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     

Wall–bounded flow and heat transfer around a circular cylinder at low Reynolds and Hartmann numbers

A two–dimensional numerical simulation is performed following a finite volume approach to analyze the forced convection heat transfer for the hydromagnetic flow around a circular cylinder at low Reynolds numbers. The cylinder is placed within a rectangular channel subjected to externally applied magnetic fields and acted upon by the magnetohydrodynamic (MHD) flow of a viscous incompressible and electrically conductive fluid. The magnetic field is applied either along the streamwise or transverse directions. The simulation is carried out for the range of Reynolds number 10 ≤ Re ≤ 80 with Hartmann number 0 ≤ Ha ≤ 10 and for different Prandtl numbers, Pr = 0.02 (liquid metal), 0.71 (air), and 7 (water) for a blockage ratio β = 0.25. The flow is steady for the above range of conditions. Apart from the channel wall, the magnetic field provides additional stability to the flow as a result of which the recirculation region behind the obstacle reduces with increasing magnetic field strength for a particular Reynolds number. The rate of heat transfer is found almost invariant at low Re whereas it increases slightly for higher Re with the applied magnetic field. The heat transfer increases as usual with the Reynolds number for all Hartmann numbers. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21025     

Effect of two immiscible multifluid flow on internal heat generation or absorption in a vertical channel in the presence of concentration

The effect of multifluid flow on internal heat generation or absorption in a vertical channel in the presence of concentration is investigated in this paper. The fluids are incompressible in both regions, that is, Region-I and Region-II, and it is assumed the transport properties of fluid flow are constant. With the help of the analytical method, all the basic equations transformed into governing coupled nonlinear ordinary differential equations are solved, and the solutions obtained for fluid velocity, temperature, and concentration. These results are illustrated by plotting graphs and for various physical parameters. Here, we can control the results by means of the heat absorption coefficient, width ratio, and viscosity ratio.     

Natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and internal heat generation

In this paper the natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and temperature dependent internal heat generation is investigated. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. An increase in the aspect ratio of the elliptical cylinder decreases the average surface temperature of the elliptical cylinder with blunt orientation, while it increases the average surface temperature of the elliptical cylinder with slender orientation. Moreover, an increase in the heat generation parameter for natural convection flow over a horizontal elliptic cylinder with constant heat flux leads to an increase in the average surface temperature of the elliptical cylinder.     

Numerical study of Williamson fluid flow and heat transfer over a permeable stretching cylinder with the effects of Joule heating and heat generation/absorption

The present study aims to discuss the Williamson fluid flow and heat transfer across a permeable stretching cylinder with heat generation/absorption effects. The effects of viscous dissipation, Joule heating, and magnetic field are also taken into account. The BVP-4C numerical solver in MATLAB is adopted for all the numerical simulations in the present study. For this, the modeled partial differential equations are translated into dimensionless ordinary differential equations using some well-developed similarity transformations. A good agreement between the numerical results of the present study and existing literature is exhibited. The dimensionless physical parameters being investigated are Reynolds number, magnetic field parameter, suction parameter, heat source/sink parameter, Williamson fluid parameter, and mixed convection parameter. The numerical calculations are also performed for the skin friction coefficient and local Nusselt number to get an understanding of the shear stress rate and heat transfer rate, respectively. Furthermore, the impact of all these physical parameters on the velocity and temperature profiles is investigated and represented throughout the literature.     

Natural convection heat transfer from a horizontal isothermal elliptical cylinder with internal heat generation

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature dependent internal heat generation. 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 cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. Results show that both the heat transfer rate and skin friction of the elliptical cylinder with slender orientation are higher than the elliptical cylinder with blunt orientation. Moreover, an increase in the heat generation parameter for natural convection flow over an isothermal horizontal elliptic cylinder leads to a decrease in the heat transfer rate from the elliptical cylinder and an increase in the skin friction of the elliptical cylinder.     

