Natural convection flow in a porous enclosure with localized heating from below

Natural convection flow in a two-dimensional fluid saturated porous enclosure with localized heating from below, symmetrical cooling from the sides and the top and rest of the bottom walls are insulated, has been investigated numerically. Darcy’s law for porous media along with the energy equation based on the 1st law of thermodynamics has been considered. Implicit finite volume method with TDMA solver is used to solve the governing equations. Localized heating is simulated by a centrally located isothermal heat source on the bottom wall, and four different values of the dimensionless heat source length, 1/5, 2/5, 3/5 and 4/5 are considered. The effect of heat source length and the Rayleigh number on streamlines and isotherms are presented, as well as the variation of the local rate of heat transfer in terms of the local Nusselt number from the heated wall. Finally, the average Nusselt number at the heated part of the bottom wall has been shown against Rayleigh number for the non-dimensional heat source length.

Natural convection from a vertical plate embedded in a stratified medium with uniform heat source

Natural convection flow from an isothermal vertical plate with uniform heat source embedded in a stratified medium has been discussed in this paper. The resulting momentum and energy equations of boundary layer approximation are made non-similar by introducing the usual non-similarity transformations. Numerical solutions of these equations are obtained by an implicit finite difference method for a wide range of the stratification parameter, X. The solutions are also obtained for different values of pertinent parameters, namely, the Prandtl number, Pr and the heat generation or absorption parameter, λ and are expressed in terms of the local skin-friction and local heat transfer, which are shown in the graphical form. Effect of heat generation or absorption on the streamlines and isotherms are also shown graphically for different values of λ.

Effects of corrugation frequency and aspect ratio on natural convection within an enclosure having sinusoidal corrugation over a heated top surface

Natural convection of a two-dimensional laminar steady-state incompressible fluid flow in a modified rectangular enclosure with sinusoidal corrugated top surface has been investigated numerically. The present study has been carried out for different corrugation frequencies on the top surface as well as aspect ratios of the enclosure in order to observe the change in hydrodynamic and thermal behavior with constant corrugation amplitude. A constant flux heat source is flush mounted on the top sinusoidal wall, modeling a wavy sheet shaded room exposed to sunlight. The flat bottom surface is considered as adiabatic, while the both vertical side walls are maintained at the constant ambient temperature. The fluid considered inside the enclosure is air having Prandtl number of 0.71. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. The results in terms of isotherms, streamlines and average Nusselt numbers are obtained for the Rayleigh number ranging from 10^3 to 10^6 with constant physical properties for the fluid medium considered. It is found that the convective phenomena are greatly influenced by the presence of the corrugation and variation of aspect ratios.

MHD natural convection flow from an isothermal horizontal circular cylinder under consideration of temperature dependent viscosity

Magnetohydrodynamic (MHD) natural convection laminar flow from an iso-thermal horizontal circular cylinder immersed in a fluid with viscosity proportional to a linear function of temperature will be discussed with numerical simulations. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equa-tions are reduced to convenient form, which are solved numerically by two very efficient methods, namely, (i) Implicit finite difference method together with Keller box scheme and (ii) Direct numerical scheme. Numerical results are presented by velocity and temperature distributions of the fluid as well as heat transfer characteristics, namely the shearing stress and the local heat transfer rate in terms of the local skin-friction coefficient and the local Nusselt number for a wide range of magnetohydrodynamic parameter, viscosity-variation parameter and viscous dissipation parameter. MHD flow in this geometry with temperature dependent viscosity is absent in the literature. The results obtained from the numerical simulations have been veri-fied by two methodologies.

Double diffusive magneto-convection fluid flow in a strong cross magnetic field with uniform surface heat and mass flux

In this study, magnetohydrodynamic natural convection boundary layer flow of an electrically conducting and viscous incompressible fluid along a heated vertical flat plate with uniform heat and mass flux in the presence of strong cross magnetic field has been investigated. For smooth integrations the boundary layer equations are transformed in to a convenient dimensionless form by using stream function formulation as well as the free variable formulation. The nonsimilar parabolic partial differential equations are integrated numerically for Pr ≪1 that is appropriate for liquid metals against the local Hartmann parameter ξ . Further, asymptotic solutions are obtained near the leading edge using regular perturbation method for smaller values of ξ . Solutions for values of ξ ≫ 1 are also obtained by employing the matched asymptotic technique. The results obtained for small, large and all ξ regimes are examined in terms of shear stress, τw, rate of heat transfer, qw, and rate of mass transfer, mw, for important physical parameter. Attention has been given to the influence of Schmidt number, Sc, buoyancy ratio parameter, N and local Hartmann parameter, ξ on velocity, temperature and concentration distributions and noted that velocity and temperature of the fluid achieve their asymptotic profiles for Sc ≥ 10:0.

