Analytical Solution of Thermocapillary Flow in Cylindrical Annuli with Curved Free Surface

In this paper we consider thermocapillary flow with interface deformation in cylindrical annuli subjected to lateral temperature gradient.Based on the assumption that Reynolds,Marangoni and capillary numbers are very small,we expanded the governing equations in terms of a small parameter,and the zeroth-order one is the Stokes problem,which can be analytically solved by use of separation of variables formulation.Solutions are obtained for the zeroth-order fluid and thermal fields as well as the first-order interfacial shapes.Streamlines,temperature distributions and interface shapes are presented and the influence of aspect ratios is investigated.     

Free Convective Heat Transfer Structures as a Function of the Width of Isothermal Horizontal Rectangular Plates

Abstract

Results are presented for the experimental investigations of free convection heat transfer from upward facing isothermal horizontal rectangular plates as a function of the plate width. Two models of the convective fluid flow structures above horizontal rectangular plates were proposed as a result of flow visualization. Solutions of these models are presented in the form of Nusselt-Rayleigh relations with the aspect ratio as a parameter. Analysis of the visualization results provided a basis for preferring the radial flow pattern at small values of the Rayleigh number, especially for square plates or at the ends of rectangular plates, and a basis for preferring the parallel flow model at large values of the Rayleigh number. From the previous experimental results and the present experimental and interferometric studies, it is shown that the transition Rayleigh number at which the flow changes from the concentric to the parallel flow pattern is a function of the width of the plate.     

Model for MHD viscoelastic nanofluid flow with prominence effects of radiation

Present phenomenon is dedicated to analyze the problem of steady state flow of an incompressible fluid model pertained to as magnetohydrodynamics viscoelastic nanofluid through a permeable plate. Continuity, momentum, energy, and concentration expressions are elaborated to comprehend nature of the fluid flow. Numerical solutions are presented. The arising mathematical problem is governed by interesting parameters which include viscoelastic parameter, magnetic field parameter, nanofluid parameter, radiation parameter, skin friction, Prandtle number, and Sherwood number. Solutions for the dimensionless velocity, temperature, and concentration fields and the corresponding skin friction, Nusselt number, and Sherwood number are determined and canvassed with the help of graphs for the distinct values of pertinent parameters.     

Heat transfer on peristaltically induced Walter's B fluid flow

This paper look at the effects of heat transfer on peristaltic flow of Walter's B fluid in an asymmetric channel. The regular perturbation method is used to solve the governing equations by taking the wave number as the small parameter. Expressions for stream function, temperature distribution, and heat transfer coefficient are presented in explicit form. Solutions are analyzed graphically for different values of arising parameters. It has been found that these parameters affect considerably the considered flow characteristics. Results show that with an increase in the Eckert and Prandtl numbers, the temperature and heat transfer coefficient increase. Further, the absolute value of the heat transfer coefficient increases with an increasing viscoelastic parameter. Comparison with published results for viscous fluid is also presented. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21021     

Mixed convection flow from a vertical flat plate with temperature dependent viscosity

A two-dimensional mixed convection flow of a viscous incompressible fluid of temperature dependent viscosity past a vertical impermeable fluid is considered. The governing equations for the flow are transformed for the regions appropriate to the forced convection, free convection and forced-free convection regimes. Solutions of the reduced equation appropriate in the forced convection and free convection regime are obtained using the perturbation technique treating ξ, the buoyancy parameter, as the perturbation parameter and those for the forced-free convection regime are obtained by the implicit finite difference method. Numerical results thus obtained are presented in terms of the local shear stress and local surface heat-flux. Effect of the viscosity variation parameter, ε, on the surface shear stress and the surface heat-flux for the fluid appropriate for Prandtl number ranging from 0.02 to 100 is shown. The perturbation solutions obtained for small and large values of ξ are found in excellent agreement with the finite difference solutions for the entire ξ regime.     

DRBEM Solution of the Natural Convective Flow of Micropolar Fluids

The main purpose of this article is to present the use of the dual reciprocity boundary element method (DRBEM) in the analysis of the unsteady natural convective flow of micropolar fluids in a differentially heated rectangular cavity. The finite-difference method (FDM) is used for time discretization. All the convective terms and vorticity boundary condition are evaluated in terms of DRBEM coordinate matrix. Solutions are obtained for several values of microstructure parameter (k), Rayleigh number (Ra), and aspect ratio (A). Prandtl number values are taken as 0.71 and 7.0. The heat transfer rate (average Nusselt number) of micropolar fluids is found to be smaller than that of Newtonian fluid. Numerical results at steady-state are given in terms of streamlines, isotherms, vorticity contours, and velocity profiles, as well as a table containing Nusselt number values for several Ra and k.     

