Short Answer:

The thermal boundary layer is the region near a solid surface where the temperature of a fluid changes from the surface temperature to the free-stream temperature. In this thin layer, heat transfer takes place between the surface and the moving fluid. The temperature gradient is highest at the surface and decreases as the distance from the wall increases.

The thickness of the thermal boundary layer depends on several factors like the velocity of the fluid, fluid properties (viscosity, thermal conductivity), and type of flow (laminar or turbulent). A thinner boundary layer allows higher heat transfer, while a thicker layer reduces it.

Detailed Explanation:

Thermal Boundary Layer

The thermal boundary layer is an important concept in the study of heat transfer and fluid flow. When a fluid flows over a heated or cooled surface, the temperature of the fluid changes as it comes in contact with the surface. The layer of fluid in which this temperature variation occurs is known as the thermal boundary layer. It represents the region where most of the heat exchange between the surface and the fluid takes place.

At the solid surface, the temperature of the fluid is equal to the surface temperature due to conduction. As we move away from the surface, the temperature gradually changes until it becomes equal to the free-stream temperature of the fluid. Beyond this point, the influence of the surface temperature becomes negligible.

Formation of Thermal Boundary Layer

When a fluid starts moving over a solid surface with a different temperature, the fluid particles in direct contact with the surface either gain or lose heat depending on the temperature difference. This heat transfer happens mainly due to conduction very close to the surface. The fluid layers farther away from the surface are affected by convection, which causes a gradual change in temperature from the wall to the free stream.

As the flow continues, the heated or cooled region grows thicker along the surface. This region is called the thermal boundary layer, and its thickness is denoted by δt. It is defined as the distance from the surface at which the temperature difference between the fluid and the surface becomes very small (usually less than 1% of the total temperature difference).

Factors Affecting Thermal Boundary Layer Thickness

Velocity of Fluid:
Higher velocity reduces the thermal boundary layer thickness because the heat is carried away more quickly by the fast-moving fluid.
Fluid Properties:
The thickness of the boundary layer depends on fluid viscosity, density, specific heat, and thermal conductivity. Fluids with high thermal conductivity transfer heat more efficiently, resulting in a thinner thermal boundary layer.
Temperature Difference:
A greater temperature difference between the surface and the fluid increases heat transfer, which can influence the growth of the boundary layer.
Type of Flow:
In laminar flow, the boundary layer grows smoothly and remains thick. In turbulent flow, the fluid mixing enhances heat transfer and reduces the thickness of the boundary layer.
Surface Roughness:
Rough surfaces cause disturbances in the flow, which promote turbulence and lead to a thinner boundary layer and improved heat transfer.

Relationship Between Velocity and Thermal Boundary Layer

The velocity boundary layer and thermal boundary layer usually exist together when a fluid flows over a surface. The velocity boundary layer shows how fluid velocity changes from zero at the wall to the free-stream value, while the thermal boundary layer shows how temperature changes from the wall temperature to the free-stream temperature.

If the fluid has a high Prandtl number (Pr), which means it has low thermal diffusivity compared to momentum diffusivity, the thermal boundary layer is thinner than the velocity boundary layer. For low Prandtl number fluids (like liquid metals), the thermal boundary layer is thicker because heat diffuses more rapidly than momentum.

Importance of Thermal Boundary Layer

Heat Transfer Calculations:
The concept of the thermal boundary layer helps in determining the convective heat transfer coefficient, which is essential in thermal engineering calculations.
Design of Heat Exchangers:
Engineers use boundary layer theory to design systems where efficient heat transfer is required, such as condensers, boilers, and radiators.
Temperature Control in Systems:
Understanding boundary layer behavior helps in maintaining proper temperature distribution in machines, engines, and cooling systems.
Prediction of Flow Behavior:
The thermal boundary layer gives information about how heat is distributed in the flow field, which is necessary for accurate thermal and fluid flow analysis.

Conclusion:

The thermal boundary layer is the region near a surface where temperature differences exist between the solid and the flowing fluid. It plays a vital role in the process of convective heat transfer. Its thickness depends on fluid properties, flow velocity, and surface conditions. A thinner thermal boundary layer indicates better heat transfer performance. Understanding and controlling this layer is very important in designing efficient thermal systems and improving energy transfer in engineering applications.