1、 and other given quantities, the nodal temperatures after 560/15 = 20 time steps （5 min） are determined to beAfter 5 min: T0 =228.9C, T1 =228.4C, T2 =226.8C, T3 =224.0C, and T4 =219.9 C（b） The time needed for transient operation to be established is determined by increasing the number of time steps
2、until the nodal temperatures no longer change. In this case steady operation is established in - min, and the nodal temperatures under steady conditions are determined to be T0 =2420C, T1 =2413C, T2 =2391C, T3 =2356C, and T4 =2306 CDiscussion The steady solution can be checked independently by obtai
3、ning the steady finite difference formulation, and solving the resulting equations simultaneously. 5-85 !PROBLEM 5-85GIVENL=0.08 mk=28 W/m-Calpha=12.5E-6 m2/sT_i=100 Cg_dot=1E6 W/m3T_infinity=20 h=35 W/m2-CDELTAx=0.02 time=300 s, parameter to be variedANALYSISM=L/DELTAx+1 Number of nodesDELTAt=15 st
4、au=（alpha*DELTAt）/DELTAx2The technique is to store the temperatures in the parametric table and recover them （as old temperatures）using the variable ROW. The first row contains the initial values so Solve Table must begin at row 2.Use the DUPLICATE statement to reduce the number of equations that ne
5、ed to be typed. Column 1 contains the time, column 2 the value of T1, column 3, the value of T2, etc., and column 7 the Row.Time=TableValue（Row-1,#Time）+DELTAtDuplicate i=1,5 T_oldi=TableValue（Row-1,#Ti）endUsing the explicit finite difference approach, the six equations for the six unknown temperatu
6、res are determined to beT1=tau*（T_old2+T_old2）+（1-2*tau）*T_old1+tau*（g_dot*DELTAx2）/k Node 1, insulatedT2=tau*（T_old1+T_old3）+（1-2*tau）*T_old2+tau*（g_dot*DELTAx2）/k Node 2T3=tau*（T_old2+T_old4）+（1-2*tau）*T_old3+tau*（g_dot*DELTAx2）/k Node 3T4=tau*（T_old3+T_old5）+（1-2*tau）*T_old4+tau*（g_dot*DELTAx2）/k
7、 Node 4T5=（1-2*tau-2*tau*（h*DELTAx）/k）*T_old5+2*tau*T_old4+2*tau*（h*DELTAx）/k*T_infinity+tau*（g_dot*DELTAx2）/k Node 4, convectionTime sT1 CT2 CT3 CT4 CT5 CRow100115106.7104.8230113.4112.5111.3345120.1119.7119117460126.8126.6126.3125.1123.3575133.3133.2132.6131.5129.2690139.9139.6139.1137.6135.571051
8、46.4146.2145.4144141.58120152.9152.6151.8150.2147.79135159.3159.1158.1156.5153.710346512171213120311851160232348012201216120611881163233349512231209119211672343510122711951170235352512301198117323635401234121912011176237355512371233120511792383570124012261208118323935851244122912111186240360012471243121411892415-86 The passive solar heating of a house through a
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