Flow over a flat plate is considered an external flow and the thickness of the boundary layer, through the Reynolds analogy, affects the heat transfer. The boundary layer starts as infinitesimal and grows along the length of the plate. The convective heat transfer coefficient thus changes along the length of the plate. The boundary layer growth is theoretically not bounded.

For a tube, the boundary layer also starts as infinitesimal however there is a physical limit to its size - the internal diameter of the tube. There is an "entry region" effect that can be significant depending on the length/diameter ratio of the tube. Many times this entry region is neglected as it is relatively short compared to the fully-developed length.

May be because boundary layer thickness over is growing limitless along plate. In contrast, in a long tube boundary layer occupies whole cross-section and is not growing streamwise.

Actually the Convective heat transfer doesn't depend on the length of particular surface, but it depends on the Surface area of the body/surface according to Q(conv) = h(conv heat transfer co efficient) *A(surface area) * (change in temperature).

Hence higher the surface area in contact, higher will be the heat transfer rate.

I Hope this helps you.

Not an expert of heat transfer, what do you mean for "internal heat transfer", is the coefficient? Then you are referring as the law Nu=f(Re)? in this case, the Reynolds number along the plate depends on the position along the lenght and is an increasing function while in a pipe it is defined by a unique lenght, the diameter.

Flow over a flat plate is considered an external flow and the thickness of the boundary layer, through the Reynolds analogy, affects the heat transfer. The boundary layer starts as infinitesimal and grows along the length of the plate. The convective heat transfer coefficient thus changes along the length of the plate. The boundary layer growth is theoretically not bounded.

For a tube, the boundary layer also starts as infinitesimal however there is a physical limit to its size - the internal diameter of the tube. There is an "entry region" effect that can be significant depending on the length/diameter ratio of the tube. Many times this entry region is neglected as it is relatively short compared to the fully-developed length.

Het transfer is function of the thermal boundary layer gradient at the wall, by Prandtl analogy related to that of the velocity boundary layer. Over a plate the boundary layer grows infinitely and so change the gradient at the wall, changing the local heat transfert. In a tube, far from the initial region, the velocity profile is constant along the the lenght and so is the thermal profile and the gradiend at the wall. Hence a uniform heat transfer.until the temperature of the fluid increases and then when an equlibrium in reached. This is valid for the case of a constant teperature of the tube, or plate wall.

Anton Noev has it correct but to be more blunt I’ll add the following.

1. The boundary layer over a flat plate develops indefinitely and grows without limit.

2. The boundary layer in a tube/pipe develops from the tube/pipe entry up to a point where the flow in the stream wise direction is fully developed. This region where the flow develops and the boundary layer grows is called the “entry length”.

3. The flow between two parallel plates each one identical to the plate in 1 above also has an entry length where boundary layers develop above the bottom plate and below the top plate. When these two separate boundary layers meet the flow becomes fully develope. In this case too the heat transfer is independent of the length of the plates.