Nusselt Number Example

D.E. Cole

> restart;

For this example, Maple V will be utilized to determine the uncertainty in the calculation of

the Nusselt number using the method presented by Kline and McClintock..

Define the functional relationship for the Nusselt number. Here:

> Nu := h*d/k;

Define the relationship for the uncertainty in the Nusselt number.

> u_Nu:=sqrt((Diff(Nu,h)*u_h)^2+(Diff(Nu,d)*u_d)^2+(Diff(Nu,k)*u_k^2));

Evaluate the derivatives in the above expression by replacing the capital "D" in Diff with "d"..

> u_Nu:=sqrt((diff(Nu,h)*u_h)^2+(diff(Nu,d)*u_d)^2+(diff(Nu,k)*u_k^2));

Insert the nominal values and uncertainties. (Watch your units!)

> h:=150: d:=20/1000: k:=0.6:

> u_h:=h*0.07: u_d:=0.5/1000: u_k:= k*0.02:

Calculate the uncertainty in the Nusselt number.

> u_Nu;

Calculate the nominal value for the Nusselt number.

> evalf(Nu);

Therefore, the result can be expressed as: 5.00 +/- 0.37.