Thermal Gradient: Definition & Calculation

Instructor: Raghav Mahalingam

Raghav has a graduate degree in Engineering and 20 years of professional experience.

This lesson defines a quantity called the thermal gradient and describes how to calculate it. The importance of thermal gradients in the field of thermal engineering along with an example is also included here.

What is a thermal gradient?

Many of us have experienced the pleasant sensation of coolness when we open the refrigerator door on a hot day and let the cool air rush past us. The phenomenon of cool air rushing past us is driven by a thermal quantity called thermal gradient.

A thermal gradient is defined by two physical quantities. The first one is temperature. Temperature is the degree of hotness or coldness of a body. For example, when we say, it's really hot today, it's a 100 degrees, we are talking about the temperature being 100°F.

The second quantity that defines thermal gradient is length. Thermal gradient is defined as the ratio of the temperature difference between two points and the distance between the two points. See Figure 1 for illustration. The temperature at point A is TA, the temperature at point B is TB, and the distance between the two points is DX.

If TB - TA is called DT, then the thermal gradient is defined as (TB - TA) / DX or DT / DX.

Figure 1. Thermal Gradient Definition

If you go back to the example of the refrigerator, the air in the fridge has a low temperature, let's say 40°F. The air outside, assuming no air conditioning, is 90°F. Let's say you are standing 1 foot from the fridge. The temperature gradient between you and the inside of the fridge is then calculated as,

(90 - 40) / 1 or 50°F / foot

Note that thermal gradient has the units of temperature divided by length.

The temperature difference between the cold air in the fridge and the outside air causes a density difference between the cold air (which is heavier) and the warm air (which is lighter). The heavier cold air rushes to replace the warm air and causes the pleasant feeling of coolness we experience.

While the above example showcased a thermal gradient in air, thermal gradients can exist in any material. For example, if the ends of an aluminum bar are exposed to two different temperatures, there will exist a temperature gradient in the bar, causing heat to flow from the hotter end to the cooler end.

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