# Uniform Fixed Gradient

Source: https://help.sim-flow.com/boundary-conditions/uniform-fixed-gradient
Last updated: 2026-10-01

## Description

The Uniform Fixed Gradient boundary condition is a derivative of [Fixed Gradient](https://help.sim-flow.com/boundary-conditions/fixed-gradient). It sets the gradient to the uniform value (throughout the entire boundary) as a constant value or as a function of time. The Uniform Fixed Gradient can be applied to all variable types (scalars, vectors).

Mathematically, the Uniform Fixed Gradient can be described as:

\[\nabla \phi \cdot \vec{n} = \frac{d\phi}{dn}(x,y,z,t) = g(t)\]

where:

- \(\phi\) is the scalar or vector field
- \(\nabla \phi\) is the gradient of the field
- \(\mathbf{n}\) is the normal vector to the boundary

## Understanding Uniform Fixed Gradient

Uniform Fixed Gradient works in the same way as [Fixed Gradient](https://help.sim-flow.com/boundary-conditions/fixed-gradient). However, the key distinction is its ability to define time-dependent values at the boundary. The Uniform Fixed Gradient enables the definition of time-dependent profiles for various dependent variables, such as pressure and temperature properties.

## Application & Physical Interpretation

The Uniform Fixed Gradient is typically applied to model scenarios where a uniform, time-dependent gradient of a variable (such as temperature or pressure) needs to be maintained across a boundary.

### Uniform Fixed Gradient in Heat Transfer applications

**Example applications**: heat exchangers, electronic cooling, engine cooling systems

To solve CHT (conjugate heat transfer) problems, the [chtMultiRegionFoam (solver)](https://help.sim-flow.com/solvers/cht-multi-region-foam) can be effectively utilized. In simulations that involve heat transfer, the Uniform Fixed Gradient is useful for modeling constant temperature gradients across solid walls. For instance, in a heat exchanger simulation, specifying a fixed temperature gradient across the surfaces can accurately represent varying levels of heat exchange.

Example Boundary Conditions set for Heat Transfer applications

| Physics | Velocity | Pressure | Thermal T |
| --- | --- | --- | --- |
| Wall Heat | Fixed Flux Pressure | No-Slip | **Uniform Fixed Gradient** |

## Uniform Fixed Gradient in SimFlow

The definition of boundary conditions in SimFlow is both simple and intuitive. To specify the Uniform Fixed Gradient, the user must navigate to the Boundary Conditions panel, select the appropriate boundary, and choose the correct option from the drop-down menu.

### Constant Value in Uniform Fixed Gradient

When the constant value of the gradient is assigned using Uniform Fixed Gradient, the definition is similar to [Fixed Gradient](https://help.sim-flow.com/boundary-conditions/fixed-gradient).

![Constant Uniform Fixed Gradient Boundary Condition in SimFlow](https://help.sim-flow.com/boundary-conditions/images/uniform-fixed-gradient/uniform-fixed-gradient-bc-01.png)

Figure 1. Constant Uniform Fixed Gradient Boundary Condition in SimFlow

### Time-dependent Uniform Fixed Gradient

The variable can also be defined as time-dependent. In SimFlow, a convenient table with graphical representation is used to define the boundary condition.

![Time-dependent Uniform Fixed Gradient Boundary Condition in SimFlow value](https://help.sim-flow.com/boundary-conditions/images/uniform-fixed-gradient/uniform-fixed-gradient-bc-02.png)

Figure 2. Time-dependent Uniform Fixed Gradient Boundary Condition in SimFlow

## Uniform Fixed Gradient - Alternatives

In this section, we propose boundary conditions that are alternative to Uniform Fixed Gradient. While they may fulfill similar purposes, they might be better suited for a specific application and provide a better approximation of physical world conditions.

Uniform Fixed Gradient - Alternatives

| Boundary Condition | Description |
| --- | --- |
| [Fixed Gradient](https://help.sim-flow.com/boundary-conditions/fixed-gradient) | fixed gradient on the boundary, without time dependency |