1
Numerical

### GATE ME 2016 Set 1

A fluid (Prandtl number, $Pr=1$) at $500$ $K$ flows over a flat plate of $1.5$ $m$ length, maintained at $300$ $K.$ The velocity of the fluid is $10\,\,m/s.$ Assuming kinematic viscosity, $v = 30 \times {10^{ - 6}}\,\,{m^2}/s,$ the thermal boundary layer thickness (in $mm$) at $0.5$ $m$ from the leading edge is _________.

Correct answer is between 5.90 and 6.25
2

### 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
${{0.6{C_2}} \over {{U_m}}}$
3
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
4
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 ___________