Heat Transfer Miscellaneous
 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 1/2 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 1/8 and 35 respectively. The Prandlt and Nusselt numbers for Q are respectively

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δ_{t} = 1 × P_{r}^{1/3} δ 1.026 For fluid Q: 1/2 = δ_{t} = 1 × P_{r}^{1/3} δ 1.026
⇒ P_{r} = 8
For fluid P: Laminar flow over flat plate Nu = 0.664 Re_{L}^{1/2} P_{r}^{1/3} = 35
Similarly for fluid Q: Nu = 0.664 Re_{L}^{1/2} P_{r}^{1/3}
= 0.664 (10^{4})^{1/2} 8^{1/3} ≃ 140Correct Option: A
δ_{t} = 1 × P_{r}^{1/3} δ 1.026 For fluid Q: 1/2 = δ_{t} = 1 × P_{r}^{1/3} δ 1.026
⇒ P_{r} = 8
For fluid P: Laminar flow over flat plate Nu = 0.664 Re_{L}^{1/2} P_{r}^{1/3} = 35
Similarly for fluid Q: Nu = 0.664 Re_{L}^{1/2} P_{r}^{1/3}
= 0.664 (10^{4})^{1/2} 8^{1/3} ≃ 140
 A pipe of 25 mm outer diameter carries steam. The heat transfer coefficient between the cylinder and surroundings is 5 W/m^{2}K. 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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Critical radius of insulation
= k h = 0.05 m 5
(r_{outer}) > r_{critical}
Thus, adding insulation shall decrease H.T. Rate.Correct Option: C
Critical radius of insulation
= k h = 0.05 m 5
(r_{outer}) > r_{critical}
Thus, adding insulation shall decrease H.T. Rate.
 For flow of fluid over a heated plate, the following fluid properties are known: viscosity = 0.001 Pa.s; specific heat at constant pressure = 1 kJ/kgK; thermal conductivity = 1 W/mK. The hydrodynamic boundary layer thickness at a specified location on the plate is 1 mm. The thermal boundary layer thickness at the same location is

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Given:
µ =0.001 Pa – s
C_{P} = 1 kJ/kg K
K_{f} = 1W/mK (Fluid thermal conductivity)
Hydrodynamic boundary layer thickness, δ = 1 mmP_{r} = μC_{P} = 0.001 × 1000 = 1 K_{f} 1
δ _{t} = δ (C_{r})^{1/3}
= 1 × (1)^{1/3} = 1 mmCorrect Option: C
Given:
µ =0.001 Pa – s
C_{P} = 1 kJ/kg K
K_{f} = 1W/mK (Fluid thermal conductivity)
Hydrodynamic boundary layer thickness, δ = 1 mmP_{r} = μC_{P} = 0.001 × 1000 = 1 K_{f} 1
δ _{t} = δ (C_{r})^{1/3}
= 1 × (1)^{1/3} = 1 mm
 The temperature distribution within the thermal boundary layer over a heated isothermal flat plate is given by
where T_{W} and T_{∞} are the temperatures of plate and free stream respectively, and y is the normal distance measured from the plate. The local Nusselt number based on the thermal boundary layer thickness δ_{t} is given by

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Only (b) satisfies the conditions
Correct Option: B
Only (b) satisfies the conditions
 For laminar forced convection over a flat plate, if the free stream velocity increases by a factor of 2, the average heat transfer coefficient

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For laminar flow, Nu = 0.664 (R_{e})^{0.5} (P_{r})^{0.33}
hL = 0.664 ρVD ^{0.5} (P_{r})^{0.23} k μ
h ∝ V^{0.5}; h ∝ √V
So when free stream velocity increases by a fact or of 2, t hen t he aver age heat transfer coefficient rises by a factor of √2.Correct Option: C
For laminar flow, Nu = 0.664 (R_{e})^{0.5} (P_{r})^{0.33}
hL = 0.664 ρVD ^{0.5} (P_{r})^{0.23} k μ
h ∝ V^{0.5}; h ∝ √V
So when free stream velocity increases by a fact or of 2, t hen t he aver age heat transfer coefficient rises by a factor of √2.