Heat Source Length Research Articles

Lattice Boltzmann Modeling for Natural Convection in Power-Law Fluids Within a Partially Heated Square Enclosure

Abstract This paper reports the numerical investigations for steady-state natural convection in power-law fluids inside a square enclosure embedded with bottom discrete heaters. The lattice Boltzmann method (LBM) is employed to model the flow and heat transfer phenomenon at different combinations of power-law index, Rayleigh number, and heat source length for a constant Prandtl number. The buoyancy force is incorporated in the collision term of the LBM through Boussinesq approximation. Simulation outcomes are furnished using streamlines, temperature contours, velocity profiles, and variation of heat transfer on the nonadiabatic walls to probe natural convection phenomena. The results indicate that the temperature and the flow fields in the enclosure are symmetric about the vertical centerline. The detailed physical interpretations have been provided for the reported results. Further, the increase in the power-law index means a rise in viscosity and a decrease in thermal energy transport for other constant parameters. The outcomes also specify that the intensity of circulation and heat transfer enhances with the increase of Rayleigh number and size of the localized heater. Finally, though, a rise in the size of the confined heat source enhances the rate of total thermal transport, it does not change the trend of fluid flow and local heat transfer rate.

MHD Convection of an Al2O3–Cu/Water Hybrid Nanofluid in an Inclined Porous Cavity with Internal Heat Generation/Absorption

In Present communication, the transference of the hybrid nanofluids due to the natural propulsive like shrinkage and relaxation of the flexible walls and the motion has serious applications in several embryonic technologies. Stimulated by the multi-disciplinary development and study in this trend, a mathematical model is suggested to explore the numerical simulation of the hybrid nanofluid flow inside a slant porous cavity to determine the impact of volume fraction, Rayleigh number, heat generation and heat source length and location on magneto-free convective with entropy analysis. The governing nonlinear problem is converted into non-dimensional partial equations via suitably adjusted transformations. Successive Under-Relaxation (SUR) technique has been incorporated to find the solutions of the non-linear problem. Variation in entropy generation and heat transfer characteristic and thermal performance criteria has been noted for various fluid parameters. The results are plotted graphically. The outcomes indicate that the thermal performance reduces more in the case of high volume fraction in comparison with low concentration. The addition of nanoparticles for several Rayleigh numbers causes the thermal performance to be declined.

Effect of line/point heat source and Hall current with induced magnetic field on free convective flow in vertical walls

In this research, the hydromagnetic natural convection of an incompressible fluid with point heat source by considering the influence of Hall current and induced magnetic field between infinite vertical walls is studied. The Laplace transform procedure is utilized to determine the analytical solutions of the acquired mathematical model with the wavelet function. With the derived solution of velocity, induced magnetic field, temperature field, and induced current density, the flow character is investigated with the influence of the physical parameters (namely Hall current, Hartmann number, and point heat source) for the presented boundary conditions. Also, the skin friction and volumetric flow rate are derived through the velocity expression. Numerical and graphical results are introduced to formalize the solution of the model. The valuable result from the investigation is that an increase in the length of the point heat source leads to enhance both components of induced current density, induced magnetic field, and primary velocity profiles. Moreover, it is noticeable that an enhancement in the Hall current has a reverse connection with both components of the induced current density, induced magnetic field, while the direct connection with the primary velocity component. There are numerous engineering applications such as the metal cutting, grinding, welding, laser hardening of metals, and many others in which the calculation of temperature field is modeled as a problem involving a point heat source.

A Study on Heat Transfer Enhancement through Various Nanofluids in a Square Cavity with Localized Heating

A two-dimensional (2D) laminar flow of nanofluids confined within a square cavity having localized heat source at the bottom wall has been investigated. The governing Navier–Stokes and energy equations have been non dimensionalized using the appropriate non dimensional variables and then numerically solved using finite volume method. The flow was controlled by a range of parameters such as Rayleigh number, length of heat source and nanoparticle volume fraction. The numerical results are represented in terms of isotherms, streamlines, velocity and temperature distribution as well as the local and average rate of heat transfer. A comparative study has been conducted for two different base fluids, ethylene glycol and water as well as for two different solids and . It is found that the ethylene glycol-based nanofluid is superior to the water-based nanofluid for heat transfer enhancement.

