Thermodynamics HW Solutions 467

Thermodynamics HW - explicit transient finite difference formulations become Left boundary node t T T C x A x A g x T T kA T T hA T T A i i i i i i

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 5 Numerical Methods in Heat Conduction 5-77 A plane wall with variable heat generation and constant thermal conductivity is subjected to combined convection, radiation, and heat flux at the left (node 0) and specified temperature at the right boundary (node 4). The explicit finite difference formulation of the left boundary and the finite difference formulation for the total amount of heat transfer at the right boundary are to be determined. Assumptions 1 Heat transfer through the wall is given to be transient and one-dimensional, and the thermal conductivity to be constant. 2 Convection heat transfer is negligible. Analysis Using the energy balance approach and taking the direction of all heat transfers to be towards the node under consideration, the
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: explicit transient finite difference formulations become Left boundary node: t T T C x A x A g x T T kA T T hA T T A i i i i i i i i Δ − Δ = Δ + Δ − + − + − + ∞ 1 1 4 4 surr 2 2 ) ( ] ) ( [ ρ εσ & Heat transfer at right surface: t T T C x A x A g x T T kA Q i i i i i i Δ − Δ = Δ + Δ − + + 4 1 4 4 4 3 surface rightt 2 2 & & Noting that , the total amount of heat transfer becomes ∑ Δ = Δ = i i t Q t Q Q & & h, T ∞ Δ x q • • • • • 0 1 2 3 4 g ( x, t ) T surr T L ∑ ∑ = + = Δ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ − Δ + Δ − Δ − = Δ = 20 1 4 1 4 4 3 4 20 1 surface right surface right 2 2 i i i i i i i i t t T T C x A x A g x T T kA t Q Q & & 5-70...
View Full Document

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.

Ask a homework question - tutors are online