HTTA 2015 09 14 Solutions

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Heat T ransfer and Thermal Analysis - A.Y. 2014/15 - Date 2015/09/14 Surname: Name: ID number: Signature: Part A 1. Draw (qualitatively but with physical accuracy) the steady-state temperature profiles in a passive flat plate made of 3 layers A, B, C and having fixed temperatures on the external surfaces, knowing that the thickness is the same for all layers and that λA >λ B >λ C. 2. Write the Fourier hypothesis, stating of which quantities the conductivity may be a function. 3. Draw the temperature profiles for the two fluids and write the expression of the logarithmic mean temperature difference for a co-current parallel-flow heat exchanger. 4. Write the expression of the total heat transfer resistance in a duct-in-duct heat exchanger where fouling is present on both sides of the wall separating the two fluids. 5. State which one between film and dropwise condensation is the most efficient and why. 6. Write the relation between the absorption, reflection and transmission coefficients for a diffuse emitter, both in total and monochromatic version. 7. Write the expression of the Peclet number. Heat T ransfer and Thermal Analysis - A.Y. 2014/15 - Date 2015/09/14 - Part B Question 1 (up to 10 points) Derive a finite difference expression for the first and second derivatives of temperature with respect to space (in 1D) using the forward, backward and centered approaches. Comment the truncation errors for two cases. Exercise 1 (up to 10 points) A flat wall is infinite along two orthogonal spatial directions, while along the third it is made of three layers, as follows (from left to right): 1. active layer A: sA = 100 mm, λA = 15 W/mK, ˙U ′′′ A = 105 W/m3; 2. passive layer B: sB = 250 mm, λB = 0.5 W/mK; 3. active layer C: sC = 100 mm, λC = 15 W/mK, ˙U ′′′ C = 105 W/m3; Both the external faces…