The influence of the length of heat sources on the external border on the temperature distribution in profiled polar-orthotropic ring plates taking into account there heat exchange with the external environment

We study the influence of N extended heat sources at external boundaries on the nonaxisymmetric temperature distribution on profiled polar-orthotropic ring plates and take into account heat exchange with the external environment. The solution of the stationary heat conduction problem for anisotropic annular plates of a random profile is resolved through the solution of the corresponding Volterra integral equation of the second kind. The formula of a temperature calculations in anisotropic annular plates of an random profile is given. The exact solution of stationary heat conductivity problem for a reverse conical polar-orthotropic ring plate is recorded. The temperature distribution in such anisotropic plate from N extended heat sources at its outer border is more complex than in the case of temperature distribution from N point heat sources at their external border.

NATURAL CONVECTION IN A MICROPOLAR NANOFLUID FILLED OPEN RECTANGULAR ENCLOSURE EMBEDDED WITH A HEATED OBJECT OF DIFFERENT GEOMETRIES

A numerical investigation has been performed to analyze heat convection through a micropolar nanofluid in an open rectangular enclosure. It embedded the inner heated object of different geometries and finite heat source length on the bottom wall with uniform heat flux. The remaining portion of the wall containing heat source and all the remaining walls are assumed as adiabatic except the top wall. Successive over-relaxation (SOR) method coupled with Gauss-Seidel iteration technique are employed in order to numerically tackled the nonlinear model momentum and energy equations. The effect of the calibrated parameters such as Rayleigh number, length of the wall heat source, the geometry of the inner block, vortex viscosity parameter, the type of nanoparticles, and the concentration of nanoparticles on the flow and thermal performance is studied. The computed results show that increasing in the Rayleigh number and the concentration of nanoparticles have a positive effect on Nusselt number whereas increasing in wall heat source length and vortex viscosity attenuates the Nusselt number. Also, the geometry of the inner block has effect in the flow pattern and the temperature distribution.

Effect of a Point/Line Heat Source on Hydromagnetic Free Convection between Vertical Walls due to Induced Magnetic Field

The hydromagnetic natural convective flow of an incompressible electrically conducting and viscous liquid amid non-conducting vertical walls with a constant point heat source/sink under the impact of the induced magnetic field has been studied. A wavelet function is used to formulate the point heat source. The considered problem is described by a group of simultaneous ODEs with significant boundary conditions, and their solutions have been acquired for the induced magnetic field, the velocity field and the temperature field by applying the Laplace technique. The skin friction, induced current density and mass flux have also been discussed. The influences of controlling parameters on the fluid flow are discussed with the tables and graphs. The valuable consequence of this investigation is that an enhancement in the length of point heat source enhances the induced magnetic field, velocity, induced current density and temperature field.

Effect of point/line heat source and Hall current on free convective flow between two vertical walls

The influence of a point heat source and Hall current on the laminar hydromagnetic free convective flow of an incompressible and electrically conducting viscous liquid between two vertical walls has been studied. A wavelet function is utilised to mathematically formulate the point or line heat source. The incidental equations on the flow have been processed subject to the Boussinesq approximation. A unified analytical solution of basic equations like thermal energy and momentum has been derived by employing Laplace transform technique. The impacts of the pertinent physical parameters, such as Hall parameter, magnetic field and point heat source, on the velocity field are explained graphically. The valuable result from the investigation is that an increase in the length of the point heat source leads to the enhancement of the velocity profiles. Moreover, it is noticeable that an enhancement of Hall current has a direct connection with the primary factor of the volumetric flow rate and skin friction.

