Explanation Given: The thickness of pipe is 6 mm . The temperature drop between inlet and exit of the pipe is 7 ° C . The inner pipe surface temperature is 120 ° C . The superheated vapor at mass flow rate is 0.3 kg / s . The length of the pipe is 10 m . The inner diameter of the of pipe is 5 cm . The thermal conductivity of pipe material is 17 W / m ⋅ K . The air temperature is 25 ° C . The constant pressure superheat is 2190 J / kg ⋅ ° C . Concept used: Write the expression for heat conduction 3-Dimension equation for pipe. 1 r ∂ ∂ r ( r ∂ T ∂ r ) + 1 r 2 ∂ ∂ ϕ ( ∂ T ∂ ϕ ) + ∂ 2 T ∂ r 2 + e ˙ g k = 1 α δ T δ t ...... (1) Here, k is thermal conductivity, e ˙ g is the heat generation, and α is thermal diffusivity. Write the expression for the heat loss. Q l o s s = m c p Δ T ...... (2) Here Q l o s s is heat loss through the pipe, m is the mass flow rate., Δ T is temperature drop between the inlet and exit of pipe. Write the expression for outer surface of area. A 1 = 2 π L r 1 Here, A 1 is the outer surface area of pipe, L is the length of the pipe, and r 1 is the outer radius of pipe. Write the expression for inner surface of area. A 2 = 2 π L r 2 ...... (3) Here, A 2 is the inner surface area of pipe, L is the length of the pipe, and r 2 is the inner radius of pipe. Write the expression for convective heat transfer. Q c o n v = h A 1 ( T − T a i r ) Rearrange to write the expression for the convective heat transfer. h = Q c o n v A 1 ( T − T a i r ) ...... (4) Here, Q c o n v is the convective heat transfer, h is the convective heat transfer, T is outer surface of pipe T a i r is the air temperature. Calculation: Here, the heat transfer is steady. 1 α δ T δ t = 0 The heat generation is zero. e ˙ g k = 0 k = 0 The heat transfer is one dimensional. 1 r 2 ∂ ∂ ϕ ( ∂ T ∂ ϕ ) = 0 and ∂ 2 T ∂ r 2 = 0 Therefore substitute 0 for e ˙ g k , 0 for 1 r 2 ∂ ∂ ϕ ( ∂ T ∂ ϕ ) , 0 for ∂ 2 T ∂ r 2 and 0 for 1 α δ T δ t in equation (1) d d r ( r d T d r ) = 0 ...... (5) The boundary condition for this problem is, Q l o s s = − k A d T ( r 1 ) d r ...... (6). Here, A is the area of pipe. The second boundary condition is, T ( r 1 ) = T 1 Here, T 1 is the inner surface temperature of pipe

Heat and Mass Transfer: Fundamentals and Applications

5th Edition

ISBN: 9780073398181

Author: Yunus A. Cengel Dr., Afshin J. Ghajar

Publisher: McGraw-Hill Education

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Chapter 2, Problem 69P

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The heat transfer coefficient as a result of convection.

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Heat and Mass Transfer: Fundamentals and Applications

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