- #1

Sahil Dev

- 21

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## Homework Statement

Getting an expression for the convective heat tarnsfer coefficient.

## Homework Equations

See attached images

## The Attempt at a Solution

I have been reading about the boundary layers.

Here is an extract of my notes corresponding to thermal boundary layer and consequently my question.

Consider flow over an isothermal plate as shown in the figure.

As seen in the figure above, at the leading edge, the temperature profile is uniform with T(y) = T∞. However, the fluid particles that come into contact with the plate, achieve thermal equilibrium at the plate’s surface temperature.

In turn, these particles exchange energy with those in the adjoining fluid layer and temperature gradients develop in the fluid. The region of the fluid in which these temperature gradients exist is the

*thermal boundary layer.*

The thickness δst of the thermal boundary layer is typically defined as the value of y for which the ratio:

With increased distance from the leading edge, the effects heat transfer penetrates further into the free stream and the thermal boundary layer grows.

The relationship between the conditions in the boundary layer and the convection heat transfer coefficient may readily be demonstrated.

At any distance, ‘x’ from the leading edge, the local surface heat flux may be obtained by applying Fourier’s law to the fluid at y =0. That is;

This expression is appropriate because at the surface, there is no fluid motion and heat transfer occurs by conduction.

Recalling, the Newton’s law of cooling, we see that;

And combining this with the expression of conduction transfer as just above;

QUESTION:

1) I do not follow how the above equations: one corresponding to heat transfer through conduction) and the other corresponding to heat transfer through convection, can eb combned to give the heat transfer coefficient?

2) I do not see the logic in combining conductive and convective heat transfer related equations to give the heat trasnfer coefficient: h.

Please can anyone help?