HTTA 2017 09 07 Solutions

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Heat T ransfer and Thermal Analysis - A.Y. 2016/17 - Date 07/09/2017 Surname: Name: ID number: Signature: (“matricola” or person code) Part A 1. Write the Fourier law and the Newton law, stating which quantities are indicated by the used symbols. 2. A system is made of (from left to right): 1) an active solid layer A (with positive heat source), 2) a passive solid layerB, 3) a fluid domain that is removing heat by convection with the right face of layer B. The left face of layerA is on the contrary perfectly adiabatic. Draw (qualitatively but with physical accuracy) the steady-state temperature profiles in the two solid layers and in the fluid domain. 3. Draw the temperature profiles T (x) for the two fluids and write the expression of the logarithmic mean tem- perature difference for a co-current parallel-flow heat exchanger if no fluid is undergoing a phase change and the heat capacity of the hot fluid is the largest one. 4. Write the finite difference (centered form) approximation of the 1D Poisson equation (for steady-state heat conduction with heat source) for a medium having constant conductivity. 5. Write the expressions of the Nusselt and Biot dimensionless groups and state the difference between the two. 6. Write the Young equation, stating which quantities are indicated by the used symbols and the measurement unit of the interfacial energy. 7. Put the following materials/substances in correct ascending order of Prandtl number values at ambient temper- ature and pressure: water, air, very viscous mineral oil, mercury. Heat T ransfer and Thermal Analysis - A.Y. 2016/17 - Date 07/09/2017 - Part B Exercise 1 (up to 15 points) A mass flow rate ˙Mh = 15 kg/s of a corrosive hot fluid (havingρh= 1200 kg/m3,cP h = 1400 J/kgK,µh = 4.0·10−4 Pa s, λh = 0.15 W/mK) is flowing within the…