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Engineering Mathematics

General Aptitude

JEE

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

$$U\left( {r,x} \right) = {C_1}$$ 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

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 ______________.

Your Input ________

Correct answer is between **6800 **and ** 6900**

3

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
___________

Your Input ________

Correct answer is between **620 **and ** 630**

4

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

$$(b+2c$$)

Number in Brackets after Paper Name Indicates No of Questions

GATE ME 2016 Set 1 (1) *keyboard_arrow_right*

GATE ME 2015 Set 1 (1) *keyboard_arrow_right*

GATE ME 2014 Set 2 (1) *keyboard_arrow_right*

GATE ME 2014 Set 1 (2) *keyboard_arrow_right*

GATE ME 2011 (1) *keyboard_arrow_right*

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GATE ME 2007 (2) *keyboard_arrow_right*

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GATE ME 2003 (1) *keyboard_arrow_right*

GATE ME 2002 (1) *keyboard_arrow_right*

GATE ME 2001 (1) *keyboard_arrow_right*

GATE ME 1996 (1) *keyboard_arrow_right*

GATE ME 1992 (1) *keyboard_arrow_right*