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     

Simulation of mixed convection heat transfer in a horizontal channel with an open cavity containing a heated hollow cylinder

The objective of this paper is to numerically investigate the mixed convective flow and heat transfer controlled by a heated hollow cylinder inside an open cavity attached with a horizontal channel. All the boundaries of the channel and cavity are perfectly insulated while the inner surface of the cylinder is heated uniformly by heat flux q. The equations of conservation of mass, momentum, and energy were solved using adequate boundary conditions by Galarkin's weighted residual finite element technique. The solution has been performed in the computational domain as a whole with proper treatment at the solid/fluid interface. Computations have been conducted for Ra = 10³–10⁵, Prandtl number Pr varying from 0.7 to 7 and ratio of solid to fluid thermal conductivities from 0.2 to 50. Results are presented in terms of streamlines, isotherms, heat transfer rate in terms of the average Nusselt number (Nu_av), drag force (D), and maximum bulk temperature (θ_max). © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21002     

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.     

Natural-convection heat transfer to air from a horizontal array of cylinders with different surface temperatures

Heat transfer measurements were made on natural convection around horizontal in-line arrays of cylinders whose surface temperatures were different from each other. Through the experiments for a three-cylinder array, a correlation was obtained for the heat transfer coefficient of the array-center cylinder. By using the correlation with some assumptions, the heat-flux distributions could be estimated for an array of five cylinders which were heated to their respective temperatures. Consequently, it was found that both the correlation and the method proposed here were useful in the estimation of heat-flux distributions for a horizontal array of cylinders. © 1998 Scripta Technica, Inc. Heat Trans Jpn Res, 26(2): 116–121, 1997     

Natural convection heat transfer in a circular enclosure

Natural convection heat transfer in a circular enclosure, one half of which was heated and the other half of which was cooled, was investigated experimentally, focusing on the effect of the inclination angle. The experiments were carried out with water. Flow and temperature field were visualized by using the aluminum and liquid-crystal suspension method. The results show that with downward heating the heat transfer coefficient increased as the inclination angle of the boundary between the heating wall and the cooling wall approached the vertical. But with upward heating, the heat transfer coefficient showed minimal change, exhibiting a small peak value when the inclination angle was γ ˜ –45°. The heat transfer coefficient of a flat circular enclosure was estimated from the circular enclosure's heat transfer coefficient. These results can be explained by the obtained flow and temperature fields. © 1999 Scripta Technica, Heat Trans Asian Res, 28(2): 152–163, 1999     

Heat transfer regulation in a rectangular enclosure using a rotating plate

The effects of an inner rotating plate with horizontal axis on the heat transfer in a differentially heated vertical enclosure were investigated experimentally. The aspect ratio of the enclosure height/width was 1 throughout the experiments. An acrylic plate with a small thermal conductivity was installed horizontally at the center of the square enclosure, and was rotated at various speeds for normal and reverse rotations by using the motor attached outside of the enclosure. Purified water was used as the working fluid. The flow pattern was sketched by a visualization experiment using aluminum powder. The heat transfer results were also compared with those from a previous paper on a rotating cylinder. It is clarified here that the heat transfer rate of the enclosure depends largely on the parameter Gr_w/Re_ω², and is characterized by three regions. The heat transfer rate of the enclosure with a rotating plate is somewhat larger than that of a rotating cylinder in the forced convection region. The rotating plate used here will be useful for regulation of wide‐ranging heat transfer. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 342–353, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10099     

Heat transfer in an inclined enclosure with an inner rotating plate

The effects of an inner rotating plate on the heat transfer in a differentially heated inclined enclosure were investigated experimentally. The aspect ratio of the enclosure (height/width) was 1 throughout the experiments. An acrylic plate with a small thermal conductivity was installed horizontally at the center of the square enclosure, and was rotated at various speeds by using a motor attached outside of the enclosure. The inclination angle of the enclosure was varied from –90° to 90°. Purified water was used for the working fluid. The flow pattern was sketched by a visualization experiment using aluminum powder. The heat transfer enhancement can be clearly seen for the inclined enclosure with the hot wall downward facing. The rotating plate used here is useful for the regulation of a wide‐ranging heat transfer rate. © 2001 Scripta Technica, Heat Trans Asian Res, 30(4): 331–340, 2001     

