A copper pipe of length 10 ,m carries steam a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The heat current flows radially outward through the cylindrical pipe.For a cylindrical shell of radius $x$ and thickness $dx$,the thermal resistan

Vedclass · Accepted Answer

$3445$

Vedclass · Answer

(B) The heat current flows radially outward through the cylindrical pipe.For a cylindrical shell of radius $x$ and thickness $dx$,the thermal resistance $dR_T$ is given by $dR_T = \frac{dx}{k(2\pi x \ell)}$.Integrating from inner radius $R_1$ to outer radius $R_2$,the total thermal resistance $R_T$ is:$R_T = \int_{R_1}^{R_2} \frac{dx}{2\pi k \ell x} = \frac{1}{2\pi k \ell} \ln\left(\frac{R_2}{R_1}ight)$.The rate of heat flow is $\frac{dQ}{dt} = \frac{\Delta T}{R_T} = \frac{2\pi k \ell (T_1 - T_2)}{\ln(R_2/R_1)}$.Given: $T_1 = 110^{\circ} C$,$T_2 = 10^{\circ} C$,$\Delta T = 100^{\circ} C$,$k = 0.38 \,kW/m/^{\circ} C$,$\ell = 10 \,m$,$R_1 = 2 \,cm$,$R_2 = 4 \,cm$.Substituting the values:$\frac{dQ}{dt} = \frac{2 	imes 3.14159 	imes 0.38 	imes 10 	imes 100}{\ln(4/2)} = \frac{2387.6}{0.6931} \approx 3444.6 \,kW$.Thus,the rate of heat flow is approximately $3445 \,kW$.

Similar Questions

Mud houses are cooler in summer and warmer in winter because

$A$ body of length $1 \; m$ having a cross-sectional area of $0.75 \; m^2$ has heat flow through it at the rate of $6000 \; J/s$. Find the temperature difference if the thermal conductivity $K = 200 \; J \cdot m^{-1} \cdot s^{-1} \cdot K^{-1}$.

The heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio $1:2$ and their lengths are in the ratio $2:1$. If the temperature difference between their ends is the same,the ratio of the rate of flow of heat through them will be:

Why does a metal bar appear hotter than a wooden bar at the same temperature? Equivalently,it also appears cooler than a wooden bar if they are both colder than room temperature.

The ratio of the diameters of two metallic rods of the same material is $2 : 1$ and their lengths are in the ratio $1 : 4$. If the temperature difference between their ends is equal,the rate of flow of heat in them will be in the ratio: (in $:1$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module