Athin electrical heating element provides a uniform heat flux qo" to the outer surface of a duct through which air flows. the duct wall has a thickness of 10 mm and a thermal conductivity of 20 w/m·k. (a) at a particular location, the air temperature is 30°c and the convection heat transfer coefficient between the air and inner surface of the duct is 100 w/m2·k. what heat flux is required to maintain the inner surface of the duct at ti = 58°c? (b) for the conditions of part (a), what is the temperature to of the duct surface next to the heater?

a)q= 2800 W/m²

b)To=59.4°C

Explanation:

Given that

L = 10 mm

K= 20 W/m·K

T=30°C

h= 100 W/m²K

Ti=58°C

a)

Heat flux q

q= h ΔT

q= 100 x (58 - 30 )

q= 2800 W/m²

b)

As we know that heat transfer by Fourier law given as

Q= K A ΔT/L

Lets take outer temperature is To

So by  Fourier law

To= Ti + qL/K

Now by putting the values

To= Ti + qL/K

To=59.4°C

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

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