Solutions For Free Convection Flow Research Articles

Approximate closed‐form solution of free convection flow past a vertical cone

AbstractThis paper presents a technique to find the closed‐form solution of the boundary‐value problem representing free convection flow past a vertical cone. Partial differential equations that govern the flow are converted into nonlinear ordinary differential equations with the aid of similarity transformations. First, a numerical solution is obtained with the help of the bvp4c package of MATLAB, and then utilizing the numerical solution, the closed‐form solution is obtained. The accuracy of the closed‐form solution is analyzed by the residual technique. Graphs of the residuals of the governing equations indicate that our approximate closed‐form solution closely matches the exact solution.

Mathematical Solutions of Free Convection Flow of Casson Fluid in Channel with Accelerated Plate

Mathematical Solutions of Free Convection Flow of Casson Fluid in Channel with Accelerated Plate

Analytical solutions for free convection flow of Casson nanofluid over an infinite vertical plate

<abstract> <p>This research article is design to elaborate the rule and significance of fractional derivative for heat transport in drilling of nanofluid. The respective nanofluid formed by the suspension of clay nanoparticles in the base fluids namely Casson fluid. The physical flow phenomenon is demonstrated with the help of partial differential equations by utilizing the respective thermophysical properties of nanoparticles. Also the geometric and thermal conditions are imposed in flow domain. In the governing equations, the partial derivative with respect to time replaced by new hybrid fractional derivative and then solved analytically for temperature and velocity field with the help of Laplace transformed. The obtained solutions for temperature and velocity are presented geometrically by Mathcad software to see the effectiveness of potent parameters. The temperature and velocity present a significant increasing trend for increasing volume fraction parameter. The obtained results for temperature as well as velocity are also compared with the existing literature and it is concluded that field variables with new hybrid fractional derivative, show more decaying trend as compare to the results with Caputo and Caputo-Fabrizio fractional derivatives.</p> </abstract>

Numerical solutions of free convection flow of nanofluids along a radiating sinusoidal wavy surface

In this article, our interest is to investigate the free convection boundary-layer flow of a nanofluid past a sinusoidal semi-infinite vertical surface in the non-absorbing medium. The contribution of surface radiative heat flux is employed in the boundary conditions with the help of Stefan-Boltzmann law. Governing equations are transformed into a non-conserved dimensionless system and integrated numerically by means of an implicit finite difference scheme. The accuracy of numerical method is assessed by a comparison of the present results with the earlier published work and it is found that there exists a favorable agreement between the two. Our problem is subject to the influence of a set of parameters, which appear due to the presence of surface radiation, nanoparticles, and transverse curvature of vertical wall. It is noticed that radiative length parameter λ and surface radiation parameter R contribute in a reduction of local skin friction coefficient and local Nusselt number.

Network Simulation solution of free convective flow from a vertical cone with combined effect of non- uniform surface heat flux and heat generation or absorption

A two dimensional mathematical model is formulated for the transitive laminar free convective, incompressible viscous fluid flow over vertical cone with variable surface heat flux combined with the effects of heat generation and absorption is considered . using a powerful computational method based on thermoelectric analogy called Network Simulation Method (NSM0, the solutions of governing nondimensionl coupled, unsteady and nonlinear partial differential conservation equations of the flow that are obtained. The numerical technique is always stable and convergent which establish high efficiency and accuracy by employing network simulator computer code Pspice. The effects of velocity and temperature profiles have been analyzed for various factors, namely Prandtl number Pr, heat flux power law exponent n and heat generation/absorption parameter Δ are analyzed graphically.

