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

Two different rods $A$ and $B$ are kept in series as shown in the figure. The variation of temperature across different cross-sections is plotted in the graph. The ratio of thermal conductivities of $A$ and $B$ is

$A$ cylindrical rod has temperatures $\theta_1$ and $\theta_2$ at its ends. The rate of heat flow is $Q$. All the linear dimensions of the rod are doubled while keeping the temperatures constant. The new rate of flow of heat is

Why do some cooking vessels have a copper coating at the bottom?

$A$ long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length $x$ of the bar from its hot end is best described by which of the following figures?

On heating one end of a rod,the temperature of the whole rod will be uniform when

Vedclass Test Series

Exam Paper Generator

Online Exam Module