Unsteady natural convection within a differentially heated enclosure of sinusoidal corrugated side walls

Numerically investigation of natural convection within a differentially heated modified square enclosure with sinusoidally corrugated side walls has been performed for different values of Rayleigh number. The fluid inside the enclosure considered is air and is quiescent, initially. The top and bottom surfaces are flat and considered as adiabatic. Results reveal three main stages: an initial stage, a transitory or oscillatory stage and a steady stage for the development of natural convection flow inside the corrugated cavity. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. Investigation has been performed for the Rayleigh number, Ra ranging from 105 to 108 with variation of corrugation amplitude and frequency. Constant physical properties for the fluid medium have been assumed. Results have been presented in terms of the isotherms, streamlines, temperature plots, average Nusselt numbers, traveling waves and thermal boundary layer thickness plots, temperature and velocity profiles. The effects of sudden differential heating and its consequent transient behavior on fluid flow and heat transfer characteristics have been observed for the range of governing parameters. The present results show that the transient phenomena are greatly influenced by the variation of the Rayleigh Number with corrugation amplitude and frequency.

Mixed convection along a vertical flat plate in a non-absorbing medium

Here mixed convection boundary layer flow of a viscous fluid along a heated vertical semi-infinite plate is investigated in a non-absorbing medium. The relationship between convection and thermal radiation is established via boundary condition of second kind on the thermally radiating vertical surface. The governing boundary layer equations are transformed into dimensionless parabolic partial differential equations with the help of appropriate transformations and the resultant system is solved numerically by applying straightforward finite difference method along with Gaussian elimination technique. It is worthy to note that Prandlt number, Pr, is taken to be small (<< 1) which is appropriate for liquid metals. Moreover, the numerical results are demonstrated graphically by showing the effects of important physical parameters, namely, the modified Richardson number (or mixed convection parameter), Ri*, and surface radiation parameter, R, in terms of local skin friction and local Nusselt number coefficients.

Natural convection flow with surface radiation along a vertical wavy surface

In this study, natural convection boundary layer flow of thermally radiating fluid along a heated vertical wavy surface is analyzed. Here, the radiative component of heat flux emulates the surface temperature. Governing equations are reduced to dimensionless form, subject to the appropriate transformation. Resulting dimensionless equations are transformed to a set of parabolic partial differential equations by using primitive variable formulation, which are then integrated numerically via iterative finite difference scheme. Emphasis has been given to low Prandtl number fluid. The numerical results obtained for the physical parameters, such as, surface radiation parameter, R, and radiative length parameter, ξ, are discussed in terms of local skin friction and Nusselt number coefficients. Comprehensive interpretation of velocity distribution is also given in the form of streamlines.

Non-Newtonian natural convection flow along an isothermal horizontal circular cylinder using modified power-law model

Laminar two-dimensional natural convection boundary-layer flow of non-Newtonian fluids along an isothermal horizontal circular cylinder has been studied using a modified power-law viscosity model. In this model, there are no unrealistic limits of zero or infinite viscosity. Therefore, the boundary-layer equations can be solved numerically by using marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning as well as shear thickening fluids in terms of the fluid velocity and temperature distributions, shear stresses and rate of heat transfer in terms of the local skin-friction and local Nusselt number respectively.

Steady natural convection of non-Newtonian power-law fluid in a trapezoidal enclosure

Numerically investigation of free convection heat transfer in a differentially heated trapezoidal cavity filled with non-Newtonian Power-law fluid has been performed in this study. The left inclined surface is uniformly heated whereas the right inclined surface is maintained as uniformly cooled. The top and bottom surfaces are kept adiabatic with initially quiescent fluid inside the enclosure. Finite volume based commercial software FLUENT 14.5 is used to solve the governing equations. Dependency of various flow parameters of fluid flow and heat transfer is analyzed including Rayleigh number, Ra ranging from 10^5 to 10^7, Prandtl number, Pr of 100 to 10,000 and power index, n of 0.6 to 1.4. Outcomes have been reported in terms of isotherms, streamline, and local Nusselt number for various Ra, Pr, n and inclined angles. Grid sensitivity analysis is performed and numerically obtained results have been compared with those results available in the literature and found good agreement.

