Abstract

This work describes a hybrid analytical‐numerical solution employing the Generalized Integral Transform Technique (GITT) to forced convection heat transfer in hydrodynamically fully developed and thermally non‐developed Newtonian laminar flow inside annular sector ducts under Dirichlet boundary conditions, considering uniform temperature entrance profile. In order to facilitate the analytical treatment and the application of the boundary conditions, a Conformal Transform was utilized to change the domain into a more suitable coordinate system. Thereafter, the GITT was applied on the energy equation to obtain the temperature field. Numerical results were obtained for quantities of practical interest, such as bulk mean temperature, local and average Nusselt number, and thermal entry length. These results were compared, as much as possible, with the parameter values available in the literature and they presented a good agreement.

Abstract

In this paper, cavity flow is simulated numerically. Forced convection in different Reynolds numbers between 100 and 5000 is simulated. Different and complex thermal boundary conditions are applied and various parameters are calculated numerically. Up wall and down walls are in constant temperature and left and right walls are thermal insulation in the first thermal boundary condition. The Left and the down walls are in constant temperature and the temperature of the up and the right walls changes linearly in the second thermal boundary condition. For the third thermal boundary condition, the left and the down walls are in constant temperature and the temperature of the up and the right walls changes sinusoidally. For this purpose, a code is written in the FORTRAN software. Streamlines, isotherms, velocity and temperature in centerlines of the cavity, Nusselt number and mean Nusselt number are obtained and shown in different figures and one table. Grid independence is surveyed and some obtained results are validated with other researchers' work. In these simulations, the Prandtl number is considered to be 0.71 because of the air’s Prandtl number. For time discretization, a fifth-order Runge-Kutta is used and for convective fluxes, averaging scheme with fourth-order damping term is applied.