Comparative analysis of a Sisko nanofluid over a stretching cylinder through a porous medium

The present article examines the Sisko nanofluid flow and heat transfer through a porous medium due to a stretching cylinder using Buongiorno's model for nanofluids. Suitable similarity transformations are used to transform the governing boundary layer equations of fluid flow into nonlinear ordinary differential equations. The finite difference method is used to solve coupled nonlinear differential equations with MATLAB software. The impact of different parameters viz., the Sisko material parameter, porosity parameter, curvature parameter, thermophoresis parameter, and Brownian diffusion parameter on the velocity and temperature distribution are presented graphically. Moreover, the effect of the involved parameters on the heat transfer rate is also studied and presented through table values. It is noticed from the numerical values that the porosity parameter reduces the velocity while enhancing the temperature. The curvature parameter enhances the velocity throughout the fluid regime and reduces the temperature near the surface while enhancing the temperature far away from the surface. The study reveals that the thermophoresis and Brownian diffusion parameters that characterize the nanofluid flow reduce the wall heat transfer rate, while the curvature parameter enhances it. This investigation of wall heating/cooling has essential applications in solar porous water absorber systems, chemical engineering, metallurgy, material processing, and so forth.     

Free Convective Flow of Electrically Conducting and Viscous Immiscible Fluid Flow in a Vertical Channel in the Presence of First‐Order Chemical Reaction

In this paper, the effects of chemical reaction on free convective flow of electrically conducting and viscous incompressible immiscible fluids are analyzed. The coupled nonlinear equations governing the heat and mass transfer are solved analytically and numerically with appropriate boundary conditions for each fluid and the solutions have been matched at the interface. The analytical solutions are solved by using regular perturbation method valid for small values of perturbation parameter and numerically by using finite difference method. The numerical results for various values of thermal Grashof number, mass Grashof number, Hartman number, viscosity ratio, width ratio, conductivity ratio, and chemical reaction parameter have been presented graphically in the presence and in the absence of electric field load parameter. In addition, the closed form expression for volumetric flow rate, Nusselt number, species concentration, and total heat rate added to the flow is also analyzed. The solutions obtained by finite difference method and perturbation method agree very well to the order of 10^?4 for small values of perturbation parameter.     

Features of the exponential form of internal heat generation,Cattaneo–Christov heat theory on water-based graphene–CNT–titanium ternary hybrid nanofluid flow

To increase energy efficiency, the flow of fluids containing nanoparticles is crucial in industrial applications notably in nuclear reactors and nuclear system cooling. In light of this, this study examines the flow of a water-based ternary hybrid nanofluid (graphene, single-walled carbon nanotubes, and titanium dioxide) across a curved stretching sheet with suction. The non-Fourier heat flux model is also considered in the modeling. The existing partial differential equations are converted into ordinary differential equations through the use of similarity variables. These ordinary differential equations are then numerically solved using the Runge–Kutta–Fehlberg fourth- and fifth-order method along with a shooting approach. The collection of graphical findings for the key variables on the temperature and velocity profiles is investigated. Results reveal that the heat transport in ternary hybrid nanoliquid rises as the heat source/sink parameter rises. The Biot number influences the thermal profile positively, whereas the increasing curvature parameter values reduce heat transport. The curvature parameter has a positive impact on skin friction but the suction parameter has a negative impact on skin friction.     

Importance of activation energy in development of chemical covalent bonding in flow of Sisko magneto-nanofluids over a porous moving curved surface

In this research work, significance of activation energy in establishment of a chemical covalent bonding during the flow Sisko fluid over a porous curved moving surface is investigated. The Buongiorno nanofluid model is further considered to incorporate the importance of Brownian motion and thermophoretic analysis of nanoparticles. Additionally, magnetic field and heat source/sink effects are also discussed in the flow and heat transfer phenomena. Appropriate transformations are used to convert nonlinear PDEs to ODEs. Impacts of all physical parameters are illustrated in the form of graphs and tables. The resistance opposed to the flow and rate of heat transfer are measured with the help of local skin friction and Nusselt number relations, respectively. Fabulous outcomes obtained and are further compared with existing literature and found correctly. Continuing the process of validation of present results, an important different technique namely Richardson's extrapolation in Maple software is used to test the accuracy of the entire numerical scheme which is followed for the present investigation. The results are well correlated with each other. For the higher values of curvature parameter, the velocity of pseudo plastic fluid enhances while the temperature profile noticed with opposite trend. Growing values of suction parameter enhance the resistive forces and reducing the velocity of the Sisko fluid flow. However, the heat source/sink parameter escalates the rate of heat transfer and temperature profile for pseudo plastic fluid. Moreover, the concentration profile of pseudo plastic fluid is found an increasing function of activation energy parameter.     

