Q. What is the value of characteristics length for sphere?

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Q. What is the value of characteristics length for cube?

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Q. “An infinite solid is one which extends itself infinitely in all directions of space”. Identify the correct option

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Q. The boundary conditions in case of transient heat conduction in infinite thick solids are

(i) t (x = 0) = t i
(ii) t (0, T) = t a for T greater than zero
(iii) t (infinity, T) = t i for T greater than zero
Identify the correct statements

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Q. The perturbation time varies as

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Q. The temperature perturbation at all the surface has penetrated to the depth (Where, T is time constant and α is thermal diffusivity.)

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Q. At the penetration depth d, there will be 1% perturbation at a time given by

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Q. A large steel ingot, which has been uniformly heated to 750 degree Celsius, is hardened by quenching it in an oil bath that is maintained at 25 degree Celsius. What length of time is required for the temperature to reach 600 degree Celsius at a depth of 1 cm? Thermal diffusivity for the steel ingot is 1.21 * 10¯⁵ m²/s. The ingot may be approximated as a flat plate

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Q. A mild steel plate 5 cm thick and initially at 40 degree Celsius temperature is suddenly exposed on one side to a fluid which causes the surface temperature to increase to and remain at 90 degree Celsius. Calculate maximum time that the slab be treated as a semi-infinitely body
For steel, thermal diffusivity = 1.25 * 10¯⁵ m²/s

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Q. Water pipes are to be buried underground in a wet soil (thermal diffusivity = 2.78 * 10¯³ m²/s) which is initially at 4.5 degree Celsius. The soil surface temperature suddenly drops to -5 degree Celsius and remains at this value for₁0 hours. Calculate the minimum depth at which the pipe be laid if the surrounding soil temperature is to remain above 0 degree Celsius. The soil may be considered as semi-infinite solid

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Q. When the surface temperature variation inside a solid are periodic in nature, the profile of temperature variation with time may assume

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Q. The surface temperature oscillates about the mean temperature level in accordance with the relation

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Q. The temperature variation of a thick brick wall during periodic heating or cooling follows a sinusoidal waveform. During a period of 24 hours, the surface temperature ranges from 25 degree Celsius to 75 degree Celsius. Workout the time lag of the temperature wave corresponding to a point located at 25 cm from the wall surface. Thermo-physical properties of the wall material are; thermal conductivity = 0.62 W/m K; specific heat = 450 J/kg K and density = 1620 kg/m³

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Q. A single cylinder 2-stroke engine operates at 1500 rpm. Calculate the depth where the temperature wave due to variation in cylinder is damped to 1% of its surface value. For the cylinder material, thermal diffusivity = 0.042 m²/hr

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Q. The temperature distribution at a certain time instant through a 50 cm thick wall is prescribed by the relation

T = 300 – 500 x – 100 x² + 140x³

Where temperature t is in degree Celsius and the distance x in meters has been measured from the hot surface. If thermal conductivity of the wall material is 20 k J/m hr degree, calculate the heat energy stored per unit area of the wall

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Q. A large plane wall, 40 cm thick and 8 m² area, is heated from one side and temperature distribution at a certain time instant is approximately prescribed by the relation:

T = 80 – 60 x +12 x² + 25 x³ – 20 x⁴

Where temperature t is in degree Celsius and the distance x in meters. Make calculations for heat energy stored in the wall in unit time.

For wall material:
Thermal conductivity = 6 W/m K and thermal diffusivity = 0.02 m²/hr

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Q. At a certain time instant, the temperature distribution in a long cylindrical fire tube can be represented approximately by the relation

T = 650 + 800 r – 4250 r²

Where temperature t is in degree Celsius and radius r is in meter. Find the rate of heat flow such that the tube measures: inside radius 25 cm, outside radius 40 cm and length 1.5 m.

For the tube material

K = 5.5 W/m K

α = 0.004 m²/hr

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Q. Time lag is given by the formula

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Q. The time constant of a thermocouple is the time taken to

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Q. A thermocouple junction of spherical form is to be used to measure the temperature of the gas stream. The junction is at 20 degree Celsius and is placed in a gas stream which is at 200 degree Celsius. Make calculations for junction diameter needed for the thermocouple to have thermal time constant of one second.
Assume the thermos-physical properties as given below
k = 20 W/ m K
h = 350 W/m² K
c = 0.4 k J/kg K
p = 8000 kg/m³

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