HTTA 2015 09 28 Solutions

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Heat T ransfer and Thermal Analysis - A.Y. 2014/15 - Date 2015/09/28 Surname: Name: ID number: Signature: Part A 1. Write the general equation for conduction in a medium having conductivity which varies with temperature 2. Derive the general integrals (before application of any b.c) giving the temperature and heat flux profiles as a function of the radius for a homogeneous sphere with heat source. Then, comment the boundary condition in correspondence of the sphere center for a full sphere. 3. Put the following materials/substances in correct descending order of conductivity: copper, diamond, bulk PVC (polyvinyl chloride), stainless steel, expanded polystyrene foam. 4. Write the continuity equation for an incompressible fluid. 5. Write the expression to determine the net energy transfer between two gray surfaces enclosing a cavity. 6. Write the finite difference approximation for the 1D, transient conduction equation with no heat source, using the explicit approach. 7. Write the Laplace-Young equation, stating the meaning of the involved terms. Heat T ransfer and Thermal Analysis - A.Y. 2014/15 - Date 2015/09/28 - Part B Question 1 (up to 10 points) Give a brief overview about the blackbody monochromatic emissive power, the Wien law and the over-band and over-full-spectrum integration of the first. Exercise 1 (up to 10 points) A mass flow rate ˙Mw = 5 kg/s of water (kinematic viscosity 6 · 10−7 m2/s, thermal conductivity 0.637 W/mK) is flowing with an inlet temperatureTwi = 15◦C within theN = 30 tubes (Di = 22 mm,De = 24 mm, made of stainless steel with conductivity λ = 15 W/mK) of a shell-and-tube counter-current heat exchanger. Shell-side, a solution (havingcP s = 3.5 kJ/kgK) is flowing with mass flow rate ˙Ms = 1.25 kg/s and it is cooled from Tsi = 80◦C to Tsu = 25◦C. The…