Explanation Given: Maximum temperature of PTFE lining is 260 ° C , thermal conductivity of pipe is 15 W/mk , inside diameter is 24 mm , wall thickness is 5 mm , outer steam temperature is 600 ° C ,convection heat transfer coefficient is 50 W/m 2 k and water temperature inside tube is 50 ° C . Concept used: Expression heat transfer through plate is given as follows: q = − k d T d r ....... (1) Here, heat flux is q , thermal conductivity is k , temperature difference is Δ T and thickness is L . Expression for heat equation for cylinder is given as follows: d d r ( r d T d r ) = 0 ....... (2) Here, temperature is T and radial distance is r . Expression heat transfer in convection mode is given as follows: q = h ( T ( r ) − T ∞ ) ....... (3) Here, convection coefficient is h , exposed surface area is A , surface temperature T ( r 1 ) and ambient temperature is T ∞ . Calculation: Integrate the equation (2) as follows: ∫ d d r ( r d T d r ) = 0 r d T d r = C 1 d T d r = C 1 r Again, integrate the above equation as follows: ∫ d T = ∫ 1 r d r C 1 T = C 1 ln r + C 2 Temperature at position r 1 is calculated as follows: T = C 1 ln r + C 2 T ( r 1 ) = C 1 ln r 1 + C 2 Temperature at position r 2 is calculated as follows: T = C 1 ln r + C 2 T ( r 2 ) = C 1 ln r 2 + C 2 Use equation (1), (3) and thermal gradient at radial position r 2 as follows: h ( T o − T ( r 2 ) ) = − k d T d r h ( T o − ( C 1 ln r 2 + C 2 ) ) = − k C 1 r 2 50 ( 873 − ( C 1 ln 0

6th Edition

ISBN: 9780073398198

Author: CENGEL

Publisher: RENT MCG

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Question

Chapter 2, Problem 76P

To determine

The formula for temperature variation in the pipe wall, temperature at inner surfaces of the pipe and comparison with maximum temperature of PTFE lining.

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Chapter 2, Problem 75P

Chapter 2, Problem 77P

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Chapter 2 Solutions

HEAT+MASS TRANSFER:FUND.+APPL.

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