## Heat Transfer Miscellaneous

#### Heat-Transfer

1. Heat transfer coefficients for free convection in gases, forced convection in gases and vapours, and for boiling water lie, respectively, in the range of

1. 5-15; 20-200 and 3000-50000 W/m2K

##### Correct Option: A

5-15; 20-200 and 3000-50000 W/m2K

1. Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The cent er slab experience a nonuniform internal heat generation with an average value equal to 10000 Wm-3, while the left and right slabs have no internal heat generation. All slabs have thickness equal to 1 m and thermal conductivity of each slab is equal to 5 Wm-1 K-1. The two extreme faces are exposed to fluid with heat transfer coefficient 100 Wm-2K -1 and bulk temperature 30°C as shown. The heat transfer in the slabs is assumed to be one dimensional and steady, and all properties are constant. If the left extreme face temperature T1 is measured to be 100°C, the right extreme faced temperature T2 is___________°C.

1. ##### Correct Option: A

1. Consider a laminar boundary layer over a heated flat plate. The free stream velocity is U. At some distance x from the leading edge the velocity boundary layer thickness is δv and the thermal boundary layer thickness is δT. If the Prandtl number is greater than 1, then

1.  Prandtl number = Molecular diffusivity of momentum Molecular diffusivity of heat

From question, since prandtl number > 1
∴ Velocity boundry thickness (δv) > thermal boundary thickness (δt)

##### Correct Option: A

 Prandtl number = Molecular diffusivity of momentum Molecular diffusivity of heat

From question, since prandtl number > 1
∴ Velocity boundry thickness (δv) > thermal boundary thickness (δt)

Direction: An un-insulated air conditioning duct of rectangular cross section 1 m × 0.5 m, carrying air at 20°C with a velocity of 10 m/s, is exposed to an ambient of 30°C. Neglect the effect of duct construction material. For air in the range of 20 – 30°C, data is as follows: thermal conductivity = 0.025 W/mK; viscosity = 18 μPa.s; Prandtl number = 0.73; density =1.2 kg/m3. For laminar flow Nusselt number is 3.4 for constant wall temperature conditions and, for turbulent flow, Nu = 0.023 Re0.8Pr0.33

1. The Reynolds number for the flow is

1.  Lc = 4A = 4 × 1 × 0.5 = 0.666 D 2 × 1.5

Reynolds number,
 Re = ρLcV = 1.2 × 0.66 × 10 = 4.4 × 105 . μ 18 × 10-6

##### Correct Option: C

 Lc = 4A = 4 × 1 × 0.5 = 0.666 D 2 × 1.5

Reynolds number,
 Re = ρLcV = 1.2 × 0.66 × 10 = 4.4 × 105 . μ 18 × 10-6

1. The heat transfer per meter length of the duct, in watts, is

1. As Re > 4000, the flow is turbulent
Nu = 0.023 Re0.8Pr0.33
hL/k = 0.023 × (4.44 × 105)0.8 × (0.73)0.33
h × 0.0667/0.25 = 683.173
h = 25.60 W/m2K
Surface area of duct
A = 2 × al + 2 × bl
where, l = length of duct
∴ A = 3l
Heat transfer rate, Q = h A(T0 – T)
Q = 25.60 × 3l × (30 – 20)
Q/l = 769W

##### Correct Option: D

As Re > 4000, the flow is turbulent
Nu = 0.023 Re0.8Pr0.33
hL/k = 0.023 × (4.44 × 105)0.8 × (0.73)0.33
h × 0.0667/0.25 = 683.173
h = 25.60 W/m2K
Surface area of duct
A = 2 × al + 2 × bl
where, l = length of duct
∴ A = 3l
Heat transfer rate, Q = h A(T0 – T)
Q = 25.60 × 3l × (30 – 20)
Q/l = 769W