Conjugate natural convection around a finned pipe in a square enclosure with internal heat generation

This work is focused on the numerical study of steady, laminar, conjugate natural convection around a finned pipe placed in the center of a square enclosure with uniform internal heat generation. Four perpendicular thin fins of arbitrary and equal dimensions are attached to the pipe whose internal surface is isothermally cooled. The sides of the enclosure are considered to have finite and equal thicknesses and their external sides are isothermally heated. The problem is put into dimensionless formulation and solved numerically by means of the finite-volume method. Representative results illustrating the effects of the finned pipe inclination angle and fins length on the streamlines and temperature contours within the enclosure are reported. In addition, results for the local and average Nusselt numbers are presented and discussed for various parametric conditions.     

Laminar combined magnetoconvection in a wavy enclosure with the effect of heat conducting cylinder

In the current work, a numerical study of the flow characteristics on combined magnetoconvection in a lid-driven square enclosure, differentially heated, is carried out. This problem is solved by using finite element method of the partial differential equations, which are the heat transfer and stream function in Cartesian coordinates. The tests are performed for different solid–fluid thermal conductivity ratio, cylinder location and Richardson number while the Prandtl number, Reynolds number, magnetic and Joule heating parameters are kept constant. One geometrical configuration is used namely two undulations. The outcome obtained shows that the heat conducting inner square cylinder affects the flow and the heat transfer rate in the enclosure. The trend of the local heat transfer is found to follow a wavy pattern. Results are presented in terms of streamlines, isotherms, average Nusselt number at the heated wavy wall, average temperature of the fluid in the enclosure and dimensionless temperature at the cylinder center for different combinations of the governing parameters.     

A numerical study of natural convection around a square,horizontal, heated cylinder placed in an enclosure

In this paper, natural convection around a tilted heated square cylinder kept in an enclosure has been studied in the range of 10³ ⩽ Ra ⩽ 10⁶. Streamfunction-vorticity formulation of the Navier–Stokes equation is solved numerically using finite-difference method in non-orthogonal body-fitted coordinate system. Detailed flow and heat transfer features for two different thermal boundary conditions are reported. Effects of the enclosure geometry has been assessed using three different aspect ratio placing the square cylinder at different heights from the bottom. The concept of heatfunction has been employed to trace the path of heat transport. It is found that the uniform wall temperature heating is quantitatively different from the uniform wall heat flux heating. Flow pattern and thermal stratification are modified, if aspect ratio is varied. Overall heat transfer also changes for different aspect ratio.     

Entropy generation in turbulent natural convection due to internal heat generation

In this study numerical predictions of entropy generation in turbulent natural convection due to internal heat generation in a square cavity are reported for the first time. Results of entropy generation analysis are obtained by solving the entropy generation equation. The values of velocity and temperature, which are the inputs of the entropy generation equation, are obtained by an improved thermal lattice-BGK model proposed in this paper. The analyzed range is wide, varying from the steady laminar symmetric state to the fully turbulent state. Distributions of entropy generation numbers, for various Rayleigh numbers, Prandtl numbers, and Eckert numbers, are given.     

Mixed convection heat transfer in a differentially heated square enclosure with a conductive rotating circular cylinder at different vertical locations

In this investigation, a numerical simulation using a finite volume scheme is carried out for a laminar steady mixed convection problem in a two-dimensional square enclosure of width and height (L), with a rotating circular cylinder of radius (R = 0.2 L) enclosed inside it. The solution is performed to analyze mixed convection in this enclosure where the left side wall is subjected to an isothermal temperature higher than the opposite right side wall. The upper and lower enclosure walls are considered adiabatic. The enclosure under study is filled with air with Prandtl number is taken as 0.71. Fluid flow and thermal fields and the average Nusselt number are presented for the Richardson numbers ranging as 0, 1, 5 and 10, while Reynolds number ranging as 50, 100, 200 and 300. The effects of various locations and solid-fluid thermal conductivity ratios on the heat transport process are studied in the present work. The results of the present investigation explain that increase in the Richardson and Reynolds numbers has a significant role on the flow and temperature fields and the rotating cylinder locations have an important effect in enhancing convection heat transfer in the square enclosure. The results explain also, that the average Nusselt number value increases as the Reynolds and Richardson numbers increase and the convection phenomenon is strongly affected by these parameters. The results showed a good agreement with further published works.     

