A small sphere of reference-grade iron with a specific heat of 447 J/kg.K and a mass of 0.515 kg is suddenly immersed in a water-ice mixture. Fine thermocouple wires suspend the sphere, and the temperature is observed to change from 15 to 14 ⁰C in 6.35s. The experiment is repeated with a metallic sphere of the same diameter, but of unknown composition with a mass of 1.263 kg. If the same observed temperature change occurs in 4.59s, what is the specific heat of the unknown material?

An uninsulated steam pipe passes through a room in which the air and walls are at 25 ⁰C. The outside diameter of the pipe is 70 mm and its surface temperature and emissivity are 200 ⁰C and 0.8 respectively. What are the surface emissive power and irradiation? If the coefficient associated with free convection heat transfer from the surface to the air is 15W/m².K. What is the rate of heat loss from the pipe? And the facilities manager wants you to recommend methods for reducing the heat loss to the room, and two options are proposed. The first option would restrict air movement around the outer surface of the pipe and thereby reducing the convection coefficient by a factor of two. The second option would coat the outer surface of the pipe with low emissivity (0.4) paint. Which of the foregoing options would you recommend?

Derive the Fourier’s differential equation in the radial system (r,θ,z) and spherical system (r,θ,Φ).

The temperature distribution across a wall 0.3m thick at a certain instant of time is

T(x) = a + bx + cx² , where T is in ⁰C and x in meters,

a = 200 ⁰C

b = -200 ⁰C

c = 30 ⁰C/m²

The wall has a thermal conductivity of 1W/mK.

On a unit surface area basis, determine the rate of heat transfer into, out of the wall and the rate of change of energy stored by the wall?

If cold surface is exposed to a fluid at 100 ⁰C, what is the convective coefficient?

Sections of a pipeline run above the ground and are supported by vertical steel shafts (k = 25 W/m K) that are 1 m long and have a cross-sectional area of 0.005m². Under normal operating conditions, the temperature variation along the length of a shaft is known to be governed by an equation of the form,

T = 100 – 150x + 10x²

Where T and x have units of ⁰C and meters respectively. Temperature variations are negligible over the shaft cross section. Evaluate the temperature and conduction heat rate at the shaft – pipeline joint (x = 0) and at the shaft – ground interface (x = 1m).

Explain the difference in the heat rates.

Question

A small sphere of reference-grade iron with a specific heat of 447 J/kg.K and a mass of 0.515 kg is suddenly immersed in a water-ice mixture. Fine thermocouple wires suspend the sphere, and the temperature is observed to change from 15 to 14 ⁰C in 6.35s. The experiment is repeated with a metallic sphere of the same diameter, but of unknown composition with a mass of 1.263 kg. If the same observed temperature change occurs in 4.59s, what is the specific heat of the unknown material?

An uninsulated steam pipe passes through a room in which the air and walls are at 25 ⁰C. The outside diameter of the pipe is 70 mm and its surface temperature and emissivity are 200 ⁰C and 0.8 respectively. What are the surface emissive power and irradiation? If the coefficient associated with free convection heat transfer from the surface to the air is 15W/m².K. What is the rate of heat loss from the pipe? And the facilities manager wants you to recommend methods for reducing the heat loss to the room, and two options are proposed. The first option would restrict air movement around the outer surface of the pipe and thereby reducing the convection coefficient by a factor of two. The second option would coat the outer surface of the pipe with low emissivity (0.4) paint. Which of the foregoing options would you recommend?

Derive the Fourier’s differential equation in the radial system (r,θ,z) and spherical system (r,θ,Φ).

The temperature distribution across a wall 0.3m thick at a certain instant of time is

T(x) = a + bx + cx² , where T is in ⁰C and x in meters,

a = 200 ⁰C

b = -200 ⁰C

c = 30 ⁰C/m²

The wall has a thermal conductivity of 1W/mK.

On a unit surface area basis, determine the rate of heat transfer into, out of the wall and the rate of change of energy stored by the wall?

If cold surface is exposed to a fluid at 100 ⁰C, what is the convective coefficient?

Sections of a pipeline run above the ground and are supported by vertical steel shafts (k = 25 W/m K) that are 1 m long and have a cross-sectional area of 0.005m². Under normal operating conditions, the temperature variation along the length of a shaft is known to be governed by an equation of the form,

T = 100 – 150x + 10x²

Where T and x have units of ⁰C and meters respectively. Temperature variations are negligible over the shaft cross section. Evaluate the temperature and conduction heat rate at the shaft – pipeline joint (x = 0) and at the shaft – ground interface (x = 1m).

Explain the difference in the heat rates.

Accepted Answer

Hi, you have posted multiple four questions in sequence. Here, we are solving the first for you.…