8. Fourier’s equation below models conduction heat transfer per unit surface are
ID: 3437043 • Letter: 8
Question
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 0000000001Explanation / Answer
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 340.0098Related Questions
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