On the combined influence of Reynolds number and cylinder spacing for flow around a row of heated square cylinders

The characteristics of forced convection heat transfer across a row of heated square cylinders kept in side-by-side arrangement are numerically investigated to examine the combined effects of Reynolds number and cylinder spacing for Ri = 0, 60 ≤ Re ≤ 160, Pr = .71, and s/d = 1.0–8.0, where the space between cylinder surfaces is s and the cylinder size is d. A numerical study was carried out using the thermal lattice Boltzmann method. The goal of this work is to explore the transitions in heat transfer phenomenon that occurs behind the cylinder and to report the corresponding regimes for heat transfer namely synchronous, quasiperiodic, and chaotic. The proposed regime of heat flow is a function of Reynolds number and spacing. The synchronous heat regime is obtained for s/d ≥ 5.0 and quasiperiodic, chaotic regimes are observed for 3.0 ≤ s/d < 5.0, s/d < 3.0, respectively at Re = 100. The instantaneous isotherms, the power spectra of the corresponding Nusselt number signals, and the significance of cylinder Nusselt number frequency are used to examine these heat flow regimes. The heat transfer regimes for a row of heated cylinders and flow regimes for a row of unheated cylinders both have comparable appearances except for the fact that the heat transfer regime is synchronous at s/d ≥ 5.0 and flow is synchronous at s/d ≥ 4.0. The chaotic or quasiperiodic heat transfer regimes occur due to merging and strong interactions between thermal blobs shed from the cylinders. Heat transfer is synchronous at a higher spacing and characterized by independent thermal blobs shedded from the cylinders. It is reported that as spacing reduces and Reynolds number increases, the mean value of the Nusselt number experienced by all cylinders increases. The important outcome of the present numerical work is that for understanding heat transfer from bluff body, the transitions that occur in heat transfer are useful.     

MHD heat transfer and entropy production of an Al2O3-water nanofluid in a horizontal cylinder

This paper deals with the effect of magnetic fields (B_r, B_θ, B_z) applied in r-, θ-, z-directions, respectively, on entropy production and heat transfer and in a horizontal cylinder filled with an Al₂O₃-water nanofluid. The results are verified using literature data. For different Richardson, Ri, and Hartmann numbers, Ha, the nanoparticles (NP) ϕ, and magnetic field orientation combined effect provide a better understanding of heat transfer and entropy optimization. The results indicate that entropy production and heat transfer and rates depend on magnetic field intensity and direction. Also, increasing Ri and NP increases entropy generation and heat transfer. Finally, applying a radial magnetic field promotes a better convective heat transfer and minimizes entropy production.     

Effect of maximum and minimum heat capacity rate on entropy generation in a heat exchanger

This paper presents a theoretical analysis of a heat exchanger with a negligible fluid flow pressure drop to determine whether it is better to operate the heat exchanger with the minimum or maximum heat capacity rate of the hot fluid from entropy generation point of view. Entropy generation numbers are derived for both cases, and the results show that they are identical, when the heat exchanger is running at a heat capacity ratio of 0.5 with heat exchanger effectiveness equaling 1. An entropy generation number ratio is defined for the first time, which has a maximum value at ε = 1/(1+R) for any inlet temperature ratio. When R equals 0.1, 0.5 and 0.9, the entropy generation number ratio receives a maximum value at an effectiveness equaling 0.91, 0.67 and 0.526, respectively. When R=0.9, the entropy generation number ratio is the same for all inlet temperature ratios at ε=0.8. The results show that the entropy generation number ratio is far from 1 depending on the inlet temperature ratio of the cold and hot fluid. The results are valid for parallel‐flow and counterflow heat exchangers. Copyright © 2010 John Wiley & Sons, Ltd.     