Impact of Partial Slip and Heat Source on MHD Mixed Convection Flow of Nanofluid in a Double Lid-Driven Cavity Containing Insulated Obstacle

The current investigation analyzes the effects of partial slip and heat generation on the mixed convection flow with heat transfer in an inclined double lid-driven square cavity containing centered square adiabatic obstacle in the presence of magnetic field. The used cavity is subjected to constant heat flux and filled with Cu-water nanofluid. The top and bottom horizontal walls are thermally insulated and move with uniform velocity while the right vertical wall is maintained at a constant low temperature. A uniform heat flux is located in a part of th left wall of the cavity while the remaining part of this wall is thermally insulated. Finite volume technique is utilized to solve dimensionless governing equations of the problem. The proposed method is validated with the previous published numerical studies which distinctly offer a good agreement. The obtained results show that changing in the heat source length affects much the flow and thermal fields than the position of heat source. The averag Nusselt number decreases when the aspect ratio of the obstacle and heat source length increases. The heat transfer rate behaves nonlinearly with inclination of the cavity.

MHD Natural Convection in a Fully Opened Parallelogrammic Enclosure Filled with Copper–Water Nanofluid and Partially Heated from its Left Sidewall

The present work examined numerically for the first time, the magneto-hydrodynamics (MHD) natural convection flow and heat transfer in a fully opened parallelogrammic enclosure filled with copper –water nanofluid and subjected to a straight magnetic field. Both the upper and lower inclined walls of the enclosure are kept cold, while its right sidewall is considered fully opened to the environment. The left sidewall of the enclosure is heated partially, while the remaining parts of it are considered thermally insulated. The ranges of this study are, Hartmann number (0 £ Ha £ 75), nondimensional heat source location (0.25 £ e £ 0.75), Rayleigh number (104 £ Ra £ 106 ), solid volume fraction (f=0.04), and the inclination angle of the upper and the lower walls (-60° £ l £ 60°). The non-dimensional heat source length is considered fixed at [ = 0.25]. For all Hartmann numbers, It was found that for [Ra =106 ] , the maximum value of the average Nusselt number corresponds to [-30° ? l ? 0°] , [ l = 0°] and [0° ? l ? 30°] when the heat source location equals to [e = 0.25] , [e = 0.5] and [e = 0.75] respectively.

Energy transport of two-phase nanofluid approach inside a three-dimensional lid-driven cubic cavity containing solid cylinder and heat source

The energy transport intensification can be achieved by an addition of nanoparticles to the host liquid. Simultaneously, a location of partial heating and the velocity of moving cavity surface can be control parameters for the thermal transmission. The present research deals with a computational investigation of mixed convective energy transport within a cubical chamber saturated by nanofluids, including the impacts of cold surface motion, local heating, and central heat-conducting cylinder. The governing equations are written using the Buongiorno's nanoliquid approach with the Boussinesq approximation in primitive dimensionless variables and are solved numerically by the finite-element technique. An investigation of the nanoliquid circulation and energy transport has resulted in an extensive range of control characteristics, namely, Reynolds number, Richardson number, nanoparticle volume fraction, dimensionless radius of solid cylinder, dimensionless heat source length and the dimensionless heat source position. It has been observed that a nonlinear impact of nanoparticles volume fraction toward the energy transport strength for high Reynolds number exists. Whilst for low Reynolds number, a growth of the nano-sized particles concentration leads to the energy transference strengthening. At the same time, a rise of the inner cylinder size characterizes a diminution of the heat transport strength.

On the optimal heat source location of partially heated energy storage process using the newly developed simplified enthalpy based lattice Boltzmann method

The present study aims to fill the knowledge gap in the partially heated energy storage process by finding the optimal heat source location. A new simplified enthalpy based lattice Boltzmann method is proposed for the present work. The new model follows the predictor–corrector step, while the traditional model follows the collision-streaming step. Compared to the traditional model, this new model has the same accuracy, but it has advantages on virtual memory saving and physical boundary treatment due to its unique structure. Besides, in the partially heated energy storage process, the heat source location can pose significant impact on the charging efficiency and the energy storage rate. The optimal heat source location is where the maximum charging efficiency and energy storage rate are achieved. Results indicate that, a small region with the length of 0.1 l can be deemed as the optimal region for the heat source location, for that the charging time and the energy storage rate at various locations inside that region are almost the same. The optimal region decreases with the increase of Rayleigh and Prandtl numbers. In addition, the optimal regions for some specific heat source lengths and Rayleigh numbers are obtained. Based on these results, a map is provided to indicate the variations of the optimal region. According to this map, the optimal heat source locations for more varied conditions can be estimated through the heat source length and the Rayleigh number, which would be quite useful and significant for the thermal design in various engineering applications.