The interaction of flame curvature and stretch,part 2: The convex premixed flame

Premixed flames with radii of curvature of the order of the preheat zone thickness are studied with activation energy asymptotics. The flames studied are convex to the fresh mixture and the flame stretch is negative as in Bunsen burner flame tips. Solutions are found which correspond to flame speeds well in excess of the adiabatic flame speed.     

Mixed convection of a permeable fluid in a vertical channel with boundary conditions of a third kind

Numerical investigation of a steady mixed convective flow through a fluid‐saturated porous media in a vertical channel with boundary conditions of the third kind including the effects of viscous dissipation and Darcy dissipation has been studied. The plates exchange heat with an external fluid. Both conditions of equal and of different reference temperatures of the external fluid are considered. First, the simpler cases of either negligible Brinkman number or negligible Grashof number are addressed with the help of analytical solutions. The combined effects of buoyancy forces and viscous dissipation are analyzed by a perturbation series method valid for small values of perturbation parameter. To relax the conditions on the perturbation parameter, the governing equations are also evaluated numerically by a shooting technique that uses the classical explicit Runge–Kutta method of four slopes as an integration scheme and the Newton–Raphson method as a correction scheme. The problem is analyzed for different values of mixed convection parameters, porous parameter for equal and unequal Biot numbers, keeping the wall temperatures symmetric or asymmetric. The graphical results illustrating the effects of various parameters on the flow as well as average velocity and Nusselt numbers are presented. Further the analytical and numerical solutions agree very well for small values of the perturbation parameter. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21019     

Solutions to harmonic and biharmonic problems with discontinuous boundary conditions by collocation methods using multiquadrics as basis functions

Behaviors of the global and local collocation methods that use multiquadrics as basis functions in solving problems having continuous boundary conditions are well known. In this paper, harmonic and biharmonic problems having discontinuous boundary conditions are solved by these methods. Solutions to two test problems are investigated. The first test problem is a heat conduction problem with discontinuous temperature at the boundary. The second test problem is the Stokes flow problem in a lid-driven square cavity. Results show that performances the global and local collocation methods depend on the shape parameter of multiquadrics, and solutions by the global collocation method are more sensitive to the shape parameter than the local collocation method.     

Conjugate natural convection about a vertical cylindrical fin with lateral mass flux in a saturated porous medium

The problem of conjugate natural convection about a vertical cylindrical fin with uniform lateral mass flux in a fluid-saturated porous medium has been studied numerically. Solutions based on the third level of truncation are obtained by the local nonsimilarity method. The effects of the surface mass flux, the conjugate convection-conduction parameter, and the surface curvature on fin temperature distribution, local heat transfer coefficient, local heat flux, average heat transfer coefficient, and total heat transfer rate are presented. A comparison with finite-difference solutions for the case of constant wall temperature was made, and found in a good agreement.     

Natural-Convection Heat Transfer in Channels With Isoflux Convex Surfaces

Numerical solutions are presented for laminar natural convection heat transfer in channels with convex surfaces that are subjected to a uniform heat flux. Simulations are conducted for several values of Grashof number (10 to 10⁴) and radius of curvature (1 to ∞). The governing elliptic conservation equations are solved in a boundary-fitted coordinate system using a collocated control-volume-based numerical procedure. The results are presented in terms of streamline and isotherm plots, inlet mass flow rates, curved wall temperature profiles, maximum hot wall temperature estimates, and average Nusselt number values. At the lowest radius of curvature, computations reveal the formation of recirculation zones in the exit section for all values of Grashof number considered. For a radius of curvature equal to or greater than 2, recirculation does not occur at any Grashof number. For values of radius of curvature between 1 and 2, the value of Grashof number at which recirculation occurs decreases with increasing values of the former. The variation in the buoyancy-induced volume flow rate is highly nonlinear with respect to the radius of curvature, and the value of the radius of curvature at which the volume flow rate is maximum increases with increasing Grashof number. The value of radius of curvature at which the maximum hot wall temperature is minimized increases with Grashof number. For all configurations studied, the average Nusselt number increases with increasing Grashof number values. Correlations for maximum wall temperature and average Nusselt number are provided.     

