8 Fouriers equation below models conduction heat transfer pe

8. Fourier’s equation below models conduction heat transfer per unit surface area as flux q through a slab of substance with thickness L.

q = -k dT/dx = -k ?T/L

The heat conduction direction is perpendicular to the surface area. The heat flux has units of W/m2, theconduction heat transfer coefficient k has units of W/m-K, and the temperature difference ?T between the outer surfaces of the substance perpendicular to L is in K or °C. Make the following calculations by hand using the data set provided in Table 1.

a) Find the best fit slope and intercept.

b) Find the standard deviation for the fit assuming that k is known without error.

c) Find the 95% confidence interval for the fit assuming that k is known without error.

d) Find the 95% confidence interval for the slope and intercept.

e) Plot the data, the fit line, and the 95% confidence interval calculated in c)

f) How many data points lie within the confidence interval? How many lie outside the CI?

7100 35 07 11 10 4584 8047682-21 Wha 0.1 0.2 m-12345678-90 0000000001

Solution

sol)

The Regression Equation is q=a+b(k)

From Excel tool

From above analysis

a) The Fitted Regression Model is q=1.3338 + 286.115(k)

Slope = 286.115 and intercept=1.3338

b) Stanadard devaiation= sqrt(MSE)= aqrt(439.06) =20.953

c) 95% confidence interval for the fit assuming that k is known without error is(233.61, 340.009)

d) 95% confidence interval for the slope is (233.613, 340.009)

and 95% confidence interval for the intercept is ( -31.6, 34.34)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.975084
R Square	0.95079
Adjusted R Square	0.944638
Standard Error	20.95389
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	67865.17	67865.17	154.5673	1.64E-06
Residual	8	3512.523	439.0654
Total	9	71377.69
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1.3338	14.31423	0.09318	0.928052	-31.6749	34.34248	-31.6749	34.34248
K	286.8115	23.06947	12.43251	1.64E-06	233.6132	340.0098	233.6132	340.0098