Numerical study of mixed convective heat transfer in a lid‐driven enclosure with rotating cylinders

A numerical simulation is performed to characterize the mixed convective transport in a three‐dimensional square lid‐driven enclosure with two rotating cylinders. The top wall is moving in the positive x‐direction, and the bottom wall is at a higher fixed temperature compared with all other isothermal walls. Both cylinders are rotating in its own plane about their centroidal axis. On the basis of rotation of both cylinders in clockwise or counter‐clockwise directions, four rotational models are studied. Various controlling parameters considered in the present study are Grashof number (10 ³ < Gr < 10 ⁵), rotating speed of the cylinder (5 < ω < 50), and the Reynolds number based on top wall movement is fixed to 100. The effect of cylinder rotation on the heat transfer of bottom wall is reported with the help of streamlines, contour plots of z‐component of vorticity, averaged and local Nusselt number, ratios of secondary flow and drag coefficient. It is observed that the heat transfer at the bottom wall is substantially dependent on the rotational model and rotational speed of the cylinder.     

Numerical analysis of the longitudinal size of the partition on natural convection heat transfer and fluid flow within a differentially heated porous enclosure

The article deals with the effect of longitudinal size and shape partition embedded within a differentially heated porous enclosure. The objective is to curtail the heat transfer rate across such porous enclosures by means of partitions embedded within. The partition shapes under consideration are straight vertical left-inclined, right-inclined, L-shaped, wavy, corrugated, and square-wave. It is sought to find the most effective combination of partition length and shape that could serve the required objective. Also, many times, due to the constructional constraints of the porous enclosure or cavity, using full-length partitions may not be feasible. In this regard, it is also sought to find the partition length that is to be maintained for achieving a significant reduction in heat transfer without much compromise. The results of the current study are useful for thermal design engineers particularly in the field of thermal insulation, solar heating application, and packed bed energy storage systems where the major challenge is to reduce the heat transfer across the system. The parameters under consideration are the longitudinal length L and Rayleigh number Ra. All the partitions under study are evaluated for bottom-wall and top-wall attached conditions. Some of the notable findings are that for smaller-sized partitions (B < 0.5), L-shaped partitions are most effective in controlling the convection heat transfer rate across the enclosure while for larger-sized partitions (L > 0.5), square-wave-shaped partitions should be preferred for effective reduction in the rate of convection heat transfer.     

Thermal transport analysis for natural convection in a porous corrugated rhombic enclosure

A numerical study of fluid flow and heat transfer, applying natural convection is carried out in a porous corrugated rhombic enclosure. A uniform heating source is applied from the bottom boundary wall while the inclined side walls are maintained to a constant cold temperature and the top corrugated wall is retained at insulated condition inside the enclosure. The heat transfer and flow features are presented for a wide spectrum of Rayleigh numbers (Ra), 10⁴ ≤ Ra ≤ 10⁶, and Darcy numbers (Da), 10^?3 ≤ Da ≤ 10^?2. The number of undulations (n) for the top and bottom walls have been varied from 1 to 13 keeping the amplitude of undulation fixed. It is revealed that the characteristics of heat transfer are conceivably modulated by changing the parameter of the undulation number on the enclosure walls, specifically at the bottom and top. The influencing control of n in altering the heat transfer rate is felt maximum on the left wall and minimum for the right wall, and there is a strong interplay between Ra and Da together with n on dictating the heat transfer characteristics. The critical value, where heat transfer rate is observed as maximum is at n = 11 and thereafter the values decrease.     

