The wall of a heat exchanger separates hot water at T_A = 90°C from cold water at TB = 10°C. To extend the heat transfer area, two-dimensional ridges are machined on the cold side of the wall, as shown in Fig. P5–76. This geometry causes non-uniform thermal stresses, which may become critical for crack initiation along the lines between two ridges. To predict thermal stresses, the temperature field inside the wall must be determined. Convection coefficients are high enough so that the surface temperature is equal to that of the water on each side of the wall.
(a) Identify the smallest section of the wall that can be analyzed in order to find the temperature field in the whole wall.
(b) For the domain found in part (a), construct a two dimensional grid with Δx = Δy = 5 mm and write the matrix equation AT = C (elements of matrices A and C must be numbers). Do not solve for T.
(c) A thermocouple mounted at point M reads 46.9°C. Determine the other unknown temperatures in the grid defined in part (b).

Transcribed Image Text:

TB TA А 10 mm 10 mm M 5 mm