The experimental data shown tabulated were obtained by passing n-butyl alcohol at a bulk temperature of 15°C over a heated flat plate (0.3-m-long, 0.9-m-wide, surface temperature of 60°C). Correlate the experimental data using appropriate dimensionless numbers and compare the line which best fits the data with Equation 5.38.

Question

GIVEN

n-butyl alcohol flowing over a heated flat plate

Bulk temperature (Tb) = 15°C

Plate surface temperature (Tp) = 60°C

Plate length (L) = 0.3 m

Plate width (w) = 0.9 m

The experimental data given above

FIND

(a) Correlate the data by appropriate dimensionless numbers

(b) Compare line which best fits the data with Equation 5.38

ASSUMPTIONS

Steady state

Alcohol flows parallel to the length of the plate

Plate temperature is uniform

SKETCH



PROPERTIES AND CONSTANTS

From Appendix 2, Table 19: For n-butyl alcohol at the average of the bulk and surface temperatures

(known as the film temperature): 37.5°C.

Answer 1

(a) The relevant variables and their primary dimensions are listed below



Note: Specific heat should be included in this list, but we suspect that it will show up as a Prandtl

number which is constant for the series of tests performed. Therefore, we can easily extract its

contribution. There are 6 variables are 4 primary dimensions, therefore, they can be correlated with

two dimensionless groups. These dimensionless groups can be determined by the Buckingham ? Theorem



Equating the primary dimensions



Equating the sums of the exponents of each primary dimension

For T: 0 = – a – e [1]

For M: 0 = a + d + e + f [2]

For t: 0 = – 3a – b – d – 3e [3]

For L: 0 = b + c – d + e – 3f [4]

There are four equations and six unknowns. Therefore, the values of two of the exponents may be

chosen for each dimensionless group.

For ?1, Let f = 1 e = 0

From equation [1]: a = 0

From equation [2]: d = – 1

From equation [3]: b = 1

From equation [4]: c = 1



For ?2, Let a = 1 d =

From equation [1]: e = – 1

From equation [2]: f = 0

From equation [3]: b = 0

From equation [4]: c = 1



The range of Prandtl number is insufficient to get a functional relationship, therefore the data can be

correlated by the Nusselt number and the Reynolds number:



Calculating ReL and Nu for each data point



On a log-log plot, these points fall roughly on a straight line



The linear regression gives the following line



(b) For this problem, Pr = 29.4. Including this in the correlation



Equation 5.38 for laminar flow over a flat plate is



which is about 7% less than our experimental data.