MHD natural convection inside an inclined trapezoidal porous enclosure with internal heat generation or absorption subjected to isoflux heating

A steady laminar two‐dimensional magneto‐hydrodynamic natural convection flow in an inclined trapezoidal enclosure filled with a fluid‐saturated porous medium is investigated numerically using a finite difference method. The left and right vertical sidewalls of the trapezoidal enclosure are maintained at a cold temperature. The horizontal top wall is considered adiabatic while the bottom wall is subjected to isoflux heating. A volumetric internal heat generation or absorption is embedded inside the trapezoidal enclosure while an external magnetic field is applied on the left sidewall of the enclosure. In the current work, the following parametric ranges of the non‐dimensional groups are used: Hartmann number is varied as , Darcy number is taken as , 10^?4, and 8 × 10^?5, Rayleigh number is varied as , Prandtl number is considered constant at Pr = 0.7, the dimensionless internal heat generation or absorption parameter is varied as Δ = ?0.2, 0, 1, and 2.0, while the trapezoidal enclosure inclination angle is varied as . The results indicated a strong flow circulation occurs when the Darcy and the Rayleigh numbers are high. In addition, it is found that the Hartmann number, internal heat generation or absorption parameter and inclination angle have an important role on the flow and thermal characteristics. It is also found that when the enclosure inclination angle and Hartmann number increase the average Nusselt number along the hot bottom wall decreases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21013     

Transient free convective flow through a vertical cylinder filled with a porous material

This article aims to explore the impressive impact of emerging parameters on transient fully evolved free convective flow inside a vertical cylinder containing a porous material. The mathematical formulation of the model related to the considered physical circumstance is presented under compatible boundary conditions. Closed‐form solutions are received for the velocity field, the temperature distribution, mass flux, skin friction, and the Nusselt number in terms of Bessel functions and modified Bessel functions of the first kind. Impressive effects of parameters such as the Darcy number $Da$, Prandtl number $\text{Pr}$, viscosity ratio $M$, and also time $t$ on both the velocity and temperature distribution have been explored employing graphs and tables. It is irradiated by analysis that flow erection, heat transfer rate, skin friction, and mass flux are admirably impacted by the Prandtl number, the Darcy number, viscosity ratio parameter, and time. It is found that both the velocity and temperature field profiles rise with the rising value of time and ultimately attain their steady state. Moreover, the Prandtl number and the viscosity ratio parameter reduce the velocity profiles, while the reverse phenomenon occurs with the Darcy number.     

Cross flow on transient double‐diffusive natural convection in inclined porous trapezoidal enclosures

This paper investigates the cross‐diffusion effects subject to exponential variable boundary conditions on transient double‐diffusive natural convection flow in an enclosure. The flow domain is a two‐dimensional inclined trapezoidal cavity filled with a porous medium. The top wall is assumed to be insulated and permeable, while the enclosure's bottom wall is subject to exponential varying temperature and concentration. The prescribed temperature and concentration are different at the vertical walls. Conservation equations are used as the governing equations. The finite element Galerkin weighted residual method, in association with the Newton‐Raphson scheme is employed to solve the system of coupled nondimensional equations. The numerical tests are confirmed with existing literature and are found to be in excellent agreement. The simulations results for stream functions, isotherms, and isoconcentrations are discussed for the various flow parameters. A sensitivity analysis using the response surface method suggests that the average Nusselt and Sherwood numbers are more sensitive to the cross‐diffusion effects. It is further observed that the cross‐diffusion terms stabilize the sensitivity to the angle of inclination.     

Numerical analysis of natural convection in an inclined trapezoidal enclosure filled with a porous medium

A theoretical study of buoyancy-driven flow and heat transfer in an inclined trapezoidal enclosure filled with a fluid-saturated porous medium heated and cooled from inclined walls has been performed in this paper. The governing non-dimensional equations were solved numerically using a finite-difference method. The effective governing parameters are: the orientation or inclination angle of the trapezoidal enclosure , which varies between 0° and 180°, the Rayleigh number Ra, which varies between 100 and 1000, the side wall inclination angle θ_s and the aspect ratio A. The side wall inclination parameter θ_s is chosen as 67°, 72° and 81° and the calculations are tested for two different values of A=0.5 and 1.0. Streamlines, isotherms, Nusselt number and flow strength are presented for these values of the governing parameters. The obtained results show that inclination angle is more influential on heat transfer and flow strength than that of the side wall inclination angle θ_s. It is also found that a Bénard regime occurs around =90°, which depends on the inclination of the side wall, Rayleigh number and aspect ratio.     

