Explanation Given: The thickness of the steel plate is 1 cm . The initial temperature of the steel plate is 600 ° C . Final temperature of the steel plate is 100 ° C . Temperature of the oil reservoir is 30 ° C . The heat transfer coefficient is 400 W / m 2 ⋅ K . Thermal conductivity is 45 W / m ⋅ K . Density of the steel plate is 7800 kg / m 2 . Specific heat of the plate is 470 W / m 2 ⋅ K . Concept used: Write the expression for the characteristic length. L = V A ....... (1) Here, L is the characteristics length, V is the volume and A is the surface area. Write the expression for the volume of the plate. V = A 2 t ′ Here, t ′ is the thickness of the plate. Substitute A 2 t ′ for V in equation (2). L = A 2 t ′ A Simplify the above equation, L = t ′ 2 ....... (2) Write the expression for the Biot number. B i = h L k Here, B i is the Biot number, h is the heat transfer coefficient and k is the thermal conductivity. Substitute t ′ 2 for L in the above equation. B i = t ′ h 2 k Substitute 400 W / m 2 ⋅ K for h , 1 cm for t ′ and 45 W / m ⋅ K for k in the above equation. B i = ( 1 cm ( 1 m 100 cm ) ) ( 400 ) 2 ( 45 ) = ( 0.01 ) ( 400 ) 90 = 0.044 Here, the Biot number is less than 0.1 . Write the expression for the variation of temperature with time by Lumped capacitance. T f − T 0 T i − T 0 = e − ( h A t ρ V c P ) Here, T f is the final temperature, T i is the final temperature, T 0 is the surrounding temperature, ρ is the density, c P is the specific heat of the steel plate and t is the time

Heat and Mass Transfer: Fundamentals and Applications

6th Edition

ISBN: 9781260440058

Author: CENGEL, Yunus

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 4, Problem 142P

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The quench time from 600°C to 100°C for the steel plate.

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Chapter 4, Problem 141P

Chapter 4, Problem 143P

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Chapter 4 Solutions

Heat and Mass Transfer: Fundamentals and Applications

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The quench time from 600 ° C to 100 ° C for the steel plate.

The quench time from 600°C to 100°C for the steel plate.

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Chapter 4 Solutions