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Heat T ransfer and Thermal Analysis - A.Y. 2014/15 - Date 2016/02/03 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. Write the definitions of the Nusselt and Biot dimensionless groups, and comment the difference between the two. 4. Write the Richardson number and the criterion to distinguish between forced, natural and mixed convection. 5. Write the expression to determine the net energy transfer between two gray surfaces enclosing a cavity. 6. Write the finite difference approximations for the first and second derivatives of temperature with respect to a spatial direction using the basic centered form. 7. Draw the temperature profiles for the two fluids and write the expression of the logarithmic mean temperature difference for a counter-current parallel-flow heat exchanger. Heat T ransfer and Thermal Analysis - A.Y. 2014/15 - Date 2016/02/03 - Part B Question 1 (up to 10 points) Derive the expression of the Grashof number. Exercise 1 (up to 10 points) In a radiator (cross-flow, both fluids unmixed) a mass flow rate ˙Mw = 1.5 kg/s of water is flowing within N = 140 tubes (Di = 5 mm, L = 1 m, negligible thickness) while the external air (atmospheric pressure, mass flow rate ˙Ma = 4.75 kg/s) is flowing between the flat plates of the radiator, that have a total surface area which is 50 times the total internal surface area of the ducts. The internal convective coefficient (for water within the ducts) hi has to be…