Unsteady natural convection within a porous enclosure of sinusoidal corrugated side walls

Numerically investigation of free convection within a porous cavity with differential heating has been performed using modified corrugated side walls. Sinusoidal hot left and cold right walls are assumed to receive sudden differentially heating where top and bottom walls are insulated. Air is considered as working fluid and is quiescent, initially. Numerical experiments reveal 3 distinct stages of developing pattern including initial stage, oscillatory intermediate and finally steady state condition. Implicit Finite Volume Method with TDMA solver is used to solve the governing equations. This study has been performed for the Rayleigh numbers ranging from 100 to 10,000. Outcomes have been reported in terms of isotherms, streamline, velocity and temperature plots and average Nusselt number for various Ra, corrugation frequency and corrugation amplitude. The effects of sudden differential heating and its resultant transient behavior on fluid flow and heat transfer characteristics have been shown for the range of governing parameters. The present results show that the transient phenomena are enormously influenced by the variation of the Rayleigh Number with corrugation amplitude and frequency.

Natural convection heat transfer in a baffled triangular enclosure

To reduce the natural convection heat loss from enclosures many researchers used convection suppression devices in the past. In this study a single baffle is used under the top tip to investigate numerically the natural convection heat loss in an attic shaped enclosure which is a cost effective approach. The case considered here is one inclined wall of the enclosure is uniformly heated while the other inclined wall is uniformly cooled with adiabatic bottom wall. The finite volume method has been used to discretize the governing equations, with the QUICK scheme approximating the advection term. The diffusion terms are discretized using central-differencing with second order accuracy. A wide range of governing parameters are studied (Rayleigh number, aspect ratio, baffle length etc.). It is observed that the heat transfer due to natural convection in the enclosure reduces when the baffle length is increased. Effects of other parameters on heat transfer and flow field are described in this study.

Natural convection due to differential heating of inclined walls and heat source placed on bottom wall of an attic shaped space

Numerical investigation of free convection heat transfer in an attic shaped enclosure with differentially heated two inclined walls and filled with air is performed in this study. The left inclined surface is uniformly heated whereas the right inclined surface is uniformly cooled. There is a heat source placed on the right side of the bottom surface. Rest of the bottom surface is kept as adiabatic. Finite volume based commercial software ANSYS 15 (Fluent) is used to solve the governing equations. Dependency of various flow parameters of fluid flow and heat transfer is analyzed including Rayleigh number, Ra ranging from 103 to 106, heater size from 0.2 to 0.6, heater position from 0.3 to 0.7 and aspect ratio from 0.2 to 1.0 with a fixed Prandtl number of 0.72. Outcomes have been reported in terms of temperature and stream function contours and local Nusselt number for various Ra, heater size, heater position, and aspect ratio. Grid sensitivity analysis is performed and numerically obtained results have been compared with those results available in the literature and found good agreement.

The effect of thermal radiation on the natural convection boundary layer flow over a wavy horizontal surface

In this article, natural convection boundary layer flow is investigated over a semi-infinite horizontal wavy surface. Such an irregular (wavy) surface is used to exchange heat with an external radiating fluid which obeys Rosseland diffusion approximation. The boundary layer equations are cast into dimensionless form by introducing appropriate scaling. Primitive variable formulations (PVF) and stream function formulations (SFF) are independently used to transform the boundary layer equations into convenient form. The equations obtained from the former formulations are integrated numerically via implicit finite difference iterative scheme whereas equations obtained from lateral formulations are simulated through Keller-box scheme. To validate the results, solutions produced by above two methods are compared graphically. The main parameters: thermal radiation parameter and amplitude of the wavy surface are discussed categorically in terms of shear stress and rate of heat transfer. It is found that wavy surface increases heat transfer rate compared to the smooth wall. Thus optimum heat transfer is accomplished when irregular surface is considered. It is also established that high amplitude of the wavy surface in the boundary layer leads to separation of fluid from the plate.

Non-Newtonian mixed convection flow from a horizontal circular cylinder with uniform surface heat flux

Mixed convection laminar two-dimensional boundary-layer flow of non-Newtonian pseudo-plastic fluids is investigated from a horizontal circular cylinder with uniform surface heat flux using a modified power-law viscosity model, that contains no unrealistic limits of zero or infinite viscosity; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning fluids in terms of the fluid temperature distributions, rate of heat transfer in terms of the local Nusselt number.