Natural convective heat transfer in trapezoidal enclosure of box-type solar cooker

This paper presents simple thermal analysis to evaluate the natural convective heat transfer coefficient, h_c12 for a trapezoidal absorber plate-inner glass cover enclosure of a double-glazed box-type solar cooker. Several indoor simulation experiments in steady state conditions have been performed to measure the temperatures of absorber plate, inner and outer glass covers, ambient air, electrical input supply and wind speed. The experimental data has been correlated by an equation of the form, Nu = CRaⁿ. The values of the constants C and n, obtained by linear regression analysis are used to calculate the convective heat transfer coefficient. The heat transfer analysis predicts that h_c12 varies from 4.84 to 6.23 W m^{−2 o}C⁻¹ for the absorber plate temperature from 54 to 141 ^oC. The results of h_c12 are compared with those of rectangular enclosure for the same absorber-inner glass cover temperatures and gap spacing. The study reveals that the values of convective heat transfer coefficient and top heat loss coefficient for rectangular enclosure are lower by 31–35% and 7% respectively.     

Heat transfer inside a horizontal channel with an open trapezoidal enclosure subjected to a heat source of different lengths

The heat transfer phenomena inside a horizontal channel with an open trapezoidal enclosure subjected to a heat source of different lengths was investigated numerically in the present work. The heat source is considered as a local heating element of varying length, which is embedded at the bottom wall of the enclosure and maintained at a constant temperature. The air flow enters the channel horizontally at a constant cold temperature and a fixed velocity. The other walls of the enclosure and the channel are kept thermally insulated. The flow is assumed laminar, incompressible, and two‐dimensional, whereas the fluid is considered Newtonian. The results are presented in the form of the contours of velocity, isotherms, and Nusselt numbers profiles for various values of the dimensionless heat source lengths (0.16 ≤ ε ≤ 1). while, both Prandtl and Reynolds numbers are kept constant at (Pr = 0.71) and (Re = 100), respectively. The results indicated that the distribution of the isotherms depends significantly on the length of the heat source. Also, it was noted that both the local and the average Nusselt numbers increase as the local heat source length increases. Moreover, the maximum temperature is located near the heat source location.     

Analysis of two‐dimensional porous fins with variable thermal conductivity

Analysis of porous fins for their higher heat transfer in comparison with solid fins with identical volumes has attracted significant attention. In this paper, a two‐dimensional thermal analysis of a porous fin having variable thermal conductivity coefficient is performed using finite difference method. Heat transfer through porous media is simulated using passage velocity from Darcy's model. The thermal conductivity of the solid phase is considered as a linear function of temperature. It is found that the temperature profile of the fin is completely two‐dimensional even for high Rayleigh and Darcy numbers (Ra = 10³～10⁴, Da = 0.01), because the temperature changes significantly along the transverse axis especially for lower Rayleigh and Darcy numbers. Also, the effects of important nondimensional parameters such as Rayleigh and Darcy numbers, porosity, Nusselt, thermal conductivity, and aspect ratio on the temperature profile are investigated. The results demonstrate that the temperature distribution is strongly dependent on the Rayleigh and Darcy numbers.     

Natural convection in a parabolic enclosure with an internal vertical heat source filled with Cu–water nanofluid

The numerical investigation of the natural convection in concave and convex parabolic enclosures with a nanofluid consisting of water and copper nanoparticles is carried out by using the finite volume method. The upper and lower walls of the enclosures are adiabatic while the sidewalls are isothermal at a cold temperature. An internal heat source of constant length (ε = 0.2) and negligible thickness is placed at various vertical positions along the center of the enclosure. It was found that the increase in the location of the heat source leads to a drop in the water and nanofluid flow circulation in both types of enclosures. For both considered Cases I and II, the average Nusselt number increases when the Rayleigh number and solid volume fraction increase. Moreover, it was concluded that Case I with δ = 0.8 is the optimum case for heat transfer enhancement for Ra = 10³ and Ra = 10⁴. Case II with δ = 0.5 is optimum for Ra = 10⁵. Both cases are satisfied when the nanofluid is used with ? = 0.2.     

