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BARC 2020 : Mini Mock 3

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Question 1

Heat is generated uniformly in a long solid cylindrical rod (diameter = 10mm) at the rate of

. The thermal conductivity of the rod material is 25W/m.K. Under steady state conditions, the temperature difference between the centre and the surface of the rod is _________ °C.

Question 2

Air at 20 °C flows past a 250 mm long plates at a velocity of 45 m/s. If the surface of the plate is maintained at 300 °C. Take properties of air as: k = 0.03638 W/m-K,

Pr = 0.682. The heat transferred from the entire plate length to air assuming unit width of the plate will be ____ W.

Question 3

The value of integral

, where

Question 4

For any three vectors

, the value of

Question 5

In an experiment, the local heat transfer over a flat plate were correlated in the form of local Nussel number as expressed by the following correlation.
$Description: Description: E:\Gate\SSC JE Mechanical Part 1\Made Easy Questions\08_Heat-Transfer_BLok_files\image076.png$
The ratio of the average convection heat transfer coefficient ( $Description: Description: E:\Gate\SSC JE Mechanical Part 1\Made Easy Questions\08_Heat-Transfer_BLok_files\image077.png$ ) over the entire plate length to the local convection heat transfer convection heat transfer coefficient (h_x) at x=L is ____________.

Question 6

A solid copper ball of mass 0.5 kg when quenched in a water bath at 30⁰C, cools from 530⁰C to 430⁰C in 10 seconds. What will be the temperature (⁰C) of the ball after the next 10 seconds?

Question 7

is a Partial differential equation whose solution is given by

The value of K is

Question 8

Consider steady-state heat conduction across the thickness in a plane composite wall (as shown in the figure) exposed to convection conditions on both sides.
Given: h_i = 20 W/m²K; h_o = 50 W/m²K; T_∞_,i= 20 °C: T_∞_,o= -2 °C; k₁ = 20 W/mK; k₂ = 50 W/mK; L₁ = 0.30 m and L₂ = 0.15 m. Assuming negligible contact resistance between the wall surfaces, the interface temperature, T (in °C), of the two walls will be

Question 9

If x is real, the maximum value of

is ____________.

Question 10

Find the net value of heat flux between two parallel, infinite plates having emissivity of 0.75 and 0.7. The planes are maintained at 450 K and 500 K.

Question 11

A real (4 × 4) matrix A satisfies the equation A² = I, where I is the (4 × 4) identity matrix. The positive eigen value of A is __________.

Question 12

If for an event A, the odds in favour of the event are 5 to 4. The probability of success of A is:

Question 13

A hot body at a temperature of 5000 °C emits radiation at a wavelength of 0.5 μm. A furnace at 500 °C will emit a radiation of wavelength______.

Question 14

The inverse Laplace transform:

Question 15

The area of the plane region bounded by the curves and x+3y²=1 is equal to ____ sq. units.

Question 16

The values of function 𝑓(x) at 5 discrete poets are given below:
$Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE ME 18-Mar\GATE-ME-2015-P2_files\image055.jpg$
using Trapezoial rule with step size or 0.1, the value or $Description: D:\GradeStack Courses\GATE Tests (Sent by Ravi)\GATE ME 18-Mar\GATE-ME-2015-P2_files\image056.png$ is_______

Question 17

Air flows at a heated plate at a velocity of 42m/s. The local skin friction coefficient of plate is 0.005. Estimate the local heat transfer coefficient(in W/m2k) at that point. The properties of air are as follows: ƿ= 0.89kg/

, μ= 2.286×

kgm/s, Cp= 1.001kJ/kgK, k= 0.04W/mK. Use St

Question 18

A scalar function is defined as f(x,y) = x² + y². Consider

as unit vectors along the x and y axis respectively. The direction at which the function increases fastest at the point (x,y) = (3,4) is

Question 19

One dimensional unsteady state heat transfer equation for a sphere with heat generation at the rate of ‘q’ can be written as

Question 20

A pipe of 25 mm outer diameter carries steam. The heat transfer coefficient between the cylinder and surroundings is 5W/m²K. It is proposed to reduce the heat loss from the pipe by adding insulation having a thermal conductivity of 0.05 W/mK. Which one of the following statements is TRUE?

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