Entropy Generation and Mixed Convection Flow Inside a Wavy-Walled Enclosure Containing a Rotating Solid Cylinder and a Heat Source.

The current study investigates the 2D entropy production and the mixed convection inside a wavy-walled chamber containing a rotating cylinder and a heat source. The heat source of finite-length h is placed in the middle of the left vertical surface in which its temperature is fixed at . The temperature of the right vertical surface, however, is maintained at lower temperature . The remaining parts of the left surface and the wavy horizontal surfaces are perfectly insulated. The governing equations and the complex boundary conditions are non-dimensionalized and solved using the weighted residual finite element method, in particular, the Galerkin method. Various active parameters are considered, i.e., Rayleigh number and , number of oscillations: , angular rotational velocity: , and heat source length: . A mesh independence test is carried out and the result is validated against the benchmark solution. Results such as stream function, isotherms and entropy lines are plotted and we found that fluid flow can be controlled by manipulating the rotating velocity of the circular cylinder. For all the considered oscillation numbers, the Bejan number is the highest for the case involving a nearly stationary inner cylinder.

Impact of Partial Slip on Magneto-Ferrofluids Mixed Convection Flow in Enclosure

Abstract Magneto-ferrofluid mixed convection flow inside a lid-driven square cavity with partial slip is investigated numerically using the finite volume method. The vertical walls of the enclosure are heated partially by a constant temperature, while the horizontal moving walls are kept adiabatic. The square enclosure is filled with a mixture of kerosene–cobalt ferrofluids. The numerical computations are obtained for various parameters of the heat source length, position of the heat source, Hartmann number, Richardson number, fraction ferromagnetic particles, and constant movement parameter. It is shown that the transfer rate is clearly affected by the augmentation of the ferromagnetic particles volume fraction under the influence of a relative magnetic field and by the opposite-direction horizontal walls movement.

Impacts of Heat Flux Distribution, Sloping Magnetic Field and Magnetic Nanoparticles on the Natural Convective Flow Contained in a Square Cavity

In the present paper, the effect of the heat flux distribution on the natural convective flow inside a square cavity in the presence of a sloping magnetic field and magnetic nanoparticles is explored numerically. The nondimensional governing equations are solved in the framework of a finite element method implemented using the Galerkin approach. The role played by numerous model parameters in influencing the emerging thermal and concentration fields is examined; among them are: the location of the heat source and its lengthH*, the magnitude of the thermal Rayleigh number, the nanoparticles shape and volume fraction, and the Hartmann number. It is found that the nanofluid velocity becomes higher when the thermal source length, the nanoparticles volume fraction and/or the thermal Rayleigh number are increased, while it decreases as the Hartmann number Ha grows and the position of the heat source moves toward the center of the lower wall of the cavity. Moreover, the temperature of the nano- fluid grows with the extension of the thermal source and decreases slowly when the heat flux position moves toward the center of the lower wall. The outcomes of the research also indicate that the average Nusselt number becomes smaller on increasing Hartmann number Ha and heat source length H*. The addition of Fe3O4 to engine oil leads to a higher rate of heat transfer with respect to the addition of SiO2 particles. Blade-shaped nanoparticles generate the highest value of the Nusselt number compared to all the other considered shapes.

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

AbstractThe 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.

Free convection of power-law fluids in enclosures with partially heating from bottom and symmetrical cooling from sides

Steady-state laminar free convection of power-law fluids in a square enclosure with partial heating from below and symmetrical cooling from sides has been investigated based on numerical simulations. The partially heating is conducted by a centrally heated heat source on the bottom wall for different values of normalised heat source length l/L (ranging from 0.2 to 0.8); power-law index n (from 0.6 to 1.8); nominal Rayleigh number (Ra) (from 103 to 106) and nominal Prandtl number Pr (from 10 to 103). An increase in the power-law index n leads to weakening of thermal advection owing to the augmentation of viscous resistance. This is reflected as an increment in the mean Nusselt number Nu‾ with decreasing value of n. Additionally, Nu‾ increases with an increase in Ra and l/L for shear thinning (i.e. n<1), Newtonian (i.e. n=1) and shear thickening (i.e. n>1) fluids. The observed influences of Ra,Pr,nandl/L on Nu‾ have been explained by physical and scaling arguments and parameterized by a correlation for the mean Nusselt number.

