Question

1. 1.08x10⁶ grams/h of a superheated fluid flows through a pipe in a power plant. The pipe is 1000 cm long, has an inner diameter of 0.05m and a wall thickness of 0.6 cm. The pipe has a thermal conductivity of 0.0017 kW/mK, and the inner pipe surface is at a uniform temperature of 393K. The temperature drop between the inlet and exit of the pipe is 7K, and the constant pressure specific heat of vapor is 2190 J/kgK. If the air temperature surrounding the tube is 298K,

(a) Determine the outer pipe surface temperature. (20 points)

(b) Find the heat transfer coefficient of convection between the outer pipe surface and the surrounding air.   (20 points)

2. Consider the base plate of a 1000 W household iron with a thickness of L = 0.6 cm, a base area of A = 145 cm², and a thermal conductivity of k = 75 W/mK. The inner surface of the base plate is loaded with a uniform heat flux generated by resistance heaters inside. When steady operating conditions are reached, the outer surface temperature of the plate is measured to be 112C. Disregarding any heat loss through the upper part of the iron,

(a) express the differential equation and boundary conditions for steady one-dimensional heat conduction through the plate, (15 points)

(b) obtain a relation for the variation of temperature in the base plate by solving the differential equation, and (15 points)

(c) evaluate the inner surface temperature of the base plate at L = 0. (15 points)

3. Consider a large 3-cm-thick stainless steel plate in which heat is generated uniformly at a rate of         5 x 10⁶ W/m³. Assuming the plate is losing heat evenly from both sides, determine the heat flux from one surface of the plate during steady operation. (15 points)

Answer 1

Given data Mass of super heated fluid (m_v) = 1.08 times 10^6 gram s/h = 1.08 times 10^6 times 10^- 3 kg/s Length of pipe (L_p) = 1000 cm = 10 m T_si = 393 k C_R = 2190 j/kg k T_00 = 298 k = 2.190 kg k d_i = 0.05 m d_0 = 0.062 m r_i = 0.025 m r_0 = 0.03/m Temperature of drop PT = 7 k (a) Total heat loss from the steam is equal to heat loss to surrounding through conduction and convection of pipe Total heat loss = m c pv times Delta T = 0.3 times 2.19 times 7 = 4.6 k /s = 4.6 kw Theta = thermal potential/thermal resistance for cylinder R_th = (ln (r_2/r_1)/2 pi K L) = T_si - T _s0/ln(r_0/r_1) (2 pi K L) 4 - 6 = (393 - T_s0) times 2 pi times 0.0