Slip Condition Effects on Unsteady MHD Fluid Flow with Radiative Heatflux over a Porous Medium

The objective of this paper is to study unsteady magneto hydrodynamic (MHD) free flow of viscoelastic fluid (Walter’s B) past an infinite vertical plate through porous medium. The temperature is assumed to be oscillating with time. The solution obtained shows different profiles of effects of slip conditions on primary and secondary velocity. Also, the effects of various parameters on temperature, concentration, primary and secondary velocity profiles were presented graphically. The result indicated the secondary velocity is enhanced with increase in slip parameter. Primary velocity demonstrated opposite trend.

Joule Heating and Thermal Radiation Effects on MHD Boundary Layer Flow of a Nanofluid over an Exponentially Stretching Sheet in a Porous Medium

A numerical study on boundary layer flow behaviour, heat and mass transfer characteristics of a nanofluid over an exponentially stretching sheet in a porous medium is presented in this paper. The sheet is assumed to be permeable. The governing partial differential equations are transformed into coupled nonlinear ordinary differential equations by using suitable similarity transformations. The transformed equations are then solved numerically using the well known explicit finite difference scheme known as the Keller Box method. A detailed parametric study is performed to access the influence of the physical parameters on longitudinal velocity, temperature and nanoparticle volume fraction profiles as well as the local skin-friction coefficient, local Nusselt number and the local Sherwood number and then, the results are presented in both graphical and tabular forms.

Heat and Mass Transfer in MHD Visco-Elastic Fluid Flow through a Porous Medium over a Stretching Sheet with Chemical Reaction

This paper presents the study of convective heat and mass transfer characteristics of an incompressible MHD visco-elastic fluid flow immersed in a porous medium over a stretching sheet with chemical reaction and thermal stratification effects. The resultant governing boundary layer equations are highly non-linear and coupled form of partial differential equations, and they have been solved by using fourth order Runge-Kutta integration scheme with Newton Raphson shooting method. Numerical computations are carried out for the non-dimensional physical parameters. Here a numerical has been carried out to study the effect of different physical parameters such as visco-elasticity, permeability of the porous medium, magnetic field, Grashof number, Schmidt number, heat source parameter and chemical reaction parameter on the flow, heat and mass transfer characteristics.

Natural convection of nanofluid over vertical plate embedded in porous medium: prescribed surface heat flux

The aim of the present paper is to analyze the natural convection heat and mass transfer of nanofluids over a vertical plate embedded in a saturated Darcy porous medium subjected to surface heat and nanoparticle fluxes. To carry out the numerical solution, two steps are performed. The governing partial differential equations are firstly simplified into a set of highly coupled nonlinear ordinary differential equations by appropriate similarity variables, and then numerically solved by the finite difference method. The obtained similarity solution depends on four non-dimensional parameters, i.e., the Brownian motion parameter （Nb）, the buoyancy ratio （Nr）, the thermophoresis parameter （Nt）, and the Lewis number （Le）. The variations of the reduced Nusselt number and the reduced Sherwood number with Nb and Nt for various values of Le and Nr are discussed in detail. Simulation results depict that the increase in Nb, Nt, or Nr decreases the reduced Nusselt number. An increase in the Lewis number increases both of the reduced Nusselt number and the Sherwood number. The results also reveal that the nanoparticle concentration boundary layer thickness is much thinner than those of the thermal and hydrodynamic boundary layers.

An efficient inverse approach for reconstructing time-and space-dependent heat flux of participating medium

The decentralized fuzzy inference method(DFIM)is employed as an optimization technique to reconstruct time-and space-dependent heat flux of two-dimensional(2D)participating medium.The forward coupled radiative and conductive heat transfer problem is solved by a combination of finite volume method and discrete ordinate method.The reconstruction task is formulated as an inverse problem,and the DFIM is used to reconstruct the unknown heat flux.No prior information on the heat flux distribution is required for the inverse analysis.All retrieval results illustrate that the time-and spacedependent heat flux of participating medium can be exactly recovered by the DFIM.The present method is proved to be more efficient and accurate than other optimization techniques.The effects of heat flux form,initial guess,medium property,and measurement error on reconstruction results are investigated.Simulated results indicate that the DFIM is robust to reconstruct different kinds of heat fluxes even with noisy data.

