MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Solids

Inner surface...

Question

Inner surface of a cylindrical shell of lenght L and material thermal conductivity K is kept at constant temprature T1 and outer surface with temprature T2 l,such that T1>T2. Radii of inner n outer surfaces are R and 2R respectivly. If cylinder is replaced by an another cylinder of lenght L/2 and radii of inner and outer surface is R/4 and R respectivly. Then the thermal conductivity becomes 'nK'. If tempratures and heat current (dQ/dt) are same in both condition ,then , find the value of 'n'?

Open in App

Solution

Suggest Corrections

thumbs-up

0

Similar questions

Q. Inner surface of a cylindrical shell of length

l

and of material of thermal conductivity

k

is kept at constant temperature

T_{1}

and outer surface of the cylinder is kept at constant temperature

T_{2}

(T_{1} > T_{2})

as shown in figure. Heat flows from inner surface to outer surface radially outward. Inner and outer radii of the shell are

R

2 R

respectively. Due to lack of space this cylinder has to be replaced by a smaller cylinder of length

\frac{l}{2}

inner and outer radii

\frac{R}{4}

R

respectively and thermal conductivity of material

n k

. If rate of radially outward heat flow remains same for same temperatures of inner and outer surface i.e.,

T_{1}

T_{2}

, then find the value of

n

Q. Inner surface of a cylindrical shell of length l and of material of thermal conductivity k is kept at constant temperature

T_{1}

and outer surface of the cylinder is kept at constant temperature

T_{2}

(T_{1} > T_{2})

such that

Due to lack of space this cylinder has to be replaced by a smaller cylinder of length

\frac{l}{2}

, inner and outer radii

\frac{R}{4}

and R respectively and thermal conductivity of material nk. If rate of radial outward heat flow remains same for same temperatures of inner and outer surface i.e.

T_{1}

T_{2}

then find the value of n.

Q. The inner and outer surfaces of a hollow spherical shell of inner radius 'a' and outer radius 'b' are maintained at temperature

T_{1}

T_{2}

(< T_{1})

. The thermal conductivity of material of the shell is k. If the rate of heat flow inner to outer surface is

\frac{d Q}{d t} = N π k a b (\frac{T_{1} - T_{2}}{b - a})

N

Q. A spherical shell of inner radius ‘

R_{1}

’ and outer radius ‘

R_{2}

’ is having variable thermal conductivity given by K =

(a_{0} T) r

a_{0}

is constant, ‘T’ is temperature in Kelvin and ‘r’ is the distance from the centre. Two surfaces of shell are maintained at temperature

T_{1}

(inner surface) and

T_{2}

(outer surface), respectively

(T_{1} > T_{2})

. The heat current flowing through the shell would be

Q. A system consist of a cylinder surrounded by a cylindrical shell. A cylinder is a radius

R

and is made of material of thermal conductivity

K

, whereas a cylindrical shell has inner radius

R

and outer radius

2 R

and is made of material of thermal conductivity twice as that of cylinder. Assuming the system in steady state and negligible heat loss across the cylindrical surface, find the effective thermal conductivity of the system, if the two ends of the combined system are maintained at two different temperatures.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Solids

CHEMISTRY

Watch in App

explore_more_icon

Explore more

Standard VIII Chemistry

Join BYJU'S Learning Program

CrossIcon