Abstract: Unsteady effects of MHD free convection flow past in an infinite vertical plate with heat source in presence of radiation with reference to all critical parameters that appear in field equations are studied in this paper. The governing equations are developed by usual Boussinesq’s approximation. The problem is solved by using perturbation technique. The results are obtained for velocity, temperature, Nusselt number and skin-friction. The effects of magnetic parameter, prandtl number, Grashof number, permeability parameter, heat source/sink parameter and radiation parameter are discussed on flow characteristics and shown by means of graphs and tables.
Abstract: In this paper, a non-similraity analysis has been
presented to exhibit the two-dimensional boundary layer flow
of magnetohydrodynamic (MHD) natural convection of tangent
hyperbolic nanofluid nearby a vertical permeable cone in the presence
of variable wall temperature impact. The mutated boundary layer
nonlinear governing equations are solved numerically by the an
efficient implicit finite difference procedure. For both nanofluid
effective viscosity and nanofluid thermal conductivity, a number of
experimental relations have been recognized. For characterizing the
nanofluid, the compatible nanoparticle volume fraction model has
been used. Nusselt number and skin friction coefficient are calculated
for some values of Weissenberg number W, surface temperature
exponent n, magnetic field parameter Mg, power law index m and
Prandtl number Pr as functions of suction parameter. The rate of heat
transfer from a vertical permeable cone in a regular fluid is less than
that in nanofluids. A best convection has been presented by Copper
nanoparticle among all the used nanoparticles.
Abstract: This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number Pr, magnetic field parameter M, Peclet number Pe, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.
Abstract: In this study, we investigated numerically heat
transfer by mixed convection coupled to radiation in a square cavity;
the upper horizontal wall is movable. The purpose of this study is to
see the influence of the emissivity ε and the varying of the
Richardson number Ri on the variation of average Nusselt number
Nu. The vertical walls of the cavity are differentially heated, the left
wall is maintained at a uniform temperature higher than the right
wall, and the two horizontal walls are adiabatic. The finite volume
method is used for solving the dimensionless Governing Equations.
Emissivity values used in this study are ranged between 0 and 1, the
Richardson number in the range 0.1 to 10. The Rayleigh number is
fixed to Ra=104 and the Prandtl number is maintained constant
Pr=0.71. Streamlines, isothermal lines and the average Nusselt
number are presented according to the surface emissivity. The results
of this study show that the Richardson number Ri and emissivity ε
affect the average Nusselt number.
Abstract: The present study focused on the investigation of the
effects of roughness elements on heat transfer during natural
convection in a rectangular cavity using numerical technique.
Roughness elements were introduced on the bottom hot wall with a
normalized amplitude (A*/H) of 0.1. Thermal and hydrodynamic
behaviors were studied using computational method based on Lattice
Boltzmann method (LBM). Numerical studies were performed for a
laminar flow in the range of Rayleigh number (Ra) from 103 to 106
for a rectangular cavity of aspect ratio (L/H) 2.0 with a fluid of
Prandtl number (Pr) 1.0. The presence of the sinusoidal roughness
elements caused a minimum to maximum decrease in the heat
transfer as 7% to 17% respectively compared to smooth enclosure.
The results are presented for mean Nusselt number (Nu), isotherms
and streamlines.