Melting heat transfer effects on stagnation point flow of micropolar fluid saturated in porous medium with internal heat generation(absorption)

The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.

Modeling of Coupled Heat and Mass Transfer in a Trapezoidal Porous Bed on a Grid

We investigate heat and mass transfer in an isosceles trapezoidal cavity, filled with charcoal considered as a granular porous medium. The Darcy-Brinkman-Forchheimer flow model is coupled to the energy and mass equations with the assumption of non-thermal equilibrium. These equations are discretized by the finite volume method with an offset mesh and then solved by the line-by-line method of Thomas. The coupling between pressure and velocity is obtained by Semi-Implicit Method for Pressure Linked Equations. (SIMPLE) algorithm. The results show that the temperature in the cavity increases when the inclination angle of the sides walls decreases. The 15° inclination is selected as being able to offer better thermal performance in the cookstove combustion chamber.

Theoretical solution of transient heat conduction problem in one-dimensional double-layer composite medium

To make heat conduction equation embody the essence of physical phenomenon under study,dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to dimensionless forms.Then,a theoretical solution model of transient heat conduction problem in one-dimensional double-layer composite medium was built utilizing the natural eigenfunction expansion method.In order to verify the validity of the model,the results of the above theoretical solution were compared with those of finite element method.The results by the two methods are in a good agreement.The maximum errors by the two methods appear when τ(τ is nondimensional time) equals 0.1 near the boundaries of ξ =1(ξ is nondimensional space coordinate) and ξ =4.As τ increases,the error decreases gradually,and when τ =5 the results of both solutions have almost no change with the variation of coordinate ξ.

Peristaltic transport of MHD Williamson fluid in an inclined asymmetric channel through porous medium with heat transfer

The intention of this investigation is to study the effects of heat transfer and inclined magnetic field on the peristaltic flow of Williamson fluid in an asymmetric channel through porous medium. The governing two-dimensional equations are simplified under the assumption of long wavelength approximation. The simplified equations are solved for the stream function, temperature, and axial pressure gradient by using a regular perturbation method. The expression for pressure rise is computed numerically. The profiles of velocity, pressure gradient, temperature, heat transfer coefficient and stream function are sketched and interpreted for various embedded parameters and also the behavior of stream function for various wave forms is discussed through graphs. It is observed that the peristaltic velocity increases from porous medium to non-porous medium, the magnetic effects have increasing effect on the temperature, and the size of the trapped bolus decreases with the increasing of magnetic effects while the trend is reversed with the increasing of Darcy number. Moreover, limiting solutions of our problem are in close agreement with the corresponding results of the Newtonian fluid model.

Optimal trajectory and heat load analysis of different shape lifting reentry vehicles for medium range application

The objective of the paper is to compute the optimal burn-out conditions and control requirements that would result in maximum down-range/cross-range performance of a waverider type hypersonic boost-glide(HBG) vehicle within the medium and intermediate ranges,and compare its performance with the performances of wing-body and lifting-body vehicles vis-a-vis the g-load and the integrated heat load experienced by vehicles for the medium-sized launch vehicle under study.Trajectory optimization studies were carried out by considering the heat rate and dynamic pressure constraints.The trajectory optimization problem is modeled as a nonlinear,multiphase,constraint optimal control problem and is solved using a hp-adaptive pseudospectral method.Detail modeling aspects of mass,aerodynamics and aerothermodynamics for the launch and glide vehicles have been discussed.It was found that the optimal burn-out angles for waverider and wing-body configurations are approximately 5° and 14.8°,respectively,for maximum down-range performance under the constraint heat rate environment.The down-range and cross-range performance of HBG waverider configuration is nearly 1.3 and 2 times that of wing-body configuration respectively.The integrated heat load experienced by the HBG waverider was found to be approximately an order of magnitude higher than that of a lifting-body configuration and 5 times that of a wing-body configuration.The footprints and corresponding heat loads and control requirements for the three types of glide vehicles are discussed for the medium range launch vehicle under consideration.

