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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Q. A low value of time constant can be achieved for a thermocouple by

(i) Increasing the wire diameter
(ii) Increasing the value heat transfer coefficient
(iii) Use light metals of low density and low specific heat

Identify the correct statements

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Q. Which of the following has units of time constant?
(Where, P is density, A is area, c is specific heat and V is volume)

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Q. “Thermal radiation suffers no attenuation in a vacuum”. Choose the correct answer

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Q. How does the body temperature falls or rises with time?

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Q. An iron billet (k = 65 W/m K) measuring 20 * 15 * 80 cm is exposed to a convective flow resulting in convection coefficient of 11.5 W/m² K. Determine the Biot number

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Q. A mercury thermometer with bulb idealized as a sphere of 1 mm radius is used for measuring the temperature of fluid whose temperature is varying at a fast rate. For mercury

k = 10 W/m K
α = 0.00005 m²/s
h = 10 W/m² K

If the time for the temperature change of the fluid is 3 second, what should be the radius of thermocouple to read the temperature of the fluid?
For the thermocouple material
k = 100 W/m K
α = 0.0012 m²/s
h = 18 W/m² K

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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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Q. A flat wall of fire clay, 50 cm thick and initially at 25 degree Celsius, has one of its faces suddenly exposed to a hot gas at 950 degree Celsius. If the heat transfer coefficient on the hot side is 7.5 W/m² K and the other face of the wall is insulated so that no heat passes out of that face, determine the time necessary to raise the center of the wall to 350 degree Celsius. For fire clay brick
Thermal conductivity = 1.12 W/m K
Thermal diffusivity = 5.16 * 10¯⁷ m²/s

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Q. Glass spheres of 2 mm radius and at 500 degree Celsius are to be cooled by exposing them to an air stream at 25 degree Celsius. Find maximum value of convective coefficient that is permissible. Assume the following property values
Density = 2250 kg/m³
Specific heat = 850 J/kg K
Conductivity = 1.5 W/m K

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Q. The transient response of a solid can be determined by the equation. (Where, P is density, V is volume, c is specific heat and A is area)

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Q. A 2 cm thick steel slab heated to 525 degree Celsius is held in air stream having a mean temperature of 25 degree Celsius. Estimate the time interval when the slab temperature would not depart from the mean value of 25 degree Celsius by more than 0.5 degree Celsius at any point in the slab. The steel plate has the following thermal physical properties
Density = 7950 kg/m³
C P = 455 J/kg K
K = 46 W/m K

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Q. An average convective heat transfer coefficient for flow of air over a sphere has been measured by observing the temperature-time history of a 12 mm diameter copper sphere (density = 9000 kg/m³ and c = 0.4 k J/kg K) exposed to air at 30 degree Celsius. The temperature of the sphere was measured by two thermocouples one located at the center and the other near the surface. The initial temperature of the ball was 75 degree Celsius and it decreased by 10 degree Celsius in 1.2 minutes. Find the heat transfer coefficient

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Q. Transient condition means

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Q. Which of the following is not correct in a transient flow process?

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