Physics: A5-mm-thick stainless steel strip (k = 21 w/m•k, rho = 8000 kg/m3, and cp = 570 j/kg•k) is being heat treated as it moves through a furnace at a speed of 1 cm/s. the air temperature in the furnace is maintained at 1020°c with a convection heat transfer coefficient of 80 w/m2•k. if the furnace length is 3 m and the stainless steel strip enters it at 20°c, determine the temperature of the strip as it exits the furnace.

A5-mm-thick stainless steel strip (k = 21 w/m•k,

Ответ:

andybiersack154

09.01.2022

Physics

$\frac{\partial T(t)}{\partial y} at\ y = 0\ is \ 1170 K/m$

Explanation:

we know that biot number is given as

$Bi = \frac{hLc}{k}$

where Lc is characteristics length

$Lc = \frac{v}{A} = \frac{LA}{2A} =\frac[5}{2} = 2.5 mm$

$bI = \frac{80\times 2.5\times 10^{-3}}{21} = 0.00952$

as biot number is less than 0.1 thus apply lumper analysis to find time constant t

$b =\frac{hA}{\rho V Cp} = \frac{h}{\rho Lc Cp}$

$b = \frac{ 80}{8000\times 2.5\times 10^{-3} \time 570} = 0.007018 s^{-1}$

$t = \frac{\frac{3}{2}}{0.01} = 150 s$

considerig temperature distiribution

temperature at mid length of furnase is

$\frac{T(t) -T_{\infity}}{20 - T_{\infity}} =E^{-bt}$

$\frac{T(t) -900}{20 - 900} =E^{-0.007018\times 150}$

T(t) = 592.885 degree c

from Newton's law of cooling determine temp gradient at surface at t = 150 s

$-k \frac{\partial T(t)}{\partial y} \at\ y = 0 is h[T(t) -T_{\infity}]$

$\frac{\partial T(t)}{\partial y} \ at\ y = 0 is \frac{h[T(t) -T_{\infity}]}{k}$

$\frac{\partial T(t)}{\partial y}\ at\ y = 0 is \frac{ 80[592.885 - 900]}{21}$

$\frac{\partial T(t)}{\partial y} at\ y = 0\ is \ 1170 K/m$

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Ответ:

benji23

11.09.2022

Physics

The population of the city after 7 years = 569,859

Step-by-step explanation:

The population of the city of Miami = 463,300

The rate of increase in population every year = 3%

The population of the city after 7 years = ?

By formula, $P_{n} = P (1 +\frac{r}{100})^{n }$

Pn is the population after 7 years

P is the current population = 463,300

r = 3 %, n = 7

$P_{7} = 463300 (1 +\frac{3}{100})^{7 }$

= 463300 (1.23)

= 569859

The population of the city after 7 years = 569,859

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