Example A thin rod has length 1 m and cross-section 1 cm x 1 cm. The left-hand end is kept at 100 C, whilst the right-hand end is insulated. T = 20°C T=100°C The heat flux across any section of area A is Rod given by dT - kA dr x = 0 s= -c(T-T.) where the conductivity k= 1000 W m ' K-!. The rod is allowed to cool along its length at a rate proportional to its difference from the ambient temperature (Newton's law of cooling); i.e. the heat source per unit length is: s=-c(T-T) where the ambient temperature T. = 20 °C and the coefficientc=25 W m K-1
Example A thin rod has length 1 m and cross-section 1 cm x 1 cm. The left-hand end is kept at 100 C, whilst the right-hand end is insulated. T = 20°C T=100°C The heat flux across any section of area A is Rod given by dT - kA dr x = 0 s= -c(T-T.) where the conductivity k= 1000 W m ' K-!. The rod is allowed to cool along its length at a rate proportional to its difference from the ambient temperature (Newton's law of cooling); i.e. the heat source per unit length is: s=-c(T-T) where the ambient temperature T. = 20 °C and the coefficientc=25 W m K-1
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter2: Steady Heat Conduction
Section: Chapter Questions
Problem 2.47P
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a) Separate the rod into 4 control sections, each with a node in the centre, then use finite-volume analysis to estimate the temperature along the length of the rod.
b) Separate the rod into 4 sections and repeat (a) with equal both temperature values and beginning conditions using the finite difference method (if necessary).
c) Write down and analytically compare with (a) and (b)
differential equation for the temperature distribution along the rod. d) Compare the results (a), (b) and (c) by using a graph and differences.
e) How to improve the results from (a) and (b)? Show it.
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