A plane wall of thickness δ has its surfaces maintained at temperatures T1 and T2. The wall is made of a material whose thermal conductivity varies with temperature according to the relation k = k0 T2. Find the expression to work out the steady state heat conduction through the wall?

The temperatures on the two sides of a plane wall are t1 and t2 and thermal conductivity of the wall material is prescribed by the relation K = k0 e (-x/δ) Where, k0 is constant and δ is the wall thickness. Find the relation for temperature distribution in the wall?

A

t 1 – t x / t 1 – t 2 = x

B

t 1 – t x / t 1 – t 2 = δ

C

t 1 – t x / t 1 – t 2 = δ/x

D

t 1 – t x / t 1 – t 2 = x/δ

Fourier's law of heat conduction is (where Q = Amount of heat flow through the body in unit time, A = Surface area of heat flow, taken at right angles to the direction of heat flow, dT = Temperature difference on the two faces of the body, dx = Thickness of the body, through which the heat flows, taken along the direction of heat flow, and k = Thermal conductivity of the body)

A

k. A. (dT/dx)

B

k. A. (dx/dT)

C

k. (dT/dx)

D

k. (dx/dT)

Fourier's law of heat conduction is (where Q = Amount of heat flow through the body in unit time, A = Surface area of heat flow, taken at right angles to the direction of heat flow, dT = Temperature difference on the two faces of the body, dx = Thickness of the body, through which the heat flows, taken along the direction of heat flow and k = Thermal conductivity of the body)

A

$${\text{kA}}\frac{{{\text{dT}}}}{{{\text{dx}}}}$$

B

$${\text{kA}}\frac{{{\text{dx}}}}{{{\text{dT}}}}$$

C

$${\text{k}}\frac{{{\text{dT}}}}{{{\text{dx}}}}$$

D

$${\text{k}}\frac{{{\text{dx}}}}{{{\text{dT}}}}$$

Consider the following statements: The Fourier heat conduction equation Q = -kA(dT/dx) presumes i. Steady-state conditions ii. Constant value of thermal conductivity. iii. Uniform temperatures at the wall surfaces iv. One-dimensional heat flow. Which of the above statements are correct?

A

(i), (ii) and (iii) are correct

B

(i), (ii) and (iv) are correct

C

(ii), (iii) and (iv) are correct

D

(i), (iii) and (iv) are correct

A furnace is made of a refractory brick wall of thickness 0.5 metre and thermal conductivity 0.7 W/m.°K For the same temperature drop and heat loss, this refractory wall can be replaced by a layer of diatomaceous earth of thermal conductivity 0.14 W/m.K and thickness __________ metre.

A

0.01

B

0.1

C

0.25

D

0.5

If the thermal conductivity of a wall material is independent of temperature, the steady state temperature distribution in the very large thin plane wall having steady, uniform surface temperature follows __________ law.

A

Hyperbolic

B

Parabolic

C

Linear

D

Logarithmic

Consider the following statements about thermal conductivity: 1) Thermal conductivity decreases with increasing molecular weight 2) Thermal conductivity of non-metallic liquids generally decreases with increasing temperature 3) Thermal conductivity of gases and liquids is generally smaller than that of solids Which of the above statements are correct?

A

1 and 2 only

B

1 and 3 only

C

2 and 3 only

D

1, 2 and 3

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.

A

870.4 W

B

345.6 W

C

791.04 W

D

238.5 W

The diagram shows heat conduction through a plane wall. The surface temperature is 475 K and it radiates heat to the surroundings at 335 K. If thermal conductivity of the material is 12.5 W/m degree, find the temperature gradient. Let convective coefficient be 80 W/m2 degree and radiation factor is 0.9

A

– 1052.4 degree celsius

B

– 2052.4 degree celsius

C

– 3052.4 degree celsius

D

– 4052.4 degree celsius

A large plane, perfectly insulated on one face and maintained at a fixed temperature T 1 on the bare face, has an emissivity of 0.84 and loses 250 W/m2 when exposed to surroundings at nearly 0 K. The radiant heat loss from another plane of the same size is 125 W/m2 when bare face having emissivity 0.42 and is maintained at temperature T 2 is exposed to the same surroundings. Subsequently these two planes are brought together so that the parallel bare faces lie only 1 cm apart and the heat supply to each is so regulated that their respective temperatures T 1 and T 2 remains unchanged. Determine he net heat flux between the planes

A

0

B

1

C

2

D

3

A plane wall of thickness δ has its surfaces maintained at temperatures T1 and T2. The wall is made of a material whose thermal conductivity varies with temperature according to the relation k = k0 T2. Find the expression to work out the steady state heat conduction through the wall?

Related Questions