Thermal diffusion effect on unsteady MHD free convective flow past an impulsively started but temporarily accelerated semi-infinite vertical plate with parabolic ramped conditions

The purpose of the present study is to analyze the problem of a free convective MHD flow of incompressible, electrically conducting, and viscous fluid past an impulsively started semi-infinite moving vertical plate. The fluid is considered to be non-gray and optically thick. The parabolic ramped temperature of the plate and thermodiffusion effect are also taken into account. A magnetic field having uniform strength is applied in the transverse direction to the fluid velocity. Solutions of dimensionless governing partial differential equations are attained on the adoption of the closed-form Laplace transformation technique. Effects of different flow parameters on the velocity field, temperature field, concentration field, Nusselt number, skin friction, and Sherwood Number are discussed graphically. It is noticed that fluid concentration, temperature, and velocity decline considerably for ascending values of Prandtl Number. Increasing Ramped parameter hikes the Nusselt number and Sherwood Number but declines skin friction.     

Vibration effects on weak turbulent natural convection in a porous layer heated from below

The objective of the current theoretical analysis is to observe the effect the vibrations have on heat convection over a wide range of parameter values. Analysing the different regimes and their corresponding dynamics leads to the evaluation of the Nusselt number that provides an answer to how the heat transfer is affected by the vibrations.Solutions for the amplitudes of stream function and temperature, as a function of time presented in this paper are evaluated via Fortran programming, by using the subroutine DVERK by Hull et al. [12] and applying a fifth- and a sixth-order Runge–Kutta–Verner numerical method of solution. The results are presented in graphs showing the amplitudes as a function of time as well as on phase diagrams with the aim of identifying the different parameter regimes and possibly identifying the regimes that enhance the heat transfer. In order to establish the stability type of the results and the type of attracting trajectory, the results were used to evaluate their corresponding Lyapunov exponents.     

Parametric study of turbulent slot-jet impingement heat transfer from concave cylindrical surfaces

Numerical investigation of convective heat transfer process from concave cylindrical surfaces due to turbulent slot-jet impingement is performed. Constant heat flux condition is specified at the concave surfaces. The flow and thermal fields in the vicinity of the surfaces are computed using the RNG k–? turbulence model with a two-layer near wall treatment. Parametric studies are carried out for various jet-exit Reynolds numbers, surface curvature, and nozzle-to-surface spacing. Results presented include streamlines, isotherms, velocity and temperature profiles in the wall-jet region, and the local Nusselt number distribution on the impingement concave wall for various parameter values in the study. The results indicate that while the jet-exit Reynolds number and the surface curvature have a significant effect on the heat transfer process, it is relatively insensitive to the jet-to-target spacing. A correlation for the average Nusselt number at the concave surface as a function of the parameters considered in the study is also derived.     

Heat transfer for Marangoni‐driven boundary layer flow

Marangoni convection induced by variation of the surface tension with temperature along a surface influences crystal growth melts and other processes with liquid–vapor interfaces, such as boiling in both microgravity and normal gravity in some cases. This paper presents the Nusselt number for Marangoni flow over a flat surface calculated using a similarity solution for both the momentum equations and the energy equation assuming developing boundary layer flow along a surface. Solutions are presented for the surface velocity, the total flow rate, and the Nusselt number for various temperature profiles, Marangoni numbers, and Prandtl numbers. For large bubbles, the predicted boundary layer thickness would be less than the bubble diameter, so the curvature effects could be neglected and this analysis could be used as a first estimate of the effect of Marangoni flow around a vapor bubble. © 2002 Scripta Technica, Heat Trans Asian Res, 31(2): 105–116, 2002; DOI 10.1002/htj.10019     

Forced convection in a helical pipe filled with a saturated porous medium

An analysis is made of laminar forced convection in a helical pipe of circular cross-section and filled by a porous medium saturated with a fluid, for the case when the curvature and torsion of the pipe are both small. The Darcy model is employed, and boundaries with either uniform flux or uniform temperature are considered. It is found that curvature induces a secondary flow at first order in the parameter ε = κa, where κ is the curvature and a is the radius of the pipe. On the other hand, the Nusselt number is unchanged to first order in ε but is increased at second order, for either set of thermal boundary conditions. The effect of torsion on the velocity appears at second order, but torsion does not affect the Nusselt number at second order.