Numerical investigation of laminar mixed convection in trombe wall channel

Abstract EN

The two dimensional steady, combined forced and natural convection in vertical channel is investigated for laminar regime.

To simulate the Trombe wall channel geometry properly, horizontal inlet and exit segments have been added to the vertical channel.

The vertical walls of the channel are maintained at constant but different temperature while horizontal walls are insulated.

A finite difference method using up-wind differencing for the nonlinear convective terms, and central differencing for the second order derivatives, is employed to solve the governing differential equations for the mass, momentum, and energy balances.

The solution is obtained for stream function, vortices and temperature as dependent variables by iterative technique known as successive substitution with over relaxation.

The flow and temperature patterns in the channel are obtained for Reynolds numbers and Grashof number ranging from 25 to 100 and (100 to 1,000,00,) respectively.

A computer program (Fortran 90) is built to calculate the fraction factor and the total average Nusselt number (Nu) also the average heat transfer Q in steady state and for Aspect ratio Ar (10) and Grashof number GR (102-105), the fluid Prandtl number is fixed at (Pr=0.733) and Reynolds number Re (25-100).

The results show reasonable representation to the relation between Nusselt number and friction factor with other parameters (Ar, GR and Re).

Nu is increased with increasing Re and GR but it decreases with Ar increase and (Q) is increased with increasing Re ,GR and Ar.

At the same time, the product friction factor(fRe) increased with (GR) and (Ar)increased and (Re) decrease.

Comparison of the result with the previous work shows a good agreement.