Abstract: This paper presents a computational study of steady
state three dimensional very high turbulent flow and heat transfer
characteristics in a constant temperature-surfaced circular duct fitted
with 900 hemispherical inline baffles. The computations are based on
realizable k-ɛ model with standard wall function considering the
finite volume method, and the SIMPLE algorithm has been
implemented. Computational Study are carried out for Reynolds
number, Re ranging from 80000 to 120000, Prandtl Number, Pr of
0.73, Pitch Ratios, PR of 1,2,3,4,5 based on the hydraulic diameter of
the channel, hydrodynamic entry length, thermal entry length and the
test section. Ansys Fluent 15.0 software has been used to solve the
flow field. Study reveals that circular pipe having baffles has a higher
Nusselt number and friction factor compared to the smooth circular
pipe without baffles. Maximum Nusselt number and friction factor
are obtained for the PR=5 and PR=1 respectively. Nusselt number
increases while pitch ratio increases in the range of study; however,
friction factor also decreases up to PR 3 and after which it becomes
almost constant up to PR 5. Thermal enhancement factor increases
with increasing pitch ratio but with slightly decreasing Reynolds
number in the range of study and becomes almost constant at higher
Reynolds number. The computational results reveal that optimum
thermal enhancement factor of 900 inline hemispherical baffle is
about 1.23 for pitch ratio 5 at Reynolds number 120000.It also shows
that the optimum pitch ratio for which the baffles can be installed in
such very high turbulent flows should be 5. Results show that pitch
ratio and Reynolds number play an important role on both fluid flow
and heat transfer characteristics.
Abstract: In this paper, the problem of steady laminar boundary
layer flow and heat transfer over a permeable exponentially
stretching/shrinking sheet with generalized slip velocity is
considered. The similarity transformations are used to transform the
governing nonlinear partial differential equations to a system of
nonlinear ordinary differential equations. The transformed equations
are then solved numerically using the bvp4c function in MATLAB.
Dual solutions are found for a certain range of the suction and
stretching/shrinking parameters. The effects of the suction parameter,
stretching/shrinking parameter, velocity slip parameter, critical shear
rate and Prandtl number on the skin friction and heat transfer
coefficients as well as the velocity and temperature profiles are
presented and discussed.
Abstract: Numerical studies were conducted using Lattice
Boltzmann Method (LBM) to study the natural convection in a square
cavity in the presence of roughness. An algorithm based on a single
relaxation time Bhatnagar-Gross-Krook (BGK) model of Lattice
Boltzmann Method (LBM) was developed. Roughness was
introduced on both the hot and cold walls in the form of sinusoidal
roughness elements. The study was conducted for a Newtonian fluid
of Prandtl number (Pr) 1.0. The range of Ra number was explored
from 10^3 to 10^6 in a laminar region. Thermal and hydrodynamic
behavior of fluid was analyzed using a differentially heated square
cavity with roughness elements present on both the hot and cold wall.
Neumann boundary conditions were introduced on horizontal walls
with vertical walls as isothermal. The roughness elements were at the
same boundary condition as corresponding walls. Computational
algorithm was validated against previous benchmark studies
performed with different numerical methods, and a good agreement
was found to exist. Results indicate that the maximum reduction in
the average heat transfer was 16.66 percent at Ra number 10^5.
Abstract: An analysis is carried out to investigate the effect of
magnetic field and heat source on the steady boundary layer flow and
heat transfer of a Casson nanofluid over a vertical cylinder stretching
exponentially along its radial direction. Using a similarity
transformation, the governing mathematical equations, with the
boundary conditions are reduced to a system of coupled, non –linear
ordinary differential equations. The resulting system is solved
numerically by the fourth order Runge – Kutta scheme with shooting
technique. The influence of various physical parameters such as
Reynolds number, Prandtl number, magnetic field, Brownian motion
parameter, thermophoresis parameter, Lewis number and the natural
convection parameter are presented graphically and discussed for non
– dimensional velocity, temperature and nanoparticle volume
fraction. Numerical data for the skin – friction coefficient, local
Nusselt number and the local Sherwood number have been tabulated
for various parametric conditions. It is found that the local Nusselt
number is a decreasing function of Brownian motion parameter Nb
and the thermophoresis parameter Nt.
