A correlation for the thermal conductivity of aluminium as a function of temperature has the following...

 

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A correlation for the thermal conductivity of aluminium as a function of temperature has the following form: k=aTecTed/T W/(m.K) You need to use this correlation in some engineering software, but you would like to avoid the expensive calls to the power and exponential functions. So you decide to fit an interpolating polynomial over the temperature range of interest to your problem. The correlation parameters for iron are: a= 1.610073; b=0.857540; c= -12.3355 × 10-4; d = d = 140.3813 (a) By hand, find the degree 2 (3-pt) Lagrange interpolating polynomial over the range 100 K to 300 K using equal increments in temperature for the sample points. (b) Use the interpolating polynomial to evaluate the thermal conductivity and report the relative error when compared to using the correlation directly for the following tempera- tures: (i) T = 200 K (ii) T = 250 K (iii) T = 400 K (c) The relative error when T = 400K is greater than 20%. Give a reason why you would expect such large error. A correlation for the thermal conductivity of aluminium as a function of temperature has the following form: k=aTecTed/T W/(m.K) You need to use this correlation in some engineering software, but you would like to avoid the expensive calls to the power and exponential functions. So you decide to fit an interpolating polynomial over the temperature range of interest to your problem. The correlation parameters for iron are: a= 1.610073; b=0.857540; c= -12.3355 × 10-4; d = d = 140.3813 (a) By hand, find the degree 2 (3-pt) Lagrange interpolating polynomial over the range 100 K to 300 K using equal increments in temperature for the sample points. (b) Use the interpolating polynomial to evaluate the thermal conductivity and report the relative error when compared to using the correlation directly for the following tempera- tures: (i) T = 200 K (ii) T = 250 K (iii) T = 400 K (c) The relative error when T = 400K is greater than 20%. Give a reason why you would expect such large error.