# Heat Transfer Coefficients and Nusselt Numbers of Various Materials

• siliconian
In summary: The calculation of the heat transfer coefficient is more complicated than the Nusselt number equation, but I'm guessing that you could find a correlation that would give you a reasonable estimate of the heat transfer coefficient for the geometry and flow conditions you are studying.In summary, the heat transfer coefficient and Nusselt number are not properties of materials but are determined by the heat conduction and convective heat transport in the gas phase near the interface. The gas flow can have a significant effect on the heat transfer coefficient, which is used to calculate the heat flow rate. To determine the heat transfer coefficient, you can either estimate it from experience or solve the detailed equations for heat transport and fluid flow.
siliconian
Hi everybody!

I am working in a solid state physics group and need to find some heat transfer data to finish my calculations. I need to find the Nusselt number Nu$=\frac{hL}{K}$ describing the heat transfer interface between a Si wafer and helium gas at a variety of temperatures. To find this I need the heat transfer coefficient $\left(h\right)$ between Si and He.

I will most likely be needing this sort of data for other materials in the future so I was wondering if someone could direct me to some sort of table for this type of data?

siliconian said:
Hi everybody!

I am working in a solid state physics group and need to find some heat transfer data to finish my calculations. I need to find the Nusselt number Nu$=\frac{hL}{K}$ describing the heat transfer interface between a Si wafer and helium gas at a variety of temperatures. To find this I need the heat transfer coefficient $\left(h\right)$ between Si and He.

I will most likely be needing this sort of data for other materials in the future so I was wondering if someone could direct me to some sort of table for this type of data?

Hi Siliconian,

Welcome to physics forums.

The heat transfer coefficient and Nussult Number are not properties of the materials. The Nussult Number is basically the dimensionless version of the heat transfer coefficient. The heat transfer coefficient is determined by heat conduction and convective heat transport in the gas in close proximity to the interface. The helium will be moving, shearing, and deforming, and its molecules will conduct heat to and from the interface. The shearing and deformation of the gas has the effect of changing the temperature gradient, which affects the rate of heat conduction. If you want to learn more about the heat transfer coefficient and the Nussult number, see Transport Phenomena by Bird, Stewart, and Lightfoot. For your situation, the heat transfer between the helium and the substrate will be dominated by the thermal resistance on the gas side of the interface. Therefore, you need to study the heat transfer behavior in the gas phase, which will be determined by the geometry and the fluid mechanics in the gas. To a large extent, the substrate will not matter.

Chet

Hey Chet,

Thanks for the reference! I will definitely check it out. If you don't mind asking me another question, is the equation wikipedia uses to describe the relationship: $h=\frac{Q}{AT}$ an oversimplification in this sort of situation? It makes sense that the heat transfer process is dominated by the thermal resistance of the gas, but I'm wondering what kind of role the fluid flow plays in this process.

The heat transfer coefficient is used to calculate the heat flow Q by the equation Q = hAΔT. But, to use this equation, you need to be able to either estimate the heat transfer coefficient from experience or solve the detailed partial differential equations for heat transport and fluid flow for the heat transfer coefficient. As I said in my previous response, the gas flow can have a substantial effect on the gas phase temperature gradient near the interface, and this is equivalent to an effect on the heat transfer coefficient. On a calm day outside, your skin temperature is much higher than when the wind is blowing. The wind movement increases the heat transfer coefficient between your skin surface and the bulk temperature of the air. Right near your skin, there is a thin thermal boundary layer, on the order of about a mm thick, over which the air temperature varies from the "free stream" air temperature to your skin temperature. The heat transfer coefficient is inversely proportional to the thickness of this boundary layer. When the wind is blowing, the thermal boundary layer becomes thinner, and the heat transfer coefficient increases.

## 1. What is a heat transfer coefficient?

A heat transfer coefficient is a measure of how easily heat can be transferred from one material to another. It represents the amount of heat that can be transferred per unit area per unit temperature difference between the two materials.

## 2. How is the heat transfer coefficient determined?

The heat transfer coefficient can be determined through experimentation or by using mathematical models. In experimental methods, the heat transfer coefficient is calculated by measuring the temperature difference between two materials and the amount of heat transferred. In mathematical models, the heat transfer coefficient is calculated using various parameters such as material properties, flow rate, and temperature difference.

## 3. What is the Nusselt number and how is it related to the heat transfer coefficient?

The Nusselt number is a dimensionless parameter that represents the ratio of convective heat transfer to conductive heat transfer. It is used to determine the heat transfer coefficient for different materials and flow conditions. The Nusselt number is directly proportional to the heat transfer coefficient, meaning that a higher Nusselt number indicates a higher heat transfer coefficient.

## 4. How do different materials affect the heat transfer coefficient?

The heat transfer coefficient is affected by various material properties, such as thermal conductivity, density, and specific heat. Materials with higher thermal conductivity will have a higher heat transfer coefficient as they can transfer heat more easily. Materials with lower density and specific heat will also have a higher heat transfer coefficient, as they can absorb and release heat more quickly.

## 5. Can the heat transfer coefficient be changed?

Yes, the heat transfer coefficient can be changed by altering the material properties, flow conditions, and geometry of the system. For example, increasing the flow rate or using materials with higher thermal conductivity can increase the heat transfer coefficient. Additionally, using different heat transfer enhancement techniques, such as fins or turbulators, can also increase the heat transfer coefficient.

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