  We introduce a new method of solution for the convective heat transfer under
forced laminar flow that is confined by two parallel plates with a distance of
2a or by a circular tube with a radius of a. The advection-conduction equation
is first mapped onto the boundary. The original problem of solving the unknown
field T(x,r,t) is reduced to seek the solutions of T at the boundary (r=a or
r=0, r is the distance from the center line shown in Fig. 1), i.e. the boundary
functions. In this manner, the original problem is significantly simplified by
reducing the problem dimensions from 3 to 2. The unknown field T(x,r,t) can be
eventually solved in terms of these boundary functions. The method is applied
to the convective heat transfer with uniform wall temperature boundary
condition and with heat exchange between flowing fluids and its surroundings
that is relevant to the geothermal applications. Analytical solutions are
presented and validated for the steady state problem using the proposed method.
