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(a) By considering numerical differentiation aT_T(x,1+1)-7(x,1), deduce that the temperature distribution along the bar at point ar Ar (x,t+1) in explicit finite-difference form is given by 'T_T(x+1)-27(x,1)+7(x-1,1) T(x,1+1)=0.87(x-1)-0.67(x,1)+0.87(x+1,1) and

(a) By considering numerical differentiation aT_T(x,1+1)-7(x,1), deduce that the temperature distribution along the bar at point ar Ar (x,t+1) in explicit finite-difference form is given by 'T_T(x+1)-27(x,1)+7(x-1,1) T(x,1+1)=0.87(x-1)-0.67(x,1)+0.87(x+1,1) and

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) By considering numerical differentiation ar T(x+1)-I(x), deduce that the temperature distribution along the bar at point dr M (x,t+1) in explicit finite-difference form is given by 8²T_T(x+1,t)-27(x,1)+7(x-1,1) Ax² T(x,t+1)=0.87(x-1,t)-0.67(x,t)+0.87(x+1,1) and
Transcribed Image Text:(a) By considering numerical differentiation ar T(x+1)-I(x), deduce that the temperature distribution along the bar at point dr M (x,t+1) in explicit finite-difference form is given by 8²T_T(x+1,t)-27(x,1)+7(x-1,1) Ax² T(x,t+1)=0.87(x-1,t)-0.67(x,t)+0.87(x+1,1) and
Q3 The heat transfer performance of a new conductor bar of length 20 cm is under inspection. The material is fully insulated such that the heat transfer is only one dimensional in axial direction (x-axis). The left end is maintained at temperature of 100°C, while the right end is maintained at temperature of 20°C, for 1>0. The distribution of the initial temperatures is shown in Figure Q3. The unsteady state heat conduction equation is given by; ax =0 Where is a thermal diffusivity of material and x is the longitudinal coordinate of the bar. The thermal diffusivity of the material is given as x=10 cm²/s, and A = 2 second.
Transcribed Image Text:Q3 The heat transfer performance of a new conductor bar of length 20 cm is under inspection. The material is fully insulated such that the heat transfer is only one dimensional in axial direction (x-axis). The left end is maintained at temperature of 100°C, while the right end is maintained at temperature of 20°C, for 1>0. The distribution of the initial temperatures is shown in Figure Q3. The unsteady state heat conduction equation is given by; ax =0 Where is a thermal diffusivity of material and x is the longitudinal coordinate of the bar. The thermal diffusivity of the material is given as x=10 cm²/s, and A = 2 second.
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