross-flow heat exchanger can typically consist of about 20 unit cells. However, because the unit cells are identical except for edge effects in the outer cells, you can restrict the model to a single unit cell.

Figure 1: Depiction of the modeled part of the micro-heat exchanger.

Because heat is transferred by convection and conduction, the model uses a Conjugate Heat Transfer interface in the laminar flow regime.

The boundary conditions are insulating for all outer surfaces except for the inlet and outlet boundaries. At the inlets for both cold and hot streams, the temperatures are constant and a laminar inflow profile with an average velocity of 50 mm/s is defined.

At the outlet, the heat transport is dominated by convection, which makes the outflow boundary condition suitable. For the flow field, the model applies the outlet boundary condition with a constant pressure.

As shown in Figure 1, you can take advantage of the model’s symmetries to model only half of the channel height. Therefore, the symmetry boundary condition applies to the channels.

Results and Discussion

Figure 2 shows the temperature at the channel walls as well as temperature isosurfaces in the device, which clearly reveal the influence of the convective term.

Figure 2: Channel wall temperature and isotherms through the cell geometry.

As can be seen in Figure 3, the temperature differs significantly between the different outlets in both hot and cold streams. This implies that the hot stream is not cooled uniformly.

Figure 3: Temperature field at the outlet boundaries.

The flow field in the channels is a typical laminar velocity profile; see Figure 4.

Figure 4: Velocity profile in the channels.

There are several quantities that describe the characteristics and effectiveness of a heat exchanger. The mixing-cup temperature of the fluid leaving the heat exchanger is calculated according to (1.4 in Ref. 2).

(1)

COMSOL Multiphysics provides built-in variables to easily calculate 〈T〉. At the upper channels, the outlet mixing-cup temperature is about 40.5°C. At the lower channels, a higher value of 43°C is found for the outlet mixing-cup temperature. The maximum pressure drop in the heat exchanger is about 92 Pa.

The overall heat transfer coefficient is another interesting quantity. It is a measure of the performance of a heat exchanger design defined as

(2)

where P is the total exchanged power and A is the surface area through which P flows. In this model, the value of heq is about 3150 W/(m2·K).

References

1. W. Ehrfeld, V. Hessel, and H. Löwe, Microreactors, John Wiley & Sons, 2000.

2. P.K. Nag, Heat and Mass Transfer, 2nd ed., Tata McGraw-Hill, 2007.

Heat_Transfer_Module/Heat_Exchangers/crossflow_heat_exchanger

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In this model, the flow will be considered nearly incompressible and independent of temperature variations. Under these assumptions, the study performs best.

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
T_cold	300[K]	300 K	Temperature, cold stream
T_hot	330[K]	330 K	Temperature, hot stream
u_avg	50[mm/s]	0.05 m/s	Average inlet velocity

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

First, create the cross section of one unit cell and extrude it.

Block 1 (blk1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 800.

In the text field, type 60.

Click

Block 2 (blk2)

In the toolbar, click

In the window for , locate the section.

In the text field, type 800.

In the text field, type 100.

In the text field, type 40.

Locate the section. In the text field, type 200.

Click

Array 1 (arr1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

From the list, choose .

In the text field, type 5.

Locate the section. In the text field, type 120.

Locate the section. Find the subsection. Click .

In the dialog box, type Channels in the text field.

Click .

Rotate 1 (rot1)

In the toolbar, click

and choose .

Click in the window and then press Ctrl+A to select all objects.

In the window for , locate the section.

In the text field, type 180.

Locate the section. In the text field, type 60.

Locate the section. From the list, choose .

In the text field, type 1.

In the text field, type 0.

Keep the existing unit cell by the following step.

Locate the section. Select the check box.

Click

Click the

button in the toolbar.

Define several selections that will help throughout the model set-up.

Definitions

Upper Inlets

In the toolbar, click

In the window for , type Upper Inlets in the text field.

Locate the section. From the list, choose .

Select Boundaries 41, 48, 55, 62, and 69 only.

Lower Inlets

In the toolbar, click

In the window for , type Lower Inlets in the text field.

Locate the section. From the list, choose .

