MyQuestionIcon

1

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

Temperature

Inner surface...

Question

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 $T_{2}$ such that $(T_{1} > T_{2})$ 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. $T_{1}$ and $T_{2}$ then find the value of n.

Open in App

Solution

Since rate of heat flow remains same in both the cases, so

$\int_{R}^{2 R} \frac{d x}{K 2 π x l} = \int_{\frac{R}{4}}^{R} \frac{d x}{n k (2 π x) \frac{l}{2}} \Rightarrow n k = 4 k \Rightarrow n = 4$

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. 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 metallic spherical shell having inner and outer radii

a

b

respectively has thermal conductivity

K = \frac{K_{0}}{r^{2}} {a \leq r \leq b}

r

is the distance from the center of the sphere. The inner surface is maintained at temperature

θ_{1}

and outer surface is maintained at temperature

θ_{2}

. Calculate the rate at which heat flows radially through the material

[θ_{2} > θ_{1}]

.

Q. A cylindrical pipe of length

L

has two layers of material of conductivity

k_{1}

k_{2}

(see figure). If the innermost surface of the cylinder is maintained at

T_{1}

and the outermost surface is at

T_{2} (< T_{1})

, calculate the radial rate of heat flow.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

What is Heat and Temperature

PHYSICS

Watch in App

explore_more_icon

Explore more

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon