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ENGR5003 / Week 8
ENGR203 2017 Q B1(a)(ii), (b)Past paperOld spec ENGR2032:114 marks17 min

ENGR203 Power and Heat 2017 Section B Q B1 (same question as ENGR263 2017 B1)[PARTIAL] official answers Left out: (a)(i) (4 marks, draw Searle's bar apparatus) and (a)(iii) (7 marks, uncertainty budget for the measured conductivity) are laboratory measurement and uncertainty analysis, not on the current ENGR5003 syllabus.

Answer ALL parts (a) - (b). [Parts (a)(i) and (a)(iii), on drawing Searle's bar apparatus and its measurement uncertainty, are not on the current syllabus and are omitted here.]

Formulas you may need
  • Fourier's law Q˙=−kAdTdx\dot Q = -kA\dfrac{dT}{dx} (on the formula sheet)
  • Q˙=hA ΔT\dot Q = hA\,\Delta T; Re=ρVLμ\mathrm{Re} = \dfrac{\rho VL}{\mu}, Pr=μcpk\mathrm{Pr} = \dfrac{\mu c_p}{k}, Nu=hLk\mathrm{Nu} = \dfrac{hL}{k} (on the formula sheet)
  • Gas past a cylindrical tube, turbulent: Nu=0.35 Re0.565Pr0.333\mathrm{Nu} = 0.35\,\mathrm{Re}^{0.565}\mathrm{Pr}^{0.333} for 2000<Re<40 0002000 < \mathrm{Re} < 40\,000, Re Pr>0.2\mathrm{Re\,Pr} > 0.2; streamline: Nu=0.35+0.47 Re0.52Pr0.3\mathrm{Nu} = 0.35 + 0.47\,\mathrm{Re}^{0.52}\mathrm{Pr}^{0.3} for 0.1<Re<20000.1 < \mathrm{Re} < 2000 (characteristic length = outer diameter) (on the formula sheet)
  1. (a(ii))
    A perfectly insulated Searle's bar of diameter 30 mm is used to determine the thermal conductivity of Nickel. If the separation between the thermocouples in the bar is approximately 200 mm, the approximate temperature rise between the thermocouples is 50∘C50^\circ\mathrm{C} and the approximate thermal conductivity is 90 W m−1 K−190\ \mathrm{W\,m^{-1}\,K^{-1}} what is the approximate heat flow along the bar?
    [2]Third
  2. (b)
    An electrically heated coil is suspended inside an evacuated fused silica tube of length 800 mm in a manner such that there is no convective or conductive heat transfer from the coil to the tube. The tube has an outer diameter of 25 mm. The coil emits 4 kW of infra-red radiation and 16% of this infra-red is absorbed by the tube. A fan is used to keep the exterior of the tube cool. Using formulae in the data sheet, determine the free stream velocity for air at 20∘C20^\circ\mathrm{C} required to keep the surface temperature of the tube below 210∘C210^\circ\mathrm{C}. For air at 110∘C110^\circ\mathrm{C} take the viscosity of air μ=22.2×10−6 kg m−1 s−1\mu = 22.2 \times 10^{-6}\ \mathrm{kg\,m^{-1}\,s^{-1}}, the heat capacity of air cp=1.0123 kJ kg−1 K−1c_p = 1.0123\ \mathrm{kJ\,kg^{-1}\,K^{-1}}, the density of air ρ=0.9213 kg m−3\rho = 0.9213\ \mathrm{kg\,m^{-3}}, the thermal conductivity of air k=0.03194 W m−1 K−1k = 0.03194\ \mathrm{W\,m^{-1}\,K^{-1}}.
    [12]