Inhomogeneous flow model of natural convection,entropy generation,and heatlines visualization in wavy I-shaped enclosure with rectangular heater

The present investigation is on examination of the natural convection and entropy generation considering the heatlines visualization of nanofluid I-shaped enclosure with two corrugated walls considering inner rectangular heater of three different heights. The influence of Brownian motion along with thermophoresis had been implemented using Inhomogeneous two-phase model of nanofluid. The governing equations were solved numerically using COMSOL software. Influence of Rayleigh number $$, Buoyancy ratio number $$, Lewis number $$, heater length $$. The results indicate that the influence of Lewis number on heat transfer bettering is stronger at high Rayleigh number $$ while its impact is negligible at a lower value of Rayleigh number (conduction mode). In addition, the total entropy generation gets its highest value at Lewis number $$. Bejan number, fluid flow strength and heat rate increase as the rectangular heater height increases. Also, higher heat transfer augmentation is taken when the heater height is $$ while increasing the heater height to $$ leads to more total entropy generation. The impact of heater height on total entropy generation is highly affected by Rayleigh number as increasing the heater height from $$ into $$, total entropy generation increases by $$ at $$ while it increases by $$ at $$.     

Effects of pressure work and radiation on natural convection flow around a sphere with heat generation

The effects of pressure work and radiation on natural convection flow around a sphere in presence of heat generation have been investigated in this paper. The governing equations are transformed into dimensionless non-similar equations by using set of suitable transformations and solved numerically by the finite difference method along with Newton's linearization approximation. Attention has been focused on the evaluation of shear stress in terms of local skin friction and rate of heat transfer in terms of local Nusselt number, velocity as well as temperature profiles. Numerical results have been shown graphically and also in tabular form for some selected values of parameter set consisting of heat generation parameter Q, radiation parameter Rd, pressure work parameter Ge and the Prandtl number Pr.     

Natural convection and radiation heat transfer in a vertical porous layer with a hexagonal honeycomb core (Part 1: numerical analysis)

Combined heat transfer characteristics were obtained numerically for three-dimensional natural convection and thermal radiation in a long and wide vertical porous layer with a hexagonal honeycomb core. We assumed that the porous layer was both homogeneous and isotropic. The pure Darcy law for fluid flow and Rosseland's approximation for radiation were used. The numerical methodology was based on an algebraic coordinate transformation technique and the transformed governing equations were solved using the SIMPLE algorithm. The effect of radiation on the heat transfer characteristics was investigated over a wide range of radiation numbers and temperature ratios for two Darcy-Rayleigh number values (Ra^* = 100 and 1000) and for a fixed aspect ratio of H/L = 1. The results are presented in the form of combined radiation and convection heat transfer coefficients and are compared with the corresponding values for pure natural convection. © 1999 Scripta Technica, Heat Trans Asian Res, 28(4): 278–294, 1999     

Numerical analysis of natural convection for a porous rectangular enclosure with sinusoidally varying temperature profile on the bottom wall

Numerical investigations of steady natural convection flow through a fluid-saturated porous medium in a rectangular enclosure with a sinusoidal varying temperature profile on the bottom wall were conducted. All the walls of the enclosure are insulated except the bottom wall which is partially heated and cooled. The governing equations were written under the assumption of Darcy-law and then solved numerically using finite difference method. The problem is analyzed for different values of the Rayleigh number Ra in the range 10 ≤ Ra ≤ 1000, aspect ratio parameter AR in the range 0.25 ≤ AR ≤1.0 and amplitude λ of the sinusoidal temperature function in the range 0.25 ≤ λ ≤ 1.0. It was found that heat transfer increases with increasing of amplitude λ and decreases with increasing aspect ratio AR. Multiple cells were observed in the cavity for all values of the parameters considered.     