Exact solutions for free convection flow of generalized Jeffrey fluid: A Caputo-Fabrizio fractional model

The present article reports the applications of Caputo-Fabrizio time-fractional derivatives. This article generalizes the idea of free convection flow of Jeffrey fluid over a vertical static plate. The free convection is caused due to the temperature gradient. Therefore, heat transfer is considered for free convection. The classical model for Jeffrey fluid is written in dimensionless form with the help of non-dimensional variables. Furthermore, the dimensionless model is converted into a fractional model called as a generalized Jeffrey fluid model. The governing equations of generalized Jeffrey fluid model have been solved analytically using the Laplace transform technique. The recovery of existing solutions in the open literature is possible through this work in terms of classical Jeffrey fluid, fractional Newtonian fluid as well as classical Newtonian fluid. For various embedded parameters, the physics of velocity and temperature profiles is studied by means of numerical computation. This report provides a detailed discussion as well as a graphical representation of the obtained results.

Similarity and analytical solutions of free convective flow of dilatant nanofluid in a Darcian porous medium with multiple convective boundary conditions

This paper deals with an analytical solution of free convective flow of dilatant nanofluid past a vertical cone/plate. A two-phase mixture model is used for nanofluid in which the Brownian motion and thermophoretic diffusivities are the important slip mechanisms between solid and liquid phases. The governing transport equations along with physically realistic thermal and mass convective boundary conditions are reduced to similarity equations using relevant similarity transformations before being solved by homotopy analysis method. The effects of the governing parameters (Brownian motion, thermophoresis, convection–conduction, convection–diffusion, Lewis number, buoyancy ratio, and power-law) on the dimensionless velocity, temperature and nanoparticle volume fraction, friction and heat transfer rates are plotted and discussed. It is found that friction factor decreases with the increase in Le and Nr for both vertical plate and cone. The local Nusselt number decreases with the increase in the thermophoresis and Brownian motion parameters for both the plate and cone. The local Sherwood number increases with the Brownian motion parameter and decreases for thermophoresis parameter. The results have been compared with the published ones and an excellent agreement has been noticed.

Non-similar solution of free convective flow of power law nanofluids in porous medium along a vertical cone and plate with thermal and mass convective boundary conditions

This paper investigates non-similar solution of free convective boundary layer flow of a viscous incompressible fluid along a vertical cone and plate embedded in a Darcian porous medium filled with power law non-Newtonian nanofluids. The effects of the thermal and mass convective boundary conditions are taken into account, which makes the present analysis practically applicable. The governing boundary layer equations are converted into a system of non-similar differential equations by using suitable transformations before being solved numerically. The effects of the controlling parameters on the dimensionless velocity, temperature, nanoparticle volume fraction, and the local Nusselt and Sherwood numbers are reported. It is found that the velocity, temperature, and concentration increase with mass transfer velocity for both the vertical plate and cone. Further, the velocity reduces whilst the temperature and concentration increase with increasing buoyancy ratio parameter for all three types of nanofluids in the case of both geometries. The local Nusselt and the local Sherwood numbers are found to be higher for dilatant nanofluids than pseudoplastic nanofluids and Newtonian fluids in each case. The numerical results for special cases are compared with the published data and an excellent agreement has been found.

Exact solutions for free convection flow of nanofluids with ramped wall temperature

This article aims to study the unsteady convection flow of nanofluids induced by free convection and the oscillating plate condition. The fluid is confined to the region over an infinite vertical flat plate with ramped wall temperature. Five different types of water-based nanofluids containing copper (Cu), silver (Ag), copper oxide (CuO), alumina ( Al2O3 and titanium oxide (TiO2 are chosen for this analysis. The Laplace transform technique is applied to obtain exact solutions of velocity and temperature for both cases of ramp and isothermal plate conditions. Ramp and isothermal solutions are compared graphically and it is found that the ramp velocity and the temperature are smaller in magnitude than isothermal velocity and temperature. Corresponding expressions for skin-friction and Nusselt number are also evaluated. The results are plotted for various physical parameters contained in the governing equations and discussed in details. Comparison with earlier results provides an excellent agreement.

FREE CONVECTION FLOW OF A SECOND-GRADE FLUID WITH RAMPED WALL TEMPERATURE

In this paper, exact solutions for free convection flow of a second-grade fluid with ramped wall temperature are obtained using the Laplace transform technique. The effects of pertinent flow parameters on velocity and skin friction are studied with the aid of various graphs. It is found that with an increasing second-grade parameter, the fluid velocity decreases for both ramped and isothermal wall temperatures and the skin friction increases. However, the magnitude of velocity in the case of the ramped temperature is quite smaller than the isothermal temperature for increasing values of the second-grade parameter.