Select Boundaries 8, 14, 20, 26, and 32 only.

Upper Outlets

In the toolbar, click

In the window for , type Upper Outlets in the text field.

Locate the section. From the list, choose .

Select Boundaries 44, 51, 58, 65, and 72 only.

Lower Outlets

In the toolbar, click

In the window for , type Lower Outlets in the text field.

Locate the section. From the list, choose .

Select Boundaries 77–81 only.

Symmetry

In the toolbar, click

In the window for , type Symmetry in the text field.

Locate the section. From the list, choose .

Select the check box.

Select one of the uppermost and lowermost boundaries, which now automatically will select all uppermost and lowermost boundaries thanks to the continuous tangency.

The next selections are needed to evaluate the equivalent heat transfer coefficient.

Outlets

In the toolbar, click

In the window for , type Outlets in the text field.

Locate the section. From the list, choose .

Locate the section. Under , click

In the dialog box, in the list, choose and .

Click .

Materials

Define the material properties.

Stainless Steel

In the toolbar, click

In the window for , type Stainless Steel in the text field.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	15	W/(m·K)	Basic
Density	rho	7800	kg/m³	Basic
Heat capacity at constant pressure	Cp	420	J/(kg·K)	Basic

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Water, liquid (mat2)

In the window for , locate the section.

From the list, choose .

Heat Transfer in Solids and Fluids (ht)

Set the reference temperature to an estimated value of (T_cold+T_hot)/2 where the flow operates.

In the window, under click .

In the window for , locate the section.

In the Tref text field, type (T_cold+T_hot)/2.

Fluid 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Inflow 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the Tustr text field, type T_hot.

Inflow 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the Tustr text field, type T_cold.

Outflow 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Outflow 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Symmetry 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

So far, the boundary conditions for heat transfer have been specified. Continue with the setup of the flow equation.

Laminar Flow (spf)

The density variations are small enough to consider the fluid as incompressible. Change the compressibility option accordingly in the physics interface. The reference temperature is set in the Heat Transfer interface.

In the window, under click .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Because of the different inlet temperatures, the densities for the hot and cold stream vary and produce different velocities when the laminar inflow boundary condition is used. In order to have the same velocity profile on each inlet, define the laminar inflow boundary condition for the hot and cold inlet boundaries separately.

Inlet 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Locate the section. In the Uav text field, type u_avg.

Inlet 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Locate the section. In the Uav text field, type u_avg.

Outlet 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Outlet 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Symmetry 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

After solving the model, the equivalent heat transfer coefficient is evaluated according to Equation 2. To do so, define the following nonlocal coupling.

Multiphysics

Nonisothermal Flow 1 (nitf1)

In the window, under click .

In the window for , locate the section.

Select the check box.

Definitions

Average on Upper Channel Walls

In the toolbar, click

and choose .

In the window for , type Average on Upper Channel Walls in the text field.

Locate the section. From the list, choose .

Select Boundaries 40, 42, 45, 47, 49, 52, 54, 56, 59, 61, 63, 66, 68, 70, and 73 only.

To select more easily these boundaries, use the button and insert the list of numbers above in the dialog box.

Study 1

In the toolbar, click

Results

Temperature (ht)

COMSOL Multiphysics automatically creates four default plots: a temperature plot, an isothermal contour plot, a slice plot for the velocity field, and a contour plot for the pressure field. The isothermal contours will be modified, to create the plot shown in Figure 2.

Isosurface

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose .

Isothermal Contours (ht)

In the window, click .

Surface 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Click in the upper-right corner of the section. From the menu, choose .

Click to expand the section. From the list, choose .

In the toolbar, click

To visualize the velocity field as in Figure 4, follow the steps below:

Slice

In the window, expand the node.

Right-click and choose .

Velocity (spf)

In the window, under click .

Surface 1

In the toolbar, click

In the window for , click in the upper-right corner of the section. From the menu, choose .

Locate the section. From the list, choose .

In the toolbar, click

To show the temperature on the outlet boundaries only, as in Figure 3, first produce a new dataset for the selection built before. Then use this dataset for a surface plot of the temperature.

Outlets

In the toolbar, click