1

### GATE ME 2015 Set 1

For flow through a pipe of radius $R,$ the velocity and temperature distribution are as follows:
$U\left( {r,x} \right) = {C_1}$ and $T\left( {r,x} \right) = {C_2}\left[ {1 - {{\left( {{r \over R}} \right)}^3}} \right],$
where ${C_1}$ and ${C_2}$ are constants. The bulk mean temperature is given by

${T_m} = {2 \over {{U_m}{R^2}}}\int\limits_0^R {u\left( {r,x} \right)T\left( {r,x} \right)rdr,}$
with ${{U_m}}$ being the mean velocity of flow. The value of ${T_m}$ is

A
${{0.5{C_2}} \over {{U_m}}}$
B
${0.5{C_2}}$
C
${0.6{C_2}}$
D
${{0.6{C_2}} \over {{U_m}}}$
2
Numerical

### GATE ME 2014 Set 2

Water flows through a tube of diameter $25mm$ at an average velocity of $1.0m/s.$ The properties of water are $\rho = 1000\,\,kg/{m^3},$ $\mu = 7.25 \times {10^{ - 4}}\,\,N.s/{m^2},$ $\,K = 0.625W/m.K,$ $Pr=4.85.$ Using $Nu=0.023$ $R{e^{0.8}}\,\,{\Pr ^{0.4}},$ the convective heat transfer coefficient (in $W/{m^2}.K$) is ______________.

Correct answer is between 6800 and 6900
3
Numerical

### GATE ME 2014 Set 1

Consider one dimensional steady state heat conduction across a wall (as shown in figure below) of thickness $30$ $mm$ and thermal conductivity $15$ $W/m.K.$ At $x=0,$ a constant heat flux, $q'' = 1 \times {10^5}\,\,W/{m^2}$ is applied. On the other side of the wall, heat is removed from the wall by convection with a fluid at ${25^ \circ }C$ and heat transfer coefficient of $250W/{m^2}.K.$ The temperature (in ${}^ \circ C$), at $x=0$ is ___________ Correct answer is between 620 and 630
4

### GATE ME 2014 Set 1

The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by ${{{T_w} - T} \over {{T_w} - {T_\infty }}} = a + b{y \over L} + c{\left( {{y \over L}} \right)^2},$ where $y$ is measured perpendicular to the plate, $L$ is the length, and $a,b$ and $c$ are arbitrary constants. ${{T_w}}$ and ${{T_\infty }}$ are wall and ambiyent temperatures, respectively. If the thermal conductivity of the fluid is $k$ and the wall heat flux is $q'',$ the Nusselt number $\,{N_u} = {{q''} \over {{T_w} - {T_\infty }}}{L \over k}$ is equal to
A
$a$
B
$b$
C
$2c$
D
$(b+2c$)

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