Unsteady Laminar Free Convection Flow Research Articles

Entropy generation and heat transfer analysis in power-law fluid flow: Finite difference method

In this article entropy generation analysis for unsteady laminar free convection flow of power-law fluid is investigated. Fluid flow is in the presence of thermal radiation and magnetic field. The flow and heat transfer are governed by coupled system of PDE's. System of partial differential equation (PDE's) governs the continuity, momentum and energy equations. Using suitable dimensionless parameters, the system of PDE's is transformed into dimensionless form. Numerical computations made employing finite difference method (FDM). This method converts the nonlinear PDE 's to simple algebraic equations and by using variational technique the approximate solution is obtained technique. Impacts of important flow variables on velocity, skin friction and Nusselt number are shown graphically. Skin friction and Nusselt number are discussed for different pertinent flow variables. Velocity, temperature, entropy and Bejan number variations through important variables are discussed in the form of graphs. The obtained results show that velocity decays against Re, Ha and Pr. Temperature is enhanced for higher values of Re, Ec, Tr and Gr. For higher estimation of Ec entropy of the system enhance while show opposite behavior for the Bejan number. Entropy of system boosts for strong magnetic field.

Fluid-structure interaction analysis of buoyancy-driven fluid and heat transfer through an enclosure with a flexible thin partition

PurposeA numerical model of an unsteady laminar free convection flow and heat transfer is studied in a cavity that comprises a vertical flexible thin partition.Design/methodology/approachThe left and right vertical boundaries are isothermal, while the horizontal boundaries are insulated. Moreover, the thin partition, placed in the geometric centerline of the enclosure, is considered to be hyper elastic and diathermal. Galerkin finite-element methods, the system of partial differential equations along with the appropriate boundary conditions are transformed to a weak form through the fluid-structure interaction and solved numerically.FindingsThe heat transfer characteristics of the enclosure with rigid and flexible partitions are compared. The effect of Rayleigh number and Young’s modulus on the maximum nondimensional stress and final deformed shape of the membrane is addressed.Originality/valueIncorporation of vertical thin flexible membrane in middle of a cavity has numerous industrial applications, and it could noticeably affect the heat and mass transfer in the enclosure.

Transient free convection flow between long vertical parallel plates with ramped wall temperature at one boundary in the presence of thermal radiation and constant mass diffusion

The unsteady laminar free convection flow between two long vertical parallel plates with ramped wall temperature at one boundary has been investigated in the presence of thermal radiation and chemical species concentration. The exact solutions of the momentum, energy and concentration equations have been obtained using the Laplace transform technique. The velocity and temperature profiles, skin-friction and Nusselt number variations are shown graphically and the numerical values of the volume flow rate, the total heat rate and species rate added to the fluid are presented in a table. The influence of different system parameters such as the radiation parameter (R), buoyancy ratio parameter (N), Schmidt number (Sc) and time (t) has been analyzed carefully. A critical analysis of the coupled heat and mass transfer phenomena is provided. The free convective flow due to ramped wall temperature has also been compared with the baseline case of flow due to constant wall temperature.

A numerical study on unsteady natural convection of air with variable viscosity over an isothermal vertical cylinder

The present study deals with the boundary layer flow and heat transfer of unsteady laminar free convection flow past a semi-infinite isothermal vertical cylinder immersed in air. The fluid viscosity is assumed to vary with the temperature. An implicit finite-difference method has been employed to solve the governing non-dimensional boundary layer equations. A parametric study is performed to illustrate the influence of variable viscosity on the velocity and temperature profiles. The numerical results reveal that the viscosity has significant influences on the transient velocity and temperature profiles, average skin-friction coefficient and the average heat transfer rate. The results indicate that as the viscosity parameter increases, the temperature and the skin-friction coefficient increase, while the velocity near the wall and the Nusselt number decrease.

Space approach to the hydro-magnetic flow of a dusty fluid through a porous medium

The technique of the state space approach and the inversion of the Laplace transformation method are applied to the non-dimensional equations of an unsteady laminar free convection flow of an incompressible, viscous, electrically conducting dusty fluid through a porous medium, which is bounded by an infinite vertical plane surface of constant temperature, in the presence of a constant magnetic field. The technique is applied to the thermal shock problem. The inversion of the Laplace transforms is carried out using a numerical approach. The numerical results of the dimensionless temperature, velocity, and induced magnetic and electric field distributions are given and illustrated graphically. The effects of the material’s parameters such as the Grashof number, the Prandtl number, the permeability parameter, the mass concentration of the particle phase, the Alfven velocity, the thermal relaxation time and the relaxation time of the particle phase on the temperature, velocity and the induced magnetic and electric fields are discussed.