Abstract: The objectives of this paper are to investigate effects of dimensionless numbers on thermal performance of the vertical closed-loop pulsating heat pipe (VCLPHP) and to establish a correlation to predict the thermal performance of the VCLPHP. The CLPHPs were made of long copper capillary tubes with inner diameters of 1.50, 1.78, and 2.16mm and bent into 26 turns. Then, both ends were connected together to form a loop. The evaporator, adiabatic, and condenser sections length were equal to 50 and 150 mm. R123, R141b, acetone, ethanol, and water were chosen as variable working fluids with constant filling ratio of 50% by total volume. Inlet temperature of heating medium and adiabatic section temperature was constantly controlled at 80 and 50oC, respectively. Thermal performance was represented in a term of Kutateladze number (Ku). It can be concluded that when Prandtl number of liquid working fluid (Prl), and Karman number (Ka) increases, thermal performance increases. On contrary, when Bond number (Bo), Jacob number (Ja), and Aspect ratio (Le/Di) increases, thermal performance decreases. Moreover, the correlation to predict more precise thermal performance has been successfully established by analyzing on all dimensionless numbers that have effect on the thermal performance of the VCLPHP.
Abstract: The present analysis considers the steady stagnation point flow and heat transfer towards a permeable shrinking sheet in an upper-convected Maxwell (UCM) electrically conducting fluid, with a constant magnetic field applied in the transverse direction to flow and a local heat generation within the boundary layer, with a heat generation rate proportional to (T-T)p Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations, which is then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results are obtained for the flow and thermal fields for various values of the stretching/shrinking parameter λ, the magnetic parameter M, the elastic parameter K, the Prandtl number Pr, the suction parameter s, the heat generation parameter Q, and the exponent p. The results indicate the existence of dual solutions for the shrinking sheet up to a critical value λc whose value depends on the value of M, K, and s. In the presence of internal heat absorption (Q
Abstract: In this paper, the problem of unsteady stagnation-point flow and heat transfer induced by a shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by the shooting method. The influence of radiation, unsteadiness and shrinking parameters, and the Prandtl number on the reduced skin friction coefficient and the heat transfer coefficient, as well as the velocity and temperature profiles are presented and discussed in detail. It is found that dual solutions exist and the temperature distribution becomes less significant with radiation parameter.
Abstract: This paper is concerned with the effect of Hartmann number on the free convective flow in a square cavity with different positions of heated square block. The two-dimensional Physical and mathematical model have been developed, and mathematical model includes the system of governing mass, momentum and energy equations are solved by the finite element method. The calculations have been computed for Prandtl number Pr = 0.71, the Rayleigh number Ra = 1000 and the different values of Hartmann number. The results are illustrated with the streamlines, isotherms, velocity and temperature fields as well as local Nusselt number.
Abstract: An empirical correlation for predicting the heat transfer coefficient for a cylinder under free convection, inclined at any arbitrary angle with the horizontal has been developed in terms of Nusselt number, Prandtl number and Grashof number. Available experimental data was used to determine the parameters for the proposed correlation. The proposed correlation predicts the available data well within ±10%, for Prandtl number in the range 0.68-0.72 and Grashof number in the range 1.4×104–1.2×1010.
Abstract: Magnetohydrodynamic free convection fluid flow and heat transfer in a square cavity filled with an electric conductive fluid with Prandtl number of 0.7 has been investigated numerically. The horizontal bottom wall of the cavity was kept at Th while the side and the top walls of the cavity were maintained at a constant temperature Tc with Th>Tc. The governing equations written in terms of the primitive variables were solved numerically using the finite volume method while the SIMPLER algorithm was used to couple the velocity and pressure fields. Using the developed code, a parametric study was performed, and the effects of the Rayleigh number and the Hartman number on the fluid flow and heat transfer inside the cavity were investigated. The obtained results showed that temperature distribution and flow pattern inside the cavity depended on both strength of the magnetic field and Rayleigh number. For all cases two counter rotating eddies were formed inside the cavity. The magnetic field decreased the intensity of free convection and flow velocity. Also it was found that for higher Rayleigh numbers a relatively stronger magnetic field was needed to decrease the heat transfer through free convection.