Buoyancy-aided momentum and heat transfer in a vertical channel with a built-in square cylinder

This study focuses on the confined upward flow and heat transfer around a square cylinder under the effect of aiding buoyancy (Richardson number, Ri=0–1) in the vertical channel for Reynolds number (Re)=1–40 and blockage ratio (BR)=25–50% for the air as working fluid. Flow is found to be steady and symmetric for the range of settings. For Re≤2, no separation zone occurs for BR=25% and 30%. However, for BR=50%, no wakes are observed for Re≤3. The onset of flow separation takes place between Re=2 and 3 for BR=25% and 30%; whereas, for BR=50%, it exists between Re=3 and 4, irrespective of the value of Ri. Heat transfer correlations have also been obtained at different values of Re, BR and Ri.     

Heat transfer around a circular cylinder in separated air flow

An experimental study has been conducted to determine the heat transfer characteristics around a circular cylinder attached to the separated flow of air shed from a fence. The fence was located vertically to the flow with a height of H = 40 mm. d/H was constant at 0.638, where d is the cylinder diameter of 25.5 mm. X/H were 0.50 and 0.775 and Y/H ranged from 0.525 to 1.50, where X and Y are, respectively, the distances between the axis of the cylinder and the front face of the fence, and the bottom wall of the test section. The Reynolds number based on the cylinder diameter and the velocity of the undisturbed flow ranged from 1.9 × 10⁴ to 6.0 × 10⁴. It was found that the maximum local Nusselt number changes drastically in the vicinity of Y/H = 1.0–1.11 and that the maximum mean Nusselt number occurs in the neighborhood of Y/H = 1.24–1.43 for X/H = 0.50 and 1.3–1.4 for X/H = 0.775. © 1999 Scripta Technica, Heat Trans Asian Res, 28(3): 211–226, 1999     

Entropy generation in an asymmetrically cooled slab with temperature‐dependent internal heat generation

The paper presents an entropy generation analysis for steady conduction in a slab with temperature‐dependent volumetric internal heat generation. The slab experiences asymmetric convective cooling on its two faces. The exact analytical solution for the temperature distribution is used to compute dimensionless local and total entropy generation rates in the slab. The total entropy generation rate depends on five dimensionless parameters: reference heat generation temperature Q, the heat generation–temperature variation parameter a, the temperature asymmetry parameter λ, and Biot numbers Bi₁ and Bi₂. Graphs illustrating the effect of these five parameters on the local and total entropy generation rates are presented and discussed. It is found that the total entropy generation in the slab can be minimized with a suitable choice of the cooling parameters. The paper corrects the flawed entropy results published recently. The present results for the special case of uniform internal heat generation confirm the results presented in a 2003 paper. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20404     

Flow and heat transfer in a porous medium saturated with a Sisko nanofluid over a nonlinearly stretching sheet with heat generation/absorption

This work is focused on steady flow and heat transfer in a porous medium saturated with a Sisko nanofluid (non‐Newtonian power‐law) over a nonlinearly stretching sheet in the presence of heat generation/absorption. Nonlinear PDEs are transformed into a system of coupled nonlinear ODEs with related boundary conditions using similarity transformation. The reduced equations are then solved numerically using the Runge–Kutta–Fehlberg fourth–fifth order method (RKF45) with Maple 14.0 software. The solutions depend on the power‐law index n and the effect of pertinent parameter such as the Brownian motion parameter, thermophoresis parameter, Lewis number, the permeability, and the heat generation/absorption on the dimensionless velocity, temperature, and nanoparticles volume fraction and also on the skin friction, local Nusselt, and Sherwood numbers are produced for values of the influence parameter. A rapprochement of the numerical results of the actual study with formerly published data detected an excellent agreement.     

Forced convection heat transfer from a circular cylinder in crossflow to air and liquids

Local and average heat transfer by forced convection from a circular cylinder is studied for Reynolds number from 2 × 10³ to 9 × 10⁴ and Prandtl number from 0.7 to 176. For subcritical flow, the local heat transfer measurement indicates three regions of flow around the cylinder: laminar boundary layer region, reattachment of shear layer region and periodic vortex flow region. The average heat transfer in each region is calculated and correlated with the Reynolds number and the Prandtl number. The Nusselt number in each region strongly depends on the Reynolds number and the Prandtl number with different power indices. An empirical correlation for predicting the overall heat transfer from the cylinder is developed from the contributions of heat transfer in these three regions.