Subtopic: Steady state heat transfer in conduction, convection and radiation
Question Statement:
In order to reduce heat loss, a steam line with a tube diameter of 1.0 cm is insulated with a material having thermal conductivity of 0.108 W m⁻¹ K⁻¹. Heat is dissipated from the outer surface of the insulating material by natural convection with a heat transfer coefficient of 12 W m⁻² K⁻¹ into the ambient at a constant temperature. The heat loss becomes maximum when the thickness of insulation is
Options:
(A) 0.5 mm
(B) 2 mm
(C) 4 mm
(D) 6.5 mm
Official Answer Key:
C
Step-by-Step Solution & Explanation
Critical radius of insulation for a cylinder: r_cr = k_ins/h = 0.108/12 = 0.009 m = 9 mm. Pipe outer radius = 1.0 cm diameter / 2 = 5 mm. Thickness of insulation at maximum heat loss = r_cr − r_pipe = 9−5 = 4 mm.
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