Abstract: An unsteady mixed free convection MHD flow of elastic-viscous incompressible fluid past an infinite vertical porous flat plate is investigated when the presence of heat Source/sink, temperature and concentration are assumed to be oscillating with time and hall effect. The governing equations are solved by complex variable technique. The expressions for the velocity field, temperature field and species concentration are demonstrated in graphs. The effects of the Prandtl number, the Grashof number, modified Grashof number, the Schimidt number, the Hall parameter, Elastic parameter & Magnetic parameter are discussed.
Abstract: Non-isothermal stagnation-point flow with consideration of thermal radiation is studied numerically. A set of partial differential equations that governing the fluid flow and energy is converted into a set of ordinary differential equations which is solved by Runge-Kutta method with shooting algorithm. Dimensionless wall temperature gradient and temperature boundary layer thickness for different combinaton of values of Prandtl number Pr and radiation parameter NR are presented graphically. Analyses of results show that the presence of thermal radiation in the stagnation-point flow is to increase the temperature boundary layer thickness and decrease the dimensionless wall temperature gradient.
Abstract: Mixed convection in two-dimensional shallow rectangular enclosure is considered. The top hot wall moves with constant velocity while the cold bottom wall has no motion. Simulations are performed for Richardson number ranging from Ri = 0.001 to 100 and for Reynolds number keeping fixed at Re = 408.21. Under these conditions cavity encompasses three regimes: dominating forced, mixed and free convection flow. The Prandtl number is set to 6 and the effects of cavity inclination on the flow and heat transfer are studied for different Richardson number. With increasing the inclination angle, interesting behavior of the flow and thermal fields are observed. The streamlines and isotherm plots and the variation of the Nusselt numbers on the hot wall are presented. The average Nusselt number is found to increase with cavity inclination for Ri ³ 1 . Also it is shown that the average Nusselt number changes mildly with the cavity inclination in the dominant forced convection regime but it increases considerably in the regime with dominant natural convection.
Abstract: Combined conduction-free convection heat transfer in
vertical eccentric annuli is numerically investigated using a finitedifference
technique. Numerical results, representing the heat transfer
parameters such as annulus walls temperature, heat flux, and heat
absorbed in the developing region of the annulus, are presented for a
Newtonian fluid of Prandtl number 0.7, fluid-annulus radius ratio 0.5,
solid-fluid thermal conductivity ratio 10, inner and outer wall
dimensionless thicknesses 0.1 and 0.2, respectively, and
dimensionless eccentricities 0.1, 0.3, 0.5, and 0.7. The annulus walls
are subjected to thermal boundary conditions, which are obtained by
heating one wall isothermally whereas keeping the other wall at inlet
fluid temperature. In the present paper, the annulus heights required
to achieve thermal full development for prescribed eccentricities are
obtained. Furthermore, the variation in the height of thermal full
development as function of the geometrical parameter, i.e.,
eccentricity is also investigated.
Abstract: We investigate properties of convective solutions of the
Boussinesq thermal convection in a moderately rotating spherical
shell allowing the inner and outer sphere rotation due to the viscous
torque of the fluid. The ratio of the inner and outer radii of the
spheres, the Prandtl number and the Taylor number are fixed to 0.4,
1 and 5002, respectively. The inertial moments of the inner and outer
spheres are fixed to about 0.22 and 100, respectively. The Rayleigh
number is varied from 2.6 × 104 to 3.4 × 104. In this parameter
range, convective solutions transit from equatorially symmetric quasiperiodic
ones to equatorially asymmetric chaotic ones as the Rayleigh
number is increased. The transition route in the system allowing
rotation of both the spheres is different from that in the co-rotating
system, which means the inner and outer spheres rotate with the
same constant angular velocity: the convective solutions transit as
equatorially symmetric quasi-periodic solution → equatorially symmetric
chaotic solution → equatorially asymmetric chaotic solution
in the system allowing both the spheres rotation, while equatorially
symmetric quasi-periodic solution → equatorially asymmetric quasiperiodic
solution → equatorially asymmetric chaotic solution in the
co-rotating system.