Many of the heat transfer processes encountered in industry involve composite systems and even involve a combination of both conduction and convection. With these composite systems, it is often convenient to work with an** overall heat transfer coefficient, **known as a **U-factor**. The U-factor is defined by an expression analogous to **Newton’s law of cooling**:

The **overall heat transfer coefficient** is related to the total thermal resistance and depends on the geometry of the problem. For example, heat transfer in a steam generator involves convection from the bulk of the reactor coolant to the steam generator inner tube surface, conduction through the tube wall, and convection (boiling) from the outer tube surface to the secondary side fluid.

In cases of combined heat transfer for a heat exchanger, there are two values for h. There is the convective heat transfer coefficient (h) for the fluid film inside the tubes and a convective heat transfer coefficient for the fluid film outside the tubes. The thermal conductivity (k) and thickness (Δx) of the tube wall must also be accounted for.

**Overall Heat Transfer Coefficient – Plane Wall**

**Overall Heat Transfer Coefficient – Cylindrical Tubes**

Steady heat transfer through multilayered cylindrical or spherical shells can be handled just like multilayered plane walls.

## Thermal Conductivity

The heat transfer characteristics of a solid material are measured by a property called the **thermal conductivity**, k (or λ), measured in **W/m.K**. It is a measure of a substance’s ability to transfer heat through a material by conduction. Note that **Fourier’s law** applies for all matter, regardless of its state (solid, liquid, or gas), therefore, it is also defined for liquids and gases.

The **thermal conductivity** of most liquids and solids varies with temperature. For vapors, it also depends upon pressure. In general:

Most materials are very nearly homogeneous, therefore we can usually write ** k = k (T)**. Similar definitions are associated with thermal conductivities in the y- and z-directions (k

_{y}, k

_{z}), but for an isotropic material the thermal conductivity is independent of the direction of transfer, k

_{x}= k

_{y}= k

_{z}= k.

From the foregoing equation, it follows that the conduction heat flux increases with increasing thermal conductivity and increases with increasing temperature difference. In general, the thermal conductivity of a solid is larger than that of a liquid, which is larger than that of a gas. This trend is due largely to differences in **intermolecular spacing** for the two states of matter. In particular, diamond has the highest hardness and thermal conductivity of any bulk material.

## Convective Heat Transfer Coefficient

As can be seen, the **constant of proportionality** will be crucial in calculations and it is known as the **convective heat transfer coefficient**, **h**. The **convective heat transfer coefficient,** h, can be defined as:

*The rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature difference.*

The **convective heat transfer coefficient** is dependent upon the physical properties of the fluid and the physical situation. The convective heat transfer coefficient is not a property of the fluid. It is an experimentally determined parameter whose value depends on all the variables influencing convection such as the **surface geometry**, the **nature of fluid motion**, the **properties of the fluid**, and the **bulk fluid velocity**.

Typically, the **convective heat transfer coefficient** for** laminar flow** is relatively low compared to the **convective heat transfer coefficient** for **turbulent flow**. This is due to turbulent flow having a **thinner stagnant fluid film layer** on the heat transfer surface.

It must be noted, this **stagnant fluid film layer** plays crucial role for the convective heat transfer coefficient. It is observed, that the fluid comes to a** complete stop at the surface**and assumes a zero velocity relative to the surface. This phenomenon is known as the no-slip condition and therefore, **at the surface, **energy flow occurs **purely by conduction. **But in the next layers both conduction and diffusion-mass movement in the molecular level or macroscopic level occurs. Due to the mass movement the rate of energy transfer is higher.