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 control in an enclosure by using a rotating plate and stratified fluids

The effects of an inner rotating plate with horizontal axis on the heat transfer between two vertical walls in a rectangular enclosure with stratified fluid layers were investigated experimentally. The aspect ratio of the enclosure height/width was 1 throughout the experiments. An acrylic plate with small thermal conductivity was installed horizontally at the center of the square enclosure, and was rotated at various speeds for normal and reverse rotations by using the motor installed outside of the enclosure. Purified water and silicon oil were used as the working fluids and were stratified in the enclosure. It is shown here that the heat transfer rate of the enclosure with stratified fluid layers differs largely from that of the enclosure with a single fluid layer. Namely, the heat transfer coefficient increases rapidly at a low rotating speed range, and maintains an almost constant value at a high rotating speed range. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(6): 489–500, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10081     

Natural convection heat transfer in the open space between two horizontal circular planes with different temperatures

A vertical cylinder maintained at room temperature is located right above a horizontal circular heated plane to constitute a narrow air space between the plane and the cylinder bottom surface. Natural convection heat transfer in the space is experimentally investigated. Average heat transfer coefficients of the heated plane are presented with the variation of space distance and Rayleigh number, and are compared with the predictions of the correlation equations which have been proposed for the space between two infinite parallel plates. Visualized flow patterns above the heated plane are also shown. The relation between the flow pattern and the heat transfer coefficient is discussed to clarify the mechanism of heat transfer in the narrow space. As a result, a heat transfer correlation is proposed, which is applicable over a wide range of space distances. © 2001 Scripta Technica, Heat Trans Asian Res, 30(6): 521–531, 2001     

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     

双绝热圆柱对水平三角腔内自然对流影响的数值研究

针对含双绝热圆柱的底部加热水平等腰三角腔内空气的稳态层流自然对流开展研究.通过有限容积法对控制方程进行了数值求解,其中瑞利数的变化范围为104 ～106,圆柱体的尺寸比则分别为0（无圆柱体）、1/8和1/4.基于计算结果对自然对流的流动与传热特性随瑞利数和尺寸比的变化规律进行了分析和讨论.结果表明,双绝热圆柱的存在较大程度上改变了三角腔内自然对流的流型和温度场分布,但对整体传热影响较小,仅略微提高了平均努赛尔数,强化传热的效果在尺寸比为1/8时较为明显.     

Effect of magnetic field on convection heat transfer inside a tilted square enclosure

Steady, laminar, natural-convection flow in the presence of a magnetic field in a tilted enclosure heated from below and cooled from top is considered. The enclosure is filled with liquid gallium. In our formulation of governing equations, mass, momentum and energy are applied to the enclosure. To solve the nonlinear governing differential equations a finite volume code based on PATANKAR's SIMPLER method is utilized. It is shown that for a given inclination angle (φ), as the value of Hartmann number (Ha) increases, the convection heat transfer reduces. Furthermore it is found that at Ra = 10⁴, value of Nusselt number depends strongly upon the inclination angle for relatively small values of Hartmann number. At Ra = 10⁵, the Nusselt number increases up to about φ = 45^o and then decrease as φ increases.     

Experimental determination of natural convection heat transfer coefficients in an attic shaped enclosure

Heat transfer by natural convection in triangular enclosures is an area of significant importance in applications such as the design of greenhouses, attics and solar water heaters. However, given its significance to these areas it has not been widely examined. In this study, the natural convection heat transfer coefficients for air in an attic shaped enclosure were determined for Grashof Numbers over the range of 10⁷ to 10⁹. It was found that the measured heat transfer coefficients could be predicted to within 5% by Ridouane and Campo's [E.H. Ridouane, A. Campo, Experimental-based correlations for the characterization of free convection of air inside isosceles triangular cavities with variable apex angles, Experimental Heat Transfer 18 (2) (2005) 81–86] equation (Eq. (1)) for natural convection in a triangular enclosure previously developed for Grashof Numbers in the range of 10⁵ to 10⁶.

equation(1)

