1

### 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
$(b+2c$)
2

### GATE ME 2011

The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two fluids $P$ and $Q$ on a flat plate are ${1 \over 2}$ and $2$ respectively. The Reynolds number based on the plate length for both the flows is ${10^4}.$ The Prandtl and Nusselt numbers for $P$ are ${1 \over 8}$ and $35$ respectively. The Prandtl and Nusselt number for $Q$ are respectively
A
$8$ and $140$
B
$8$ and $70$
C
$4$ and $70$
D
$4$ and $35$
3

### GATE ME 2010

Match the following

List-${\rm I}$
$P.$ Compressible flow
$Q.$ Free surface flow
$R.$ Boundary layer flow
$S.$ Pipe flow
$T.$ Heat convection

List-${\rm II}$
$U.$ Renolds number
$V.$ Nussult number
$W.$ Weber number
$X.$ Froude number
$Y.$ Mach number
$Z.$ Skin friction coefficient

A
$P - U,\,\,Q - X,\,\,R - V,\,\,S - Z,\,\,T - W$
B
$P - W,\,\,Q - X,\,\,R - Z,\,\,S - U,\,\,T - V$
C
$P - Y,\,\,Q - W,\,\,R - Z,\,\,S - U,\,\,T - X$
D
$P - Y,\,\,Q - W,\,\,R - Z,\,\,S - U,\,\,T - V$
4

### GATE ME 2007

The temp distribution within the Laminar thermal boundary layer over a heated isothermal flat plate is given by
$\left( {T - {T_w}} \right)/\left( {{T_\infty } - {T_w}} \right) = \left( {3/2} \right)\,\,\left( {y/{\delta _t}} \right) - \left( {1/2} \right){\left( {y/{\delta _t}} \right)^3},$
where ${{T_w}}$ and ${{T_ \propto }}$ are the temp of plate and free stream respectively, and $'y'$ is the normal distance measuread from the plate. The ratio of Average to the local Nussult number based on the thermal boundary layer thickness ${{\delta _t}}$ is given by
A
$1.33$
B
$1.5$
C
$2.0$
D
$4.64$

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