There
are different gases present in our atmosphere which are used as cryogenic
fluids, example Helium, Nitrogen, Oxygen, etc., as boiling points of these gases are below cryogenic temperature. The
boiling point of liquid Nitrogen is 77.2 K and the freezing point is 63 K. In
this present work cryogenic gas is intended to flow through a circular micro
channel and a two dimensional numerical simulation is carried out for an
internal convective laminar flow through the channel, subjected to constant
wall heat flux to see the axial back conduction in the solid substrate of the
tube which leads to conjugate heat transfer. Nitrogen gas is used as working
fluid to flow through the microtube. Thermo-physical properties (e.g. density,
viscosity, specific heat and thermal conductivity) of nitrogen gas change
appreciably with the temperature, thus thermo-physical properties function of
temperature are used as UDF as described in numerical simulation chapter. The
micro channel of 0.4 mm diameter and 60 mm length are kept constant and δsf (i.e. ratio of wall thickness (δs) to inner radius (δf))
is varied such as 1, 2, 3, 4 & 5 throughout the simulation. Other variable
parameters are Reynold's number varies as 100 & 500 and ksf(i.e.
solid conductivity ratio to fluid conductivity ratio) varies from 22.07931 to 45980.71. In this work it is tried to find out
most suitable material i.e. ks value as well as suitable wall
thickness of the microtube i.e. δs value with the help of change in different parameters. After the completion of
the numerical analysis the conclusions found are, (i) wall conductivity ratio
and wall thickness ratio play dominant role in the effect of axial back
conduction, (ii) there exist an optimum ksf value at which average
Nusselt number (Nuavg) is maximum while other parameters are kept constant, (iii) at higher value of δsf, average Nusselt number
becomes lower, (iv) Nuavg increases with increase in flow rate i.e.
increasing value of Reynolds number.

**Keywords: **Axial back conduction, conjugate heat transfer, microchannel,
constant heat flux, optimum Nusselt number, cryogenic fluid