SxwP C W W P Sxwe E Consider the one-dimensional control volume in Figure 8.1. Integration of equation (8.3) over the control volume and over a time interval from t to t + At gives 1+ 1+At 1+A1 pc -dV dt = dv dt + sdV dt at CV CV CV This may be written as e [i+At dt dV = t 1+ (8.4) 1+ dt + SAV dt dx e (8.5) - In equation (8.6) superscript 'o' refers to temperatures at time t; temperatures at time level + At are not superscripted. The same result as (8.6) would be obtained by substituting (TpTp)/At for OT/Ot so this term has been discretised using a first- order (backward) differencing scheme. Higher order schemes, which may be used to discretise this term, will be discussed briefly later in this chapter. If we apply central differencing to the diffusion terms on the right hand side equation (8.5) may be written as 1+AI TE-TP Tp-Tw dt " | [ ( k 1 T6 - TP) - ( K A TB - TW)]di ke pc (Tp Tp) AV = ] [ ( k A t 1+ + "J" T sor a SXPE kwA (8.7)