SAMPLE MAE 310 Heat Transfer Fundamentals Spring 2015 Quiz 1 15 of final grade February 9 2015 Closed books notes Problem 1 30 points Consider the steady state temperature distribution within a composite wall composed of Materials A and B The conduction process is one dimensional a Within which material does uniform volumetric generation occur 6 points b What is the boundary condition at x LA 6 points c How would the temperature distribution change if the thermal conductivity of Material A were doubled 6 points d How would the temperature distribution change if the thermal conductivity of Material B were doubled 6 points e Sketch the heat flux distribution q x through the composite wall 6 points Problem 2 30 points Electric current flows through a long rod generating thermal energy at a uniform volumetric rate of q 2 106 W m3 The rod is concentric with a hollow ceramic cylinder creating an enclosure that is filled with air The thermal resistance per unit length due to radiation between the enclosure surfaces is R rad 0 3 m K W and the coefficient associated with free convection in the enclosure is h 20 W m2K a Construct a thermal circuit that can be used to calculate the surface temperature of the rod Tr Label all temperatures heat rates and thermal resistances and evaluate each thermal resistance 15 points b Calculate the surface temperature of the rod for the prescribed conditions 15 points 1 SAMPLE Problem 3 40 points A spherical flame with a diameter of Df 20 cm generates thermal energy at a rate of q 5 kW The flame confined in a spherical combustor is covered by two insulation layers as shown in the figure below The outside surface of the combustor is exposed to air with T 27 C and a convection coefficient h 100 W m2K Insulation kins 1W m K Do 120 cm Ts Di 40 cm 1 Refractory k ref 4 W m K D f 20 cm Tf T 27 oC h 100 W m 2 K a Neglecting radiation on the outside surface of the combustor construct a thermal circuit to evaluate Tf and Ts Label all temperatures heat rates and thermal resistances and evaluate each thermal resistance 10 points b Calculate the surface temperature of the combustor Ts using this circuit 10 points c Calculate the inner temperature of the combustor Tf using this circuit 10 points d Modify the thermal circuit by considering thermal radiation on the outside surface of the combustor Evaluate if the contribution of radiation should be considered in this problem 10 points 2 Heat conduction equations Cartesian coordinates Heat conduction equations Cylindrical coordinates Heat conduction equations Spherical coordinates Thermal resistance for convection Rt conv 1 hA Thermal resistance for radiation Rt rad 1 hr A Fin efficiency f qf q f max qf hA f b 2 Ts Tsur hr Ts2 Tsur