Chapter 5 Numerical Methods in Heat Conduction 5-89 A long solid bar is subjected to transient two-dimensional heat transfer. The centerline temperature of the bar after 10 min and after steady conditions are established are to be determined. Assumptions 1Heat transfer through the body is given to be transient and two-dimensional. 2 Heat is generated uniformly in the body. 3 The heat transfer coefficient also includes the radiation effects. PropertiesThe conductivity and diffusivity are given to be k= 28 W/m⋅°C and . α=×−12 106m/s2•••4 5 6g••••••h, T∞1 2 37 8 9h, T∞h, T∞h, T∞Analysis The nodal spacing is given to be Δx=Δx=l=0.1 m. The explicit finite difference equations are determined on the basis of the energy balance for the transient case expressed as &&QGVCTTtimimiAll sideselementielement∑+=−+ρ1ΔThe quantities do not change with time, and thus we do not need to use the superscript i for them. The general
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This note was uploaded on 01/22/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.