GATE Past Year Questions: Free & Forced Convection Notes | Study Heat Transfer - Mechanical Engineering

Grash of number = inertia force x 

Given data;


Volume,
V = 2×1×2=4 m³
Heat generated,
Q = q_G × V = 100 × 4 = 400 W
Convection heat transfer from face PQRS,

At the inlet of pipe
x = O
q "_wi = 2500 x 0 = 0
At the exit of pipe,
x = 1

Average heat transfer,

Net heat transfer

By solving above equation, we get
T_o = 62° C

Heat transfer through pipe wall,

Q = mC_P(T₀–T_i), amount of heat gained by the water
2355 = 0.01 × 4180 (T₀ – 20)
T₀ = 76.33°C

5000 = 1000 (Tso – 76.33)
Tso = 81°C

Forlaminar flow, Nu = 0.664 (Re)^0.5 (Pr)^0.33

So when free stream velocity increases by a factor of 2, then the average heat transfer coefficient rises by a factor of √2.

Prandtl number = 

When

(Nu)_q for constant wall heat flux and (Nu)_T at constant wall temperature for a hydrodynamically and thermally fully developed laminar flow through a circular pipe of constant cross-section is 4.36 and 3.66 respectively.

In case of uniform heat flux, bulk mean temperature varies linearly. The difference between bulk mean temperature and wall temperature is constant in thermally developed region so bulk tempeature,

Here,

So, Q and R in thermally developed region.