Question

It is claimed that the temperature profile in a medium must be perpendicular to an insulated surface. Is this a valid claim? Explain.

Short answer

Answer: No, the temperature profile in a medium doesn't always have to be perpendicular to an insulated surface. The perpendicular nature of the temperature profile depends on the dominant heat transfer mechanism (conduction, convection, or radiation) and the presence of driving forces such as external heat sources or fluid flow. In cases where heat conduction is the dominant heat transfer mechanism, the temperature profile is more likely to be perpendicular to the insulated surface, whereas, in cases dominated by convection or radiation, the temperature profile may not necessarily be perpendicular.

Step-by-step solution

Understanding heat transfer

Heat transfer is the flow of thermal energy due to a temperature difference between two objects. There are three main types of heat transfer: conduction, convection, and radiation. In an insulated surface, heat transfer is restricted, thus maintaining a minimal amount of heat loss or gain in the system.

Temperature profile in a medium

A temperature profile is a graphical representation of how the temperature changes within a medium (i.e., solid, liquid, gas) across a specific region. The temperature profile shows the spatial variations and helps to predict and control thermal performance.

Analysing the claim of temperature profile perpendicularity

The claim states that the temperature profile in a medium must be perpendicular to an insulated surface. To analyze this, let's consider the following aspects: 1. In the absence of any driving force, such as external heat sources or movement of the medium, the temperature profile will be uniform, and there will be no temperature gradient. In this case, the claim is not valid as there is no temperature profile to discuss. 2. When a temperature gradient is present in the medium due to an external heat source or thermal resistance, the temperature profile tends to be perpendicular to the insulated surface when heat conduction is the dominant heat transfer mechanism. This is because the heat transfer occurs mostly along the temperature gradient, and perpendicularity ensures minimal heat loss through the insulated surface. 3. If heat transfer is dominated by convection or radiation instead of conduction, the temperature profile may not be strictly perpendicular to the insulated surface. In these cases, other factors such as fluid flow, medium properties, and the presence of heat sources can also affect the direction of heat transfer, thus affecting the temperature profile.

Conclusion

In conclusion, the claim that the temperature profile in a medium must be perpendicular to an insulated surface is not always valid. The perpendicular nature of the temperature profile largely depends on the dominant heat transfer mechanism and the presence of driving forces such as external heat sources or fluid flow. In cases where heat conduction is the dominant heat transfer mechanism, the temperature profile is more likely to be perpendicular to the insulated surface, whereas, in cases dominated by convection or radiation, the temperature profile may not necessarily be perpendicular.