Abstract: This work aims to provide a comprehensive study on the heat transfer and entropy generation rates of a horizontal channel partially filled with a porous medium which experiences internal heat generation or consumption due to exothermic or endothermic chemical reaction. The focus has been given to the local thermal non-equilibrium (LTNE) model. The LTNE approach helps us to deliver more accurate data regarding temperature distribution within the system and accordingly to provide more accurate Nusselt number and entropy generation rates. Darcy-Brinkman model is used for the momentum equations, and constant heat flux is assumed for boundary conditions for both upper and lower surfaces. Analytical solutions have been provided for both velocity and temperature fields. By incorporating the investigated velocity and temperature formulas into the provided fundamental equations for the entropy generation, both local and total entropy generation rates are plotted for a number of cases. Bifurcation phenomena regarding temperature distribution and interface heat flux ratio are observed. It has been found that the exothermicity or endothermicity characteristic of the channel does have a considerable impact on the temperature fields and entropy generation rates.
Abstract: Unsteady natural convection and heat transfer in a square cavity partially filled with porous media using a thermal
non-equilibrium model is studied in this paper. The left vertical wall is
maintained at a constant hot temperature Th and the right vertical wall
is maintained at a constant cold temperature Tc, while the horizontal
walls are adiabatic. The governing equations are obtained by applying
the Darcy model and Boussinesq approximation. COMSOL’s finite
element method is used to solve the non-dimensional governing
equations together with specified boundary conditions. The governing
parameters of this study are the Rayleigh number (Ra = 10^5, and Ra = 10^6 ), Darcy namber (Da = 10^−2, and Da = 10^−3),
the modified thermal conductivity ratio (10^−1 ≤ γ ≤ 10^4), the inter-phase heat transfer coefficien (10^−1 ≤ H ≤ 10^3) and the
time dependent (0.001 ≤ τ ≤ 0.2). The results presented for
values of the governing parameters in terms of streamlines in both
fluid/porous-layer, isotherms of fluid in fluid/porous-layer, isotherms
of solid in porous layer, and average Nusselt number.
Abstract: This article presents a numerical study of the doublediffusive
mixed convection in a vertical channel filled with porous
medium by using non-equilibrium model. The flow is assumed
fully developed, uni-directional and steady state. The controlling
parameters are thermal Rayleigh number (RaT ), Darcy number (Da),
Forchheimer number (F), buoyancy ratio (N), inter phase heat transfer
coefficient (H), and porosity scaled thermal conductivity ratio
(γ). The Brinkman-extended non-Darcy model is considered. The
governing equations are solved by spectral collocation method. The
main emphasize is given on flow profiles as well as heat and solute
transfer rates, when two diffusive components in terms of buoyancy
ratio are in favor (against) of each other and solid matrix and fluid
are thermally non-equilibrium. The results show that, for aiding flow
(RaT = 1000), the heat transfer rate of fluid (Nuf ) increases upto a
certain value of H, beyond that decreases smoothly and converges
to a constant, whereas in case of opposing flow (RaT = -1000),
the result is same for N = 0 and 1. The variation of Nuf in (N,
Nuf )-plane shows sinusoidal pattern for RaT = -1000. For both cases
(aiding and opposing) the flow destabilize on increasing N by inviting
point of inflection or flow separation on the velocity profile. Overall,
the buoyancy force have significant impact on the non-Darcy mixed
convection under LTNE conditions.