Sketch the variation in local heat transfer coefficient along the length of conduit.

Question

A heat transfer equipment utilizes 5 mm diameter, 10 cm long smooth circular cross-sectioned conduits drilled horizontally in a plate longitudinally on which a constant heat flux is imposed uniformly. Air enters each conduct at 27⁰C with a men velocity of 3.0 m/s and leavest at 77⁰C. If 20 conduits are arranged in the plate, calculate the following.

1. total rate of heat removed from the plate,
2. exit conduit wall temperature, and
3. local heat transfer coefficient at the exit of each conduit.

Sketch the variation in local heat transfer coefficient along the length of conduit.

The following correlations are known for convection heat transfer:

1. Nu_d = 4.364, for fully developed laminar flow,
2. Nu_d = 0.023 Re  for turbulent flow,
3. Nu_z = 1.3 $\left [ \frac{Re_{d}pr}{\left ( z/d \right )} \right ]^{\frac{1}{3}}$ developing flow with $\left [ \frac{Re_{d}pr}{\left ( z/d \right )} \right ]> 10$ 

‘z’ is the axial location from the inlet along the length of conduit. Properties or air at 52⁰C: C = 1006 J/kg-K, p = 1.1774 kg/m³, v = 18.22 ´ 10^–6 m²/s, K = 0.028 W/m-