Question

The thermal conductivity of aluminium is kAl = 225W/(m·C), while that of iron is kFe = 75W/(m·C). Cubes of aluminium and iron are prepared with cross-sectional area A = 0.04m2 (i.e., 400 cm2) and thickness L = 0.2m.

(a) The aluminium cube is placed between a hot reservoir at TH = 80C and a cold reservoir at TC = 20C. Determine the rate at which heat flows through the aluminium cube.
(b) The iron cube is placed between a hot reservoir at TH = 80C and a cold reservoir at TC = 20C. Determine the rate at which heat flows through the iron cube.
(c) The two cubes are placed side-by-side (i.e., in parallel) between a hot reservoir at TH = 80C and a cold reservoir at TC = 20C. (i) Determine the effective thermal conductivity of this parallel arrangement of cubes. (ii) Determine the rate at which heat flows through the two cube in parallel.
(d) The two cubes are placed one-after-the-other (i.e., in series) between a hot reservoir at TH = 80C and a cold reservoir at TC = 20C. (i) Determine the effective thermal conductivity of this series arrangement of cubes. (ii) Determine the rate at which heat flows through the two cubes in series.

Answer 1

Rate of heat flow, KAST H = F = d H = Rate of heat flow &= amount of heat flow t=time k = thermal conduefivity A= cross-section do thickness. @Foz aluminium KAI = 255 w/m.e A=0.04 m² d = 0.2m ST= TH - Te =(80-20) = 60°C 60°C .H= KAN AST 255 * 0.04x60 0.2 - 3060 Wisec 6 For Iron, kre = 75w/me H- Kre AST - 75x0.04x60-goo w/see I d For sale by side arrangement (series comme chior): Kett - KAIXIF - 255x75 - 57.95 N/me 255 +75 KAI + Kre cao see .H Kett AST 57.95 x 0.04x60 0.2

Space for Rough Work © for parallel connection Kett - Kre Are + KAN AAN Ape + AM (kre + KAL) (as Are = Ane] 2 255+75 -320 – 330 = 165 W/mc Kest AAT - 165 x 0.04x60 lago w : He rest - 1980 w/sec 0.2 L