#### Convective Heat Transfer over a Flat Plate: Screencast

The convective heating of four fluids in laminar flow over a flat plate is explored. The effects of the Reynolds and Prandtl numbers on the relative thicknesses of the momentum and thermal boundary layers are compared. The velocity profile is based on the Blasius solution for laminar flow.

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Outlines the procedure to solve convection problems.

We suggest that after watching this screencast, you list the important points as a way to increase retention.

##### Important Equations:

Often the goal of convection problems involving flow over a flat plate is to calculate the total heat flow (in Watts). You can do so using the following equation:

\[q = \bar{h} A(T_S\,-\,T_{\infty})\]

where \(\bar{h}\) = average heat transfer coefficient (W/m^{2}-K),

\(A\) = surface area of the plate (m^{2}),

\(T_S\) = surface temperature of the plate (°C),

and \(T_{\infty}\) = temperature of the fluid far from the plate (°C).

To calculate \(\bar{h}\) you need to use a correlation. Two common correlations are

\(\overline{Nu}_L = \left( 0.037Re_L ^{4/5} \,-\, 871 \right) Pr^{1/3}\) and \(\overline{Nu}_L = 0.664Re_L ^{1/2} Pr^{1/3}\)

where \[\overline{Nu}_L = \frac{\bar{h}L}{k}\]

is the average Nusselt number based on the length of the plate, \(L\), and the thermal conductivity of the fluid, \(k\).

\[Re_L = \frac{\rho U_{\infty} L}{\mu} = \frac{U_{\infty} L}{\nu}\]

is the Reynolds number based on the speed of the fluid far from the plate, \(U_{\infty}\), and

\(Pr = \nu/\alpha\)

is the fluid’s Prandtl number, which is a property that can be looked up for a given temperature. Because the temperature of the plate and the temperature of the fluid are different, the usual approach is the use a “film” temperature when looking up fluid properties. The film temperature is just the average of the two:

\[T_{film} = \frac{T_{\infty} + T_S}{2}\]

Before using a given correlation, you must be certain that the Reynolds and Prandtl numbers are within a range appropriate for that correlation. In the first correlation above, \(Re_L\) must be less than about 10^{8} and \(Pr\) must be between about 0.6 and 60. For the second correlation, \(Pr\) must be larger thant about 0.6 and the flow must be laminar, meaning that \(Re_L\) must be less than about 500,000.

##### Important Definitions:

Kinematic viscosity: (with units of m2/s) \[\nu = \frac{\mu}{\rho}\] Thermal diffusivity: (with units of m2/s) \[\alpha = \frac{k}{\rho c_p}\]