Lattice Boltzmann Modeling of Natural Convection in a Large-Scale Cavity Heated From Below by a Centered Source

Turbulent natural convection in a large-scale cavity has taken a great attention thanks to its importance in many engineering applications such as building. In this work, the lattice Boltzmann method (LBM) is used to simulate turbulent natural convection heat transfer in a small room of housing heated from below by means of a heated floor. The ceiling and the four vertical walls of the room are adiabatic except for a portion of one vertical wall. This portion simulates a glass door with a cold temperature θc = 0. The cavity is filled by air (Pr = 0.71) and heated from below with uniformly imposed temperature θh = 1. The effects of the heat source length (Lr) and Rayleigh number (Ra) on the flow structure and heat transfer are studied for ranges of 0.2 ≤ Lr ≤ 0.8 and 5 × 106 ≤Ra ≤ 108. The heat transfer is examined in terms of local and mean Nusselt numbers. The results show that an increase in Rayleigh number or in heat source length increases the temperature in the core of the cavity. The flow structure shows that turbulent natural convection regime is fully developed for Ra = 108. Correlations for mean Nusselt number as a function with Ra for different values of Lr are expressly derived.

Natural convection flow of a hybrid nanofluid in a square enclosure partially filled with a porous medium using a thermal non-equilibrium model

Buoyancy-driven flow inside a superposed enclosure filled with composite porous-hybrid nanofluid layers was investigated numerically using a local thermal nonequilibrium model for the heat transfer between the fluid and the solid phases. The bottom wall of the enclosure was partly heated to provide a heat flux, while the other parts of the wall were thermally insulated. The top and vertical walls of the enclosure were maintained at constant cold temperatures. The Darcy-Brinkman model was adopted to model the flow inside the porous layer. The Galerkin finite element method was used to solve the governing equations using the semi-implicit method for pressure linked equations algorithm. The selected parameters are presented for the Rayleigh number (Ra), 103 ≤ Ra ≤ 107, the Darcy number (Da), 10−7 ≤ Da ≤ 1, the porous layer thickness (S), 0 ≤ S ≤ 1, the modified conductivity ratio (γ), 10−1 ≤ γ ≤ 104, the interphase heat transfer coefficient (H), 10−1 ≤ H ≤ 1000, the heat source length (B), 0.2, 0.4, 0.6, 0.8 and 1, and the nanoparticle volume fraction (ϕ), 0 ≤ ϕ ≤ 0.2. It has been concluded that the rate of heat transfer of hybrid nanofluid (Cu−Al2O3/water) is higher than with the pure fluid. Furthermore, at Ra ≤ 105, the heat transfer rate maintains its maximum value when S reaches the critical value (S = 0.3). The values of S, Da, and B were found to have a significant effect on the heat removal from the heat source. Increasing the values of γ and H can strongly enhance the heat transfer rate and satisfy the thermal equilibrium case.

SIMULATION OF THERMAL DECOMPOSITION IN AN OPEN CAVITY: ENTROPY ANALYSIS

ABSTRACT This paper presents a numerical analysis of entropy generation in a two-dimensional rectangular channel where the inlet flow undergoes thermal decomposition resulting from a chemical reaction. The model considered viscosity and thermal conductivity to be dependent of temperature. Irreversibility due to mass transport was included in the entropy generation analysis. Relevant applications of this study are possible for the design of power generation systems and reactors. The effects of the Reynolds number, Schmidt number, and length of the heat source on thermal fluid dynamics, mass transfer, and irreversibility were also investigated. It was found that thermal decomposition increases at: a) low Reynolds numbers, b) low Schmidt numbers, and c) increased length of heat source. Additionally, overall entropy generation increased when Reynolds number and length of heat source were increased, although in all cases, overall irreversibility attains a minimum value at a specific Schmidt number.