Gas Flow Development Through Tandem Heat Exchangers Inside Exhaust Nozzle by Using Porous Medium Model

A computational study on the flow development through tandem double-U-shaped-tubes compact heat exchangers inside exhaust nozzle is presented.In order to simplify the computational process on modeling the flow field,the compact heat exchanger is modeled as a porous matrix by using an isotropic porous medium assumption,which makes two-dimensional numerical simulation realistic.With the use of an existed quadratic relation which connects the pressure drop with the inlet velocity in the external part of the heat exchanger,the permeability and drag coefficient in the porous medium model are determined and a corresponding computational method validation is also made.Two schemes of tandem double-U-shaped-tubes compact heat exchangers are numerically analyzed.In relative to the baseline scheme,the modified scheme is improved by smoothing the nozzle expansion,varying heat exchanger mounting angle and installing boat-tail ramp at the trailing edge of the last heat exchanger.The results show that the pressure losses due to the existence of local recirculation zones and inappropriate distribution of the flow field are reduced in the modified scheme.The pressure loss coefficient is decreased from 1.7% under the baseline scheme to 1.2% under the modified scheme.

Consideration of transient heat conduction in a semi-infinite medium using homotopy analysis method

In the current work, transient heat conduction in a semi-infinite medium is considered for its many applications in various heat fields. Here, the homotopy analysis method （HAM） is applied to solve this problem and analytical results are compared with those of the exact and integral methods results. The results show that the HAM can give much better approximations than the other approximate methods： Changes in heat fluxes and profiles of temperature are obtained at different times and positions for copper, iron and aluminum.

Melting effect and Cattaneo-Christov heat flux in fourth-grade material flow through a Darcy-Forchheimer porous medium

The melting phenomenon in two-dimensional(2 D)flow of fourth-grade material over a stretching surface is explored.The flow is created via a stretching surface.A Darcy-Forchheimer(D-F)porous medium is considered in the flow field.The heat transport is examined with the existence of the Cattaneo-Christov(C-C)heat flux.The fourth-grade material is electrically conducting subject to an applied magnetic field.The governing partial differential equations(PDEs)are reduced into ordinary differential equations(ODEs)by appropriate transformations.The solutions are constructed analytically through the optimal homotopy analysis method(OHAM).The fluid velocity,temperature,and skin friction are examined under the effects of various involved parameters.The fluid velocity increases with higher material parameters and velocity ratio parameter while decreases with higher magnetic parameter,porosity parameter,and Forchheimer number.The fluid temperature is reduced with higher melting parameter while boosts against higher Prandtl number,magnetic parameter,and thermal relaxation parameter.Furthermore,the skin friction coefficient decreases against higher melting and velocity ratio parameters while increases against higher material parameters,thermal relaxation parameter,and Forchheimer number.

Effects of the porous medium and water-silver biological nanofluid on the performance of a newly designed heat sink by using first and second laws of thermodynamics

The aim of this numerical investigation is to evaluate the laminar forced convection of biologically synthesized water-silver nanofluid through a heat sink(HS)filled with porous foam(PHS)using first and second laws of thermodynamics.The impacts of inlet velocity(V=0.5–3 m·s^-1)and volume fraction of nanofluid(φ=0–1%)on the performance metrics of HS are assessed and the outcomes are compared with those of the non-porous HS(NHS).The outcomes revealed that for both the PHS and NHS,the increase of V causes an intensification in convection coefficient,pumping power,and entropy generation due to fluid friction,while the maximum CPU temperature,thermal resistance,and entropy generation due to the heat transfer reduces by boosting V.Also,it was found that the augmentation of V results in intensification in convection coefficient,pumping power,overall hydrothermal performance,and frictional entropy generation,while the opposite is true for maximum CPU temperature,thermal resistance,and thermal entropy generation.Furthermore,it was reported that,except forφ=0.5%,the overall hydrothermal performance of NHS is better than that of PHS,while PHS has better second-law performance than NHS in all the studied cases.Also,it can be concluded that the best hydrothermal performance for PHS belongs toφ=1%and V=0.5 m·s^-1,while for NHS,these values are 1%and 2 m·s^-1.

