ขอ solution manual ของ Applied mathematics and modeling for chemical engineers Richard G. Rice, D. Do Duong หน่อยครับ หรือใครมีเฉลยข้อ 3.3 ครับ
3.3 Thin, metallic circular fins of thickness b can be attached to cylindrical pipes as heat transfer promoters. The fins are exposed to an ambient temperature Ta, and the root of each fin contacts the pipe at position r=R1,where the temperature is constant, Tw. The fins loses heat to ambient air though a transfer coefficient h. The metallic fin transmits heat by conduction in the radial direction.
(a) Show that the steady-state heat balance on an elementary annular element of fin yields the equation
(1/r)d/dr(rdT/dr) - (2h/bk)(T-Ta) = 0
(b) Define a dimensionless radial coordinate as
x = r (sqrt)(2h/bk)
and introduce y=T-Ta, and thus show the elementary equation
x2 (d2y/dx2) + x(dy/dx) - x2y = 0
describes the physical situration.
(c) Apply the method f Frobenius and find the roots of the indicial equation to show that c1, c2, 0.
ขอ solution manual ของ Applied mathematics and modeling for chemical engineers Richard G. Rice, D. Do Duong
3.3 Thin, metallic circular fins of thickness b can be attached to cylindrical pipes as heat transfer promoters. The fins are exposed to an ambient temperature Ta, and the root of each fin contacts the pipe at position r=R1,where the temperature is constant, Tw. The fins loses heat to ambient air though a transfer coefficient h. The metallic fin transmits heat by conduction in the radial direction.
(a) Show that the steady-state heat balance on an elementary annular element of fin yields the equation
(1/r)d/dr(rdT/dr) - (2h/bk)(T-Ta) = 0
(b) Define a dimensionless radial coordinate as
x = r (sqrt)(2h/bk)
and introduce y=T-Ta, and thus show the elementary equation
x2 (d2y/dx2) + x(dy/dx) - x2y = 0
describes the physical situration.
(c) Apply the method f Frobenius and find the roots of the indicial equation to show that c1, c2, 0.