5. Two faces of a slab are maintained at two different temperatures, T1> T2. All other faces are perfectly insulated, so

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5 Two Faces Of A Slab Are Maintained At Two Different Temperatures T1 T2 All Other Faces Are Perfectly Insulated So 1 (79.03 KiB) Viewed 41 times

5. Two faces of a slab are maintained at two different temperatures, T1> T2. All other faces are perfectly insulated, so heat can flow only along x-direction. Temperatures are measured at five different locations along the width, L, of the slab, as shown in the table. T 91 T(x) 2' ➤X X (mm) T (°C) 0 25.97 25.27 24.57 121.92 23.86 162.56 23.06 40.64 81.28 a) Plot temperature against distance x in a scatter plot. b) Perform a linear regression of T on x. c) What is r² value? Is ² value reasonable enough to make linear model acceptable. d) Use Excel or Python to calculate Standard Error of Estimate (or MSE). e) What is the estimated temperature at x = 50 mm? Make sure to report it as an interval estimate with the associated confidence level. f) Now perform a polynomial regression of degree 2. Calculate MSE for the quadratic model. Is it any better than the linear model? 6. Consider the regression model you chose in the above problem. g) Now perform a polynomial regression of degree 3. Calculate MSE for the cubic model. Is it any better than the previous two models? h) Which regression would you use? Explain the reasoning for your decision. a) What is the estimated temperature at x = 50 mm? Make sure to report it as an interval estimate with the associated confidence level. b) What is estimated? Make sure to report it as an interval estimate with the associated confidence level. c) If thermal conductivity of the slab material is k = 400 use Fourier's law of thermal conduction (Q = k) to calculate heat flux, Make sure to report it as an interval estimate with the associated confidence level.