Homotopy analysis solution of free convection flow on a horizontal impermeable surface embedded in a saturated porous medium

In this paper, the analytic solution of the buoyancy-driven flow over a horizontal impermeable flat plate embedded in a saturated porous medium is derived using the newly developed analytic method, namely the homotopy analysis method (HAM). The HAM results show great agreement comparing with numerical results. HAM contains an auxiliary parameter ℏ that provides a simple way of controlling and adjusting the convergence region. The resultant analytic solution is valid for all acceptable values of the temperature exponent parameter λ.

Analytical solutions for free convection flow of a particulate suspension past an infinite vertical surface

Continuum equations governing steady, laminar, free convection flow of a particulate suspension past an infinite porous vertical flat plate are developed. These equation account for particulate viscous effects which are absent from most two-phase flow models. Analytical solutions for inviscid and viscous particle phase of uniform density distribution are obtained. Graphical results for velocity and temperature profiles of both phases based on the analytical solutions are presented and discussed. In addition, tabulated results for the skin-friction coefficients of both phases and the Nusselt number of the fluid phase are shown. A parametric study of some of the physical parameters involved in the problem is conducted to elucidate interesting features of the solutions.

Non-similar solutions of free convection flow over a vertical frustum of a cone for constant wall temperature

The laminar free convection flow and heat transfer over a vertical frustum of a cone is studied. The governing boundary layer equations are solved using local non-similarity method for constant wall temperature case. Local similarity and the local non-similarity two- and three-equation models are constructed and the resulting equations are solved numerically. Results obtained from two- and three-equation models are in good agreement. The numerical values of the flow and temperature functions required to calculate the surface skin friction and heat transfer rate have been reported for various values of Prandtl numbers.

Finite element solutions for free convection flow around an LMFBR debris tray

The finite element method is used to study heat transfer from a core debris bed in a liquid metal fast breeder reactor after a postulated meltdown incident. The system contains heat releasing uranium oxide core debris which is being cooled by laminar free convection flow of the sodium coolant in the primary vessel. Both 2-dim. and axisymmetric models are examined. Solutions for Gr H · Pr values up to 10 8 were obtained. At the highest value of Gr H · Pr, conduction was still the dominant mode of heat transfer and the contribution of convection is only just becoming significant in the 2-dim. cases. The UO 2 heat release rates are many orders of magnitude lower than would occur in actual designs. Even so the solutions are of practical value and are a step towards predicting the behaviour at realistic conditions.

A new variational technique to free convection boundary layer flow and heat transfer

A new variational method based on the governing principle of dissipative processes is developed for the solution of coupled non-linear equations arising in free convection boundary layer flow and heat transfer. The method is applied to get the approximate solution of free convection flow along a semi-infinite vertical plate. It is found that the rate of heat transfer computed for various Prandtl numbers using the present variational approach is quite close to exact known results. The result of present investigation is found to be better than that of well-known Karman-Pohlhausen integral method.

Local Nonsimilarity Solution of Free Convection Flow and Heat Transfer from an Inclined Isothermal Plate

The effect of the angle of inclination on free convection flow and heat transfer from an isothermal surface is analyzed by the local nonsimilarity method of solution. An inclination parameter ξ as obtained from the analysis is tan γ/4 (Grx/4)1/4, where γ is the angle of inclination measured from the vertical and Grx is the local Grashof number, based on the component of the gravity vector along the surface. Numerical solutions of the equations are obtained for Prandtl numbers of 0.1, 0.7, 6 and 275. Results show an appreciable effect of ξ on the velocity field, and practically none on the temperature field, except for very large angles of inclination from the vertical or for very small values of the Prandtl number. In the limiting case of very large Prandtl number, ξ has no effect either on the velocity or the temperature field.