Transient Convection on a Vertical Cylinder with Variable Viscosity and Thermal Conductivity

A numerical analysis is performed to study the influence of temperature-dependent viscosity and thermal conductivity on the unsteady laminar free-convection flow over a vertical cylinder. It was assumed that the viscosity of the fluid is an exponential function and that the thermal conductivity is a linear function of the temperature. The governing boundary-layer equations are converted into a nondimensional form and a Crank-Nicolson type of implicit finite difference method is used to solve the governing nonlinear set of equations. Numerical results are obtained and presented for air and water, with different parameters for viscosity and thermal conductivity variation. The transient effects of velocity and temperature are analyzed. The effects of varying physical parameters on the average skin-friction coefficient and the average rate of heat transfer are also depicted. For each Prandtl number, the flow characteristics such as the temperature and the average heat transfer rate for the fluid with variable viscosity first coincide with and then deviate from that of the fluid with constant properties and finally reach the steady state asymptotically. When the viscosity-variation parameter is larger, the higher velocity is observed in a region near the wall and it gives a higher average Nusselt number and lower average skin friction. But an increase in the thermal conductivity variation parameter leads to an increase in the average skin-friction coefficient and average Nusselt number.

Transient free convection flow over an isothemal vertical cylinder with temperature dependent viscosity

A numerical analysis is performed to study the influence of temperature-dependent viscosity and Prandtl number on unsteady laminar free convection flow over a vertical cylinder. The governing boundary layer equations are converted into a non-dimensional form and a Crank-Nicolson type of implicit finite-difference method is used to solve the governing non-linear set of equations. Numerical results are obtained and presented for different viscosityvariation parameters and Prandtl numbers. Transient effects of velocity and temperature are analyzed. The heat transfer characteristics against the viscosity-variation parameter are analyzed with the help of average skin-friction and Nusselt number and are shown graphically.

UNSTEADY NATURAL CONVECTION IN OPEN‐ENDED VERTICAL CONCENTRIC ANNULI

A finite‐difference scheme is developed for solving the boundary layer equations governing the unsteady laminar free convection flow in open ended vertical concentric annuli. The initial condition considered for the creation of the thermal transient corresponds to a step change in temperature at the inner annulus boundary while the outer wall is maintained adiabatic. Numerical results for a fluid of Pr = 0.7 in an annulus of radius ratio 0.5 are presented. The results show the developing velocity and pressure fields with respect to space and time. Also, the important relationship between the annulus height and the induced flow rate is presented for various values of the time parameter starting from quiescence to the final steady state.

Double diffusive unsteady free convection on two-dimensional and axisymmetric bodies in a porous medium

The unsteady laminar free convection flow of an incompressible electrically conducting fluid over two-dimensional and axisymmetric bodies embedded in a highly porous medium with an applied magnetic field has been studied. The unsteadiness in the flow field is caused by the variation of the wall temperature and concentration with time. The coupled nonlinear partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. It is observed that the skin friction, heat transfer and mass transfer increase with the permeability parameter but decrease with the magnetic parameter. The results are strongly dependent on the variation of wall temperature and concentration with time. The skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist or oppose the thermal buoyancy force. However, the mass transfer is found to be higher for small values of the ratio of the buoyancy parameters than for large values

The skin friction in the unsteady free-convection flow past an accelerated plate

In this paper the unsteady laminar free-convection flow of a viscous incompressible fluid, past an accelerated infinite vertical porous plate subjected to a constant suction (or injection) in considered. Numerical results for the skin-friction on the plate are obtained for the class of accelerated motions whose velocity is of the formU0t n wheret is time,U0 a constant, andn is a positive integer. The skin friction tends to zero with increasingt when the Grashof number Gr=λ2, the Prandtl number σ=1,n=0, and λ>0 which corresponds to suction.

Unsteady hydromagnetic free convection flow past an accelerated infinite vertical porous plate

Unsteady laminar free convection flow of a viscous incompressible and electrically conducting fluid past an accelerated vertical infinite porous plate subjected to a suction velocity proportional to (time)−1/2 is studied in presence of a uniform horizontal magnetic field. Results are discussed with the effects of the Grashof number Gr, and the magnetic field parameterM for Pr (the Prandtl number)=0.71 and 7.0 representing air and water respectively at 20 °C.

Unsteady Hydromagnetic Free Convection Flow past a Vertical Infinite Flat Plate

Unsteady laminar free convection flow of viscous incompressible and conducting fluids past a vertical infinite flat plate whose temperature or heat flux varies as some power of time is studied in the presence of a constant horizontal magnetic field. Results are reported for several values of Prandtl numbers for stepwise variations either in the plate temperature or in heat flux.

Effect of suction upon unsteady laminar free convection flow on a vertical infinite flat plate

Unsteady laminar free convection flow past a vertical infinite flat plate subjected to suction is considered. Exact solutions of momentum and energy equations are obtained in two cases: (1) When the plate temperature is proportional to some power of time and (2) when the heat flux at the plate is proportional to some power of time. It is assumed that the suction velocity varies as (time)−1/2. Expressions for the temperature and velocity profiles are obtained in closed forms in both the cases. Effect of suction on velocity, temperature, skin friction and rate of head transfer is studied for Prandtl numbers 0.02, 0.1, 0.72, 1 and 10.