A common application is to a layer of liquid, such as water, when there is a temperature difference  across this layer. This could be due to the liquid evaporating or being heated from below. There is a surface tension at the surface of a liquid that depends on temperature, typically as the temperature increases the surface tension decreases. Thus if due to a small fluctuation temperature, one part of the surface is hotter than another, there will be flow from the hotter part to the colder part, driven by this difference in surface tension, this flow is called the Marangoni effect. This flow will transport thermal energy, and the Marangoni number compares the rate at which thermal energy is transported by this flow to the rate at which thermal energy diffuses.
For a liquid layer of thickness , viscosity  and thermal diffusivity , with a surface tension  which changes with temperature at a rate , the Marangoni number can be calculated using the following formula:
When Ma is small thermal diffusion dominates and there is no flow, but for large Ma, flow (convection) occurs, driven by the gradients in the surface tension. This is called Bénard-Marangoni convection.