HTTA 2016 07 18 Solutions

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Heat T ransfer and Thermal Analysis - A.Y. 2015/16 - Date 2016/07/18 Surname: Name: ID number: Signature: Part A 1. Write the Fourier hypothesis, stating of which quantities the conductivity may be a function. 2. Write the finite difference approximation of the 1D conduction equation without heat source: ρc ∂T ∂τ = λ ∂ 2T ∂x 2 using the basic centered form for the space derivative and 1) the explicit approach, 2) the implicit approach, for the time dependence. 3. Put the following materials/substances in correct descending order (i.e., from larger to smaller) of conductivity: water, glass wool, aluminium, diamond, air, stainless steel, iron. 4. Write the definitions and the physical meaning of two primary dimensionless groups (e.g not Ra or Pe) related to convection. 5. Write a commonly used criterion to distinguish between forced, natural and mixed convection. 6. Write the Wien law and its physical meaning. 7. Draw (qualitatively but with physical accuracy, including no violation of the Second Principle) the temperature profiles for the two fluids in a counter-current parallel flow heat exchanger when no fluid is undergoing a phase transition and the mass flow rate heat capacity of the hot fluid is larger than that of the cold fluid. Heat T ransfer and Thermal Analysis - A.Y. 2015/16 - Date 2016/07/18 - Part B Exercise 1 (up to 15 points) A flat wall is infinite along two orthogonal spatial directions, while along the third it is made of (from left to right): • an active layer A (λA = 2 W/mK, sA = 0.3 m), in which a heat source ˙U ′′′ A is present; • a vacuum interspace, subdivided into two parts by a layer S of negligible thickness, that behaves as a black body; • two passive layers B (λB = 5 W/mK, sB = 0.1 m) and C (λC = 1 W/mK, sC = 0.2 m). Knowing that the system is in steady…