Effects of Solid Matrix and Porosity of Porous Medium on Heat Transfer of Marangoni Boundary Layer Flow Saturated with Power-Law Nanofluids

The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.

Piezoelectric Power Harvesting Process via Phase Changes of Low-Boiling-Point Medium Together with Water for Recovering Low-Temperature Heats

Low-temperature thermal energy conversions down to exergy zero to electric power must contribute energy sustainability. That is to say, reinforcements of power harvesting technologies from extremely low temperatures less than 373 K might be at least one of minimum roles for the current generations. Then, piezoelectric power harvesting process for recovering low-temperature heats was invented by using a unique biphasic operating medium of an underlying water-insoluble/low-boiling-point medium (i.e. NOVEC manufactured by 3M Japan Ltd.) in small quantity and upper-layered water in large quantity. The higher piezoelectric power harvesting densities were naturally revealed with an increase in heating temperatures. Excessive cooling of the operating medium deteriorated the power harvesting efficiency. The denser operating medium was surpassingly helpful to the higher piezoelectric power harvesting density. Concretely, only about 5% density increase of main operating medium (i.e. water with dissolving alum at 0.10 mol/dm3) came to the champion piezoelectric power harvesting density of 92.6 pW/dm2 in this study, which was about 1.4 times compared to that with the original biphasic medium of pure water together with a small quantity of NOVEC.

MHD Heat and Mass Transfer of an Oscillatory Flow over a Vertical Permeable Plate in a Porous Medium with Chemical Reaction

The problem of magneto-hydro-dynamic (MHD) mass and heat transfer of an oscillatory fluid in two-dimensional viscous, electrically conducting over an infinite vertical permeable moving plate in a saturated porous medium with the presence of a transverse magnetic field and chemical reaction is analytically presented. The governing equations, momentum, energy, and concentration are solved. Various flow parameters effects on velocity, temperature and concentration fields are discussed. It is found that, the fluid velocity increases with increasing both the permeability and chemical reaction parameters. While, it increases with decreasing the magnetic field parameter. Furthermore, the concentration increases with increasing chemical reaction parameters.

Inverse Problem on Heat Conduction in Heterogeneous Medium

Under consideration is a nonclassical stationary problem on heat conduction in a body with the pre-set surface temperature and heat flow. The body contains inclusions at unknown locations and with unknown boundaries. The body and inclusions have different constant thermal conductivities. The author explores the possibility of locating inclusions. The article presents an integral criterion based on which a few statements on identification of inclusions in a body are proved.

An Investigation into the Effect of Porous Medium on Performance of Heat Exchanger

In this paper, a detailed numerical investigation of two-dimensional laminar forced convection in a porous channel with inlet and outlet slot is presented. A uniform heat flux is applied on one wall of channel and another wall is isolated. The flow in the porous medium is modeled using the Brinkman-Forchheimer-extended Darcy model in which the inertia and boundary effects are taken into consideration and thermal dispersion effects are not included in the energy equation. Parametric studies are conducted to evaluate the effects of particle diameter, Reynolds number on the heat transfer and friction factor. Nusselt number and friction factor are developed for efficient design of a porous heat exchanger based on the present configuration. In order to solve this problem Fluent software was used.

Analytic Solution for Fluid Flow over an Exponentially Stretching Porous Sheet with Surface Heat Flux in Porous Medium by Means of Homotopy Analysis Method

In this paper, the analytical solution of a viscous and incompressible fluid towards an exponentially stretching porous sheet with surface heat flux in porous medium, for the boundary layer and heat transfer flow, is presented. The equations of continuity, momentum and the energy are transformed into non-linear ordinary differential by using similarity transformation. The solutions of these highly non-linear ordinary differential equations are found analytically by means of Homotopy Analysis Method (HAM). The result obtained by HAM is compared with numerical results presented in the literature. The accuracy of the HAM is indicated by close agreement of the two sets of results. By this method, an expression is obtained which is admissible for all values of effective parameters. This method has the ability to control the convergence of the solution.