Mechanical Engineering - Heat and Mass Transfer - Fins and Transient Heat Conduction

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Question - 1

A plate of asbestos material having thickness 5 cm is maintained at 300°C. It is suddenly put in surrounding at 30°C. Assume p = 2000 kg/m3, c = 100 J/kg-K, K = 10 W/m-K and convection heat transfer coefficient h = 90 W/m-K. What will be the temperature of slab after 100 s.

  • A 140.20°C
  • B 278.93°C
  • C 110.20°C
  • D Data is insufficient

Question - 2

Match List I (Parameter) with List II (Definition) and select the correct answer using the codes given below the lists.

List I List II
P. Time constant of a thermometer of radius r0 \(\frac { h{ r }_{ 0 } }{ { K }_{ fluid } } \)
Q. Biot number for sphere of radius r0 \(\frac { K }{ h } \)
R. Critical thickness of insulation for a wire of radius r0 \(\frac { h{ r }_{ 0 } }{ { K }_{ solid } } \)
S. Nusselt number for a sphere of radius r0 \(\frac { h\pi { r }_{ 0 }l }{ \rho CV } \)
  • A P Q R S 4 3 2 1
  • B P Q R S 1 2 3 4
  • C P Q R S 2 3 4 1
  • D P Q R S 4 1 2 3

Question - 3

In order to achieve maximum heat dissipation, the fin should be designed in such a way that

  • A it should have maximum lateral surface at the root side of the fin
  • B it should have maximum lateral surface towards the tip side of the fin
  • C it should have maximum lateral surface near the centre of the fin
  • D it should have minimum lateral surface near the centre of the fin

Question - 4

Consider the following statements:
Assertion (A) Lumped capacity analysis of unsteady heat conduction assumes a constant uniform temperature througout a solid body.
Reason (R) The surface convection resistance is very large compared with the internal conduction resistance. Of these statements

  • A both A and R are true and R is the correct explanation of A
  • B both A and R are true but R is not a correct explanation of A
  • C A is true but R is false
  • D A is false but R is true

Question - 5

A fin of length l protrudes from a surface held at temperature To; it being higher than the ambient temperature Ta. The heat dissipation from the free end of the fin is stated to be negligibly small. What is the temperature gradient \(\left( \frac { dT }{ dx } \right) _{ x=l }\) at the tip of the fin?

  • A Zero
  • B \(\frac { { T }_{ o }-{ T }_{ l } }{ l } \)
  • C h(To - Ta)
  • D \(\frac { { T }_{ l }-{ T }_{ a } }{ { T }_{ o }-{ T }_{ a } } \)

Question - 6


The value of m for this pin fin is

  • A \(\sqrt { \frac { h }{ kl } } \)
  • B \(2\sqrt { \frac { h }{ Kd } } \)
  • C \(2\sqrt { \frac { hl }{ Kd } } \)
  • D \(\sqrt { \frac { 4Kd }{ h } } \)

Question - 7


If a = 5 mm and K = 54 W/m-°C, h = 90 W/m2-°C, then

  • A m = 50
  • B m = 48.06
  • C m = 42.07
  • D m = 60.73

Question - 8

Select the condition at which heat transfer from insulated tip can be considered the case of fin of infinite length.

  • A m = 0.75, L = 3
  • B m = 1, L = 3
  • C m = 3, L = 0.72
  • D m = 2, L = 1.2

Question - 9

Two identical long rods are attached to base of heat source having (T0 = 100 °C). If K1 = 43 W/m-K, then K2 (in W/m-K) is

  • A 400
  • B 376.43
  • C 339.56
  • D 471.26

Question - 10

In the given long fin, T1 = 120°C, T2 = 90°C and d0 = 1.5 cm and surrounding temperature T\(\infty \) = 30°C then, K (in W/m-K) is (approximate) (h = 15 W/m2-K)

  • A 300
  • B 400
  • C 350
  • D 275
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