Engineering, 31.08.2019 03:30, EmiSiddiqi4037

Drive an expression for heat transferred by a finite extended rod of uniform cross-section area with perfect insulated free end .

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answered: buddyclayjohnson

Assumptions:

Unidimensional heat transfer. Conduction coefficient is constant. $T_{\infty} < T_{s}.$

Explanation:

Use the appropriated heat transfer equation (cylindrical coordinates),

$\frac {1}{r} \frac {d}{dr} (\ r \frac {dT}{dr}) + \frac {q}{k} \ = \ 0$

After separating variables and integrating we obtained the following expression,

$r\frac{dT}{dr} \ = \ - \frac{q}{2k} \ r^{2} \ + \ C_{1}$

After repeating the procedure state above we obtained the following expression,

$T(r) \ = \ - \frac{q}{2k} \ r^{2} \ + \ C_{1} ln(r) \ + \ C_{2}$

According to the image attached, the corresponding boundary values for the system are

$\left \{ {{\frac{dT}{dr}=0 \ , \ r={0}} \atop {T(r_{0})=T_{s}}} \right.$

Then, the temperature distribution in the rod along r axis corresponds to,

$T(r) \ = \ \frac{qr_{0}^{2}}{4k} (1 \ - \frac{r^2}{r_{0}^{2}} ) \ + \ T_{s}$

After deriving the function, we obtained the expression that follows,

$\frac{dT}{dr} \ = \ - \frac{qr}{2k}$

Evaluating the previous expression at the surface of the rod,

$\frac{dT}{dr} \lvert_{r = r_{0}}} \ = (- \frac{qr_{0}}{2k})$

The heat transferred by the finite extended rod corresponds to,

$q_{r} = -k(2 \pi L) \frac{dT}{dr}$

Replacing the derivate term, we obtained the expression that follows,

$q_{r} = -k(2 \pi L) \ (- \frac{qr_{0}}{2k})\\q_{r} \ = \ \pi \ L \ {q \ r_{0}$

Drive an expression for heat transferred by a finite extended rod of uniform cross-section area with

answered: Guest

Infrared sensor is most used sensor in wireless technology where remote controlling functions and detection of surrounding objects/ obstacles are involved. this post will discuss about what is infrared sensor, its working principle, how it works, types, applications, advantages and disadvantages. what is infrared sensor

ir sensor is a simple electronic device which emits and detects ir radiation in order to find out certain objects/obstacles in its range. some of its features are heat and motion sensing.

ir sensors use infrared radiation of wavelength between 0.75 to 1000µm which falls between visible and microwave regions of electromagnetic spectrum. ir region is not visible to human eyes. infrared spectrum is categorized into three regions based on its wavelength i.e. near infrared, mid infrared, far infrared.

wavelength regions of infrared spectrum

near ir – 0.75µm to 3 µm
mid ir – 3 µm to 6 µm
far ir – > 6 µm
1 introduction to infrared sensor

fig. 1 – introduction to infrared sensor

working principle of infrared sensor

infrared sensors works on three fundamental physics laws:

planck’s radiation law: any object whose temperature is not equal to absolute zero (0 kelvin) emits radiation.
stephan boltzmann law: the total energy emitted at all wavelengths by a black body is related to the absolute temperature.
wein’s displacement law: objects of different temperature emit spectra that peak at different wavelengths that is inversely proportional to temperature.
key elements of infrared detection system

the key elements of infrared detection system are:

ir transmitter

ir transmitter acts as source for ir radiation. according to plank’s radiation law, every object is a source of ir radiation at temp t above 0 kelvin. in most cases black body radiators, tungsten lamps, silicon carbide, infrared lasers, leds of infrared wavelength are used as sources.

transmission medium

as the name suggests, transmission medium provides passage for the radiation to reach from ir transmitter to ir receiver. vacuum, atmosphere and optical fibers are used as medium.

ir receiver

generally ir receivers are photo diode and photo transistors. they are capable of detecting infrared radiation. hence ir receiver is also called as ir detector. variety of receivers are available based on wavelength, voltage and package.

ir transmitter and receivers are selected with matching parameters. some of deciding specifications of receivers are photosensitivity or responsivity, noise equivalent power and detectivity.

answered: Guest

Yes. It’s the best product on the market for leaks.

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Drive an expression for heat transferred by a finite extended rod of uniform cross-section area with...