Question

Can we define the convection resistance for a unit surface area as the inverse of the convection heat transfer coefficient?

Short answer

Answer: Yes, the convection resistance for a unit surface area can be defined as the inverse of the convection heat transfer coefficient. This relationship is mathematically expressed as R_c = 1/h, where R_c represents convection resistance and h represents the convection heat transfer coefficient.

Step-by-step solution

Understand Convection Heat Transfer

Convection heat transfer occurs when a fluid (liquid or gas) moves over a solid surface, carrying heat away or towards the surface. The fluid heats up (or cools down) by direct contact with the surface and transfers the heat to (or from) the surroundings.

Define the Convection Heat Transfer Coefficient

The convection heat transfer coefficient (h) is a measure of the effectiveness of heat transfer through convection. It is usually expressed in W/(m^2 K), which represents the heat transfer rate (in watts) for a unit surface area (in square meters) per unit temperature difference between the surface and the fluid (in kelvins). In other words, the higher the value of h, the more effective the convection heat transfer process is.

Define Convection Resistance

Convection resistance is a measure of how much resistance there is against heat transfer by convection. It is the thermal resistance due to the presence of a fluid surrounding a solid surface. Just like electrical resistance, thermal resistance can be seen as an opposition to heat flow; when there is more resistance, there will be less heat transfer.

Relationship between Convection Heat Transfer Coefficient and Convection Resistance

Convection resistance (R_c) can be defined as the inverse of the product of the convection heat transfer coefficient (h) and the surface area (A). Mathematically, R_c = \dfrac{1}{hA} For a unit surface area, as mentioned in the exercise, the surface area (A) will be equal to 1 m^2. Therefore, the convection resistance for a unit surface area can be written as: R_c = \dfrac{1}{h}

Conclusion

Yes, we can define the convection resistance for a unit surface area as the inverse of the convection heat transfer coefficient. This is mathematically demonstrated as R_c = \dfrac{1}{h}, where R_c is the convection resistance and h is the convection heat transfer coefficient.