Nu=0.286A−0.286Gr1/4.$Nu=0.286A^{-0.286}G{r}^{1/4}\text{.}$

Heat transfer enhancement of free convection from a heated horizontal plate

A device was developed to enhance heat transfer from heated horizontal plates. The device consists of six straight gutters with slits at the center for the introduction of air. Heat transfer coefficients were measured for several device heights above the heated surface. A height of about 10 mm was found to give rise to the highest heat transfer coefficients. In this case heat transfer rates were 1.2 to 1.4 times larger than those for smooth plates. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 26 (1): 30–38, 1997     

Numerical analysis of convective heat transport in a porous semi‐trapezoidal enclosure with radiation effect

A theoretical and numerical study of natural convection of two‐dimensional laminar incompressible flow in a semi‐trapezoidal porous enclosure in the presence of thermal radiation is conducted. The semi‐trapezoidal enclosure has an inclined left wall that in addition to the right vertical wall is maintained at a constant temperature, whereas the remaining (horizontal) walls are adiabatic. The Darcy‐Brinkman isotropic model is utilized. The governing partial differential equations are transformed using a vorticity stream function and nondimensional quantities and the resulting governing nonlinear dimensionless equations are solved using the finite difference method with incremental steps. The impacts of the different model parameters (Rayleigh number [Ra], Darcy number [Da], and radiation parameter [Rd]) on the thermofluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with the greater Darcy parameter (permeability). The flow is accelerated with the increasing buoyancy effect (Rayleigh number) and heat transfer is also increased with a greater radiative flux. The present numerical simulations are more relevant to hybrid porous media solar collectors.     

Suppression of natural convection heat transfer coefficients in an attic shaped enclosure

The use of convection suppression devices has been widely discussed in the literature as a means of reducing natural convection heat loss from enclosed spaces. In this study the use of a single baffle was examined as a possible low cost means of suppressing heat loss by natural convection in an attic shaped enclosure.     

Numerical estimation of pressure drop and heat transfer characteristics in annular‐finned channel heat exchangers with different channel configurations

In this numerical investigation, three‐dimensional analysis has been used to study the effect of finned channels configuration of (circular, square, and triangular shape) and fin spacing with four rows in staggered arrangements. The finite volume method with k‐ ω turbulent model is applied to estimate the heat transfer and flow characteristics. The results illustrate that the development of the boundary layer between the fins surfaces is credited to the finned channels configuration, fin spacing, and Reynolds number. Moreover, the results of pressure drop and heat transfer with various channel configuration and different fin spacings (1.6, 2, and 4 mm) are presented and validated with the available correlations. The triangular‐finned channel with 1.6 mm fin spacing offered higher heat transfer enhancement followed by square‐ and circular‐finned channels. A considerable agreement was observed when the current findings and the existing correlations were compared, with a maximum deviation of 15% for all the cases.     

Numerical analysis of conjugate heat transfer in a partially open square cavity with a vertical heat source

Conjugate heat transfer in partially open square cavity with a vertical heat source has been numerically studied. The cavity has an opening on the top with several lengths and three different positions. The other walls of cavity were assumed adiabatic. The heat source was located on the bottom wall of cavity and it has got a width such as Printed Circuit Boards (PCB). Steady state heat transfer by laminar natural convection and conduction is studied numerically by solving two dimensional forms of governing equations with finite difference method. The results were reported for various governing parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁶), conductivity ratio, opening position, opening length, PCB distance and PCB height. The numerical results were discussed with streamlines, isotherms, Nusselt number and velocity profiles on x- and y-directions. It is found that ventilation position has a significant effect on heat transfer.     

Magnetohydrodynamic mixed convection in a horizontal channel with an open cavity

The development of magnetic field effect on mixed convective flow in a horizontal channel with a bottom heated open enclosure has been numerically studied. The enclosure considered has rectangular horizontal lower surface and vertical side surfaces. The lower surface is at a uniform temperature T_h while other sides of the cavity along with the channel walls are adiabatic. The governing two-dimensional flow equations have been solved by using Galarkin weighted residual finite element technique. The investigations are conducted for different values of Rayleigh number (Ra), Reynolds number (Re) and Hartmann number (Ha). Various characteristics such as streamlines, isotherms and heat transfer rate in terms of the average Nusselt number (Nu), the Drag force (D) and average bulk temperature (θ_av) are presented. The results indicate that the mentioned parameters strongly affect the flow phenomenon and temperature field inside the cavity whereas in the channel these effects are less significant.