Heat Transfer Miscellaneous


  1. 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 104. 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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    δt
    =
    1
    × Pr-1/3
    δ1.026

    For fluid Q: 1/2 =
    δt
    =
    1
    × Pr-1/3
    δ1.026

    ⇒ Pr = 8
    For fluid P: Laminar flow over flat plate Nu = 0.664 ReL1/2 Pr1/3 = 35
    Similarly for fluid Q: Nu = 0.664 ReL1/2 Pr1/3
    = 0.664 (104)1/2 81/3 ≃ 140

    Correct Option: A

    δt
    =
    1
    × Pr-1/3
    δ1.026

    For fluid Q: 1/2 =
    δt
    =
    1
    × Pr-1/3
    δ1.026

    ⇒ Pr = 8
    For fluid P: Laminar flow over flat plate Nu = 0.664 ReL1/2 Pr1/3 = 35
    Similarly for fluid Q: Nu = 0.664 ReL1/2 Pr1/3
    = 0.664 (104)1/2 81/3 ≃ 140


  1. A pipe of 25 mm outer diameter carries steam. The heat transfer coefficient between the cylinder and surroundings is 5 W/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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    Critical radius of insulation

    =
    k
    h

    =
    0.05
    m
    5

    (router) > rcritical
    Thus, adding insulation shall decrease H.T. Rate.

    Correct Option: C

    Critical radius of insulation

    =
    k
    h

    =
    0.05
    m
    5

    (router) > rcritical
    Thus, adding insulation shall decrease H.T. Rate.



  1. 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
    CP = 1 kJ/kg K
    Kf = 1W/mK (Fluid thermal conductivity)
    Hydrodynamic boundary layer thickness, δ = 1 mm

    Pr =
    μCP
    =
    0.001 × 1000
    = 1
    Kf1

    δ t = δ (Cr)-1/3
    = 1 × (1)-1/3 = 1 mm

    Correct Option: C

    Given:
    µ =0.001 Pa – s
    CP = 1 kJ/kg K
    Kf = 1W/mK (Fluid thermal conductivity)
    Hydrodynamic boundary layer thickness, δ = 1 mm

    Pr =
    μCP
    =
    0.001 × 1000
    = 1
    Kf1

    δ t = δ (Cr)-1/3
    = 1 × (1)-1/3 = 1 mm


  1. The temperature distribution within the thermal boundary layer over a heated isothermal flat plate is given by

    where TW 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 δt is given by









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    Only (b) satisfies the conditions

    Correct Option: B

    Only (b) satisfies the conditions



  1. 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 (Re)0.5 (Pr)0.33

    hL
    = 0.664
    ρVD
    0.5(Pr)0.23
    kμ

    h ∝ V0.5; 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 (Re)0.5 (Pr)0.33

    hL
    = 0.664
    ρVD
    0.5(Pr)0.23
    kμ

    h ∝ V0.5; 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.