Numerical study of radiation‐convection heat transfer

In this study, the authors attempted to introduce a simulation technique for radiation‐convection heat transfer in the high‐temperature fields of industrial furnaces, boilers, and gas turbine combustors. The convection effect was analyzed by a differential equation, but the radiation effect was analyzed by an integral equation. Thus, it was not easy to arrange both effects using the same type of equations. Then, the authors introduced the zone method and Monte Carlo method for the integral equation of the radiation effect and the finite difference method for the differential equation of the convection effect. A three‐dimensional analysis of the high‐temperature furnace was performed by this simulation technique to obtain its temperature distribution. Furthermore, another radiation‐convection heat transfer analysis in the low‐temperature living room was performed by the same technique. Finally, the authors tried to develop a computer software for radiation‐convection heat transfer and described their idea of software construction for the above. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(5): 391–407, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10042     

Experimental study of natural convection heat transfer in a semicircular enclosure

An experimental study of natural convection heat transfer in a differentially heated semicircular enclosure was carried out. The flat surface was heated and the radial surface was cooled isothermally. The effects of angle of enclosure inclination on the heat transfer across semicircular regions of several radii were measured for Rayleigh numbers Ra_R ranging from 6.72 × 10⁶ to 2.33 × 10⁸, using water as the working fluid. The angle of inclination varied from −90 degrees to 90 degrees with radii R of 50, 40, and 30 mm. The flow patterns were sketched from the results of a visualization experiment using aluminum powder. The temperature measurements in the enclosure were carried out using liquid crystals and thermocouples. The results indicate that different flow patterns were encountered as the angle of inclination varied, and the heat transfer rate was largely dependent on the flow pattern. In particular, enhanced heat transfer rates can be obtained when plume-like flow occurs along both hot and cold walls in the case of an upward-facing hot wall. Heat transfer for the inclined enclosure can be predicted using the equation for a vertical enclosure presented in this paper. © 1998 Scripta Technica, Inc. Heat Trans Jpn Res, 26(2): 131–142, 1997     

Numerical exploration of thermal radiation and Biot number effects on the flow of a non‐Newtonian MHD Williamson fluid over a vertical convective surface

A theoretical and computational study of the magnetohydrodynamic flow and free convection heat transfer in an electroconductive polymer on the external surface of a vertical plate under radial magnetic field is presented. The Biot number effects are considered at the vertical plate surface via modified boundary conditions. The Williamson viscoelastic model is employed which is representative of certain industrial polymers. The nondimensional, transformed boundary layer equations for momentum and energy are solved with the second‐order accurate implicit Keller box finite difference method under appropriate boundary conditions. Validation of the numerical solutions is achieved via benchmarking with earlier published results. The influence of Weissenberg number (ratio of the relaxation time of the fluid and time scale of the flow), magnetic body force parameter, stream‐wise variable, and Prandtl number on thermo fluid characteristics are studied graphically and via tables. A weak elevation in temperature accompanies increasing Weissenberg number, whereas a significant acceleration in the flow is computed near the vertical plate surface with increasing Weissenberg number. Nusselt number is reduced with increasing Weissenberg number. Skin friction and Nusselt number are both reduced with increasing magnetic field effect. The model is relevant to the simulation of magnetic polymer materials processing.     

Numerical study of convective heat transfer in T‐bifurcating channel

A numerical study of a three‐dimensional turbulent flow in a rectangular T‐bifurcating duct was performed. It focused on the analysis of heat transfer in the branching duct at 90 to the main flow. Including separation and reattachment phenomena, the flow seemed to be anisotropic. The closure system of the full set of Navier–Stokes equations governing the flow was based on the on one point statistical modeling using a low Reynolds number second‐order full stress transport model. For several aspect ratios, results show that in addition to the recirculation zone in the branching duct close to the upstream side; pairs of streamwise vortices were generated downstream of the junction zone with their centers moving towards the symmetry plane. The effect of the aspect ratio of the branching section in enhancing this phenomenon and flow rate effect on the heat transfer were particularly analyzed in this paper.