Pyrex-glass spheres 2 cm in diameter and initially at 100°C are cooled by a stream of air at 30°C. The convective heat transfer coefficient is estimated to be 60 W/m² K.

(a) Determine the controlling heat transfer resistance.

(b) Determine the time needed for the center of the spheres to reach 50°C if the external resistance is assumed to be dominant. (c)

Determine the time needed for the center of the spheres to reach 50°C if both resistances are considered.

(d) Repeat your calculations in

(c) if instead of an air stream we use a stream of liquid water at 30°C which gives a heat transfer coefficient of 1,500 W/m² K.

Table 5.3.:

FIGURE 5.12:

Transcribed Image Text:

Geometry A. Slab B. Cylinder C. Sphere Series Solution Y = = = + = 22, + sin (22) cos (25)exp(-22T) T-T 4 sin (2) 0 Your - To - T = = a = roots of tan (2) - Bi=0 Jo (2,5) (2+BP) J (2) exp(-2t) Y = 17 - = 2B 1 n=1 n=1 Tag To 4 sin (2) 2^, + A, sin (22) 2 T-T Y = -- = A roots of A (A) - Jo (2) Bi=O 1 (2) 2-12, (2, + B) Jo (2) n=1 =4Bi n=1 -exp(-2) 2Bi [2 + (Bi-1)] sin(2) 2 [22 +Bi(Bi-1)] ---7-6Bi- = n=1 -exp(-2) 2 roots of 2, cot (2) +Bi-1=0 [2+ (Bi-1)] sin (2)- 2 sin(21,) [22+Bi(Bi-1)] -sin(25)exp(-^+) exp(-2t) Mathematica Notebook (M.T.5.3-A) (M.T.5.3-B) (M.T.5.3-C)