Abstract:
The problem of heat transfer due to free convection in a channel formed
by two parallel, isoflux, vertical plates is of considerable importance in electronic
cooling applications, thermosiphons, the optimum spacing of plates or components,
industrial stacks, heat exchangers, nuclear power plants and combustion involving
vertical walls. Although in each implementation other physical considerations are
necessary, fully developed flow with symmetric isoflux boundary condition offers a
fundamental heat transfer problem. Thus, here, the fully developed laminar natural
convective flow of a viscous fluid in a channel formed by heated infinitely long vertical
plates is investigated. Using boundary layer approximations, the basic governing
equations of continuity, momentum and energy are combined into a single equation
and solved analytically for a symmetric uniform heat flux boundary condition to find
the velocity and temperature profiles and heat transfer coefficients for the flow. The
closed-form solutions that are presented are strightforward and simple compared to
previous solutions existing in the literature. For Rayleigh numbers sufficiently small
to ensure a fully developed flow, it is found that the local Nusselt number based
on local wall to bulk temperature difference is 4.118. Furthermore the pressure and
mass flow rates for this particular geometry are also investigated.
