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Abstract: Keywords: Natural convection, anisotropic porous medium, inversion of density.Abstract. The natural convection in the porous medium has attracted considerable attention with its applications in various industrial sectors, such as the agro-alimentary, the pharmaceutical and oil processing industries. The present work is about the study of the phenomenon of natural convection at 4°C on the vertical plate lining in an anisotropic porous medium in permeability. The wall of the vertical surface is subjected to a constant temperature with defined hydrodynamic conditions and thermal limits. Generalized Darcy’s law was used to establish the governing equations of the system. The control parameters governing the system are respectively the permeability ratio K*, the angle ϴ of the major axis and the inversion parameter R. The general basic equations were solved numerically using Runge-Kutta and shooting method. There was validated against previous work. The effect of these parameters on the heat transfer was highlighted. From the analysis result, it comes out the following conclusions: The convective flow is significantly affected by the anisotropic parameter; heat transfer along the vertical surface is maximum (minimum) when the main shaft having the high permeability is oriented parallel (perpendicular) to the gravitational field; the rate of heat transfer is depending on the inversion parameter R. The convective transfer rate illustrated by the local Nusselt number is symmetric with respect to R=0.45, where it reaches its smallest value. It is inversely proportional to the distribution of the thickness of boundary layer. A high convective transfer rate corresponds to a low boundary layer thickness and this inversely.
Abstract: The present paper investigates the role of heat transfer on peristaltic transport of Jeffery liquid in a porous tube. The effect of variable viscosity and slip impacts are taken into account. The closed-form solutions are obtained with the help of long wavelength and small Reynolds number. The results of physiological parameters on velocity, pressure rise, frictional force, trapped bolus, and temperature are plotted graphically. It is seen that the pressure rise and the frictional forces decline with an expansion in the viscosity parameter. The study further demonstrates that an increase in the value of the slip parameter significantly alters the pressure rise, frictional force, and temperature. Moreover, the volume of trapped bolus increases with an increase in the value of the velocity slip parameter.
Abstract: The present work investigates heat enhancement through a moving porous fin of trangular profile. The interaction between the fluid and the porous media in not locally thermodynamic equilibrium. The transport through the porous medium is derived using Darcy’s model. The calculations are carried out using the two-dimensional Differential Transformation Method (2D DTM), which is an analytical solution technique that can be applied to various types of differential equations. The approximate analytical solutions are validated using the numerical solution obtained via the inbuilt numerical solver in MATLAB (pdepe). The results reveal that the 2D DTM can achieve accurate results in predicting the solution of such problems. The impact of the thermal parameters on temperature distribution is performed using the closed-form solution generated by DTM.
Abstract: In this article, we introduce a new thermal conductivity calibration function in modeling heat transfer through extended surfaces. The variable thermal conductivity functions are studied on a stand alone basis and further compared to one another. The calculations are carried out using the Variational Iteration Method (VIM) which is an analytical solution technique. The series solutions are bench-marked against the numerical results obtained by applying the Runge-Kutta fourth order method coupled with shooting technique. The effects of some physical parameters such as the thermogeometric fin parameter and thermal conductivity gradient, on temperature distribution are illustrated and explained.
Abstract: The significance of this paper is to analyse thermal decomposition and reactant consumption in a stockpile of reactive materials, such as that of coal, hay or wood, for example. The study is modelled in a rectangular slab and a two-step combustion process like the one taking place in fuel combustion of an automobile is assumed. The coupling of Runge-Kutta-Fehlberg (RKF) method and Shooting technique is applied to solve the differential equations governing the problem. The combustion process that is so complicated is investigated by consideration of effects of some embedded kinetic parameters, such as the activation energy, on the temperature and the reactant (O2) consumption. It was discovered that parameters such as the activation energy, tend to lower the temperature of the system and correspondingly reduce the O2 consumption rate, whereas parameters like the rate of reaction, increase the temperature during the combustion process, to reduce the O2 concentration of the system. The results also indicate that parameters like the rate of reaction, which increase the temperature profiles, fast-track the exothermic chemical reaction to deplete the reactant faster. However, those that reduce the temperature of the system preserve the reactant concentration.
Abstract: Magnetohydrodynamics (MHD) boundary layer slip Casson fluid flow over a dissipated moving cylinder is explored. Casson fluid model is employed as a non-Newtonian material that demonstrates the phenomenon of yield stress. Blood material is considered to be an example of Casson liquid. The non-linear partial differential quantities are transformed into expressions of ordinary derivatives through transformation of similarity variables. These equations are computed for numeric solutions by using Runge-Kutta method along with shooting scheme. The impact of pertinent constraints on the fluid velocity and temperature are examined through graphs. The coefficient of the skin friction and the rate of heat transfer are found numerically. Comparing of the present study with the earlier results is also presented. We observed that the coefficient of skin friction increases for higher values of Hartmann number.
Abstract: The awareness of heat and mass transfer in nanofluid flows with magnetohydrodynamic conditions over cone and wedge is very significant for design of heat exchangers, transpiration, fiber coating, etc. With this initiation, we construct a mathematical model to investigate the chemical reaction effects on electrically conducting magnetohydrodynamic nanofluid flow over a cone and a wedge. For this purpose, we also consider a nonlinear thermal radiation, viscous dissipation, Joule heating with non-uniform heat source/sink. The transformed equations are solved by using shooting technique based on RK fourth order method. Effects of pertinent parameters of concern on the common profiles are conversed (in two cases). It is perceived that the momentum, temperature and concentration boundary layers are non-uniform for the flow over a wedge and a cone Key words: MHD, Non-linear Radiation, nanofluid, Chemical Reaction, heat generation.
Abstract: The present study concerns steady two-dimensional laminar mixed convective boundary layer Casson nanofluid flow along a stretching or shrinking sheet with multiple slip boundary conditions in a non-Darcian porous medium. The effect of viscous dissipation and non-linear radiation are considered. The governing partial differential equations, together with boundary conditions are transformed into a system of dimensionless coupled ordinary differential equations. Galerkin weighted residual method is then employed to solve the transformed coupled ordinary differential equations. The effect of various controlling parameters on dimensionless velocity, temperature, nanoparticle volume fraction, velocity gradient, temperature gradient and nanoparticle volume fraction gradient are presented graphically and discussed. The present approach is validated by comparing the result of this work and those available in the literature, and they are found to be in excellent agreement.
Abstract: Study reveals the axisymmetric squeezing flow of nanofluids through two parallel plates. Both Copper (Cu) and Silver (Ag) nanoparticles along with water treated as base fluid have been taken into consideration. Viscous dissipation effect and velocity slip both enhance the present study. The non-dimensional form of governing nonlinear ODEs is obtained with the suitable choice of similarity transformation. The complex ODEs are solved analytically imposing Adomain Decomposition Method (ADM). The influence of emerging parameters such as nanoparticle volume fraction, unsteadiness parameter, Eckert number, etc. have been described by visualizing graphically and the tabular values represent the unknown coefficient and computation is made for various values of physical parameters. The present result is compatible with the earlier which confirms the accuracy of the solution procedure. It reveals that point of inflection is marked in the velocity profiles of both Ag and Cu water nanofluids for the effects of various physical parameters. Squeezing number play a vital role in the velocity profile and it is observed that near the lower plate Ag nanoparticle dominates over Cu nanoparticles and further, after the middle of the channel the effect is reversed. 2010 Mathematics Subject Classification: 76D05, 76D10, 76M60, 76S05. *Corresponding Author’s Email: HYPERLINK "mailto:email@example.com" firstname.lastname@example.org Mobile No.: (+91)-9937169245