Effect of Viscous Dissipation and Axial Conduction in Thermally Developing Region of the Channel Partially Filled with a Porous Material Subjected to Constant Wall Heat Flux

The present investigation has been undertaken to assess the effect of viscous dissipation and axial conduction on forced convection heat transfer in the entrance region of a parallel plate channel with the porous insert attached to both walls of the channel. The flow field is unidirectional. Flow in the porous region corresponds to Darcy-Brinkman model and the clear fluid region to that of plane Poiseuille flow. The effects of the parameters Darcy number, Da, Peclet number, Pe, Brinkman number, Br and a porous fraction γp on the local heat transfer coefficient are analyzed graphically. Effects of viscous dissipation employing the Darcy model and the clear fluid compatible model have been studied.

Analysis of One Dimensional Advection Diffusion Model Using Finite Difference Method

In this paper, one dimensional advection diffusion model is analyzed using finite difference method based on Crank-Nicolson scheme. A practical problem of filter cake washing of chemical engineering is analyzed. The model is converted into dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the Crank-Nicolson spatial derivative scheme is used in space domain and forward difference scheme is used in time domain. The scheme is found to be unconditionally convergent, stable, first order accurate in time and second order accurate in space domain. For a test problem, numerical results are compared with the analytical ones for different values of parameter.

Numerical Solution of Steady Magnetohydrodynamic Boundary Layer Flow Due to Gyrotactic Microorganism for Williamson Nanofluid over Stretched Surface in the Presence of Exponential Internal Heat Generation

This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number Pr, magnetic field parameter M, Peclet number Pe, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.

Throughflow Effects on Thermal Convection in Variable Viscosity Ferromagnetic Liquids

The problem of thermal convection in temperature and magnetic field sensitive Newtonian ferromagnetic liquid is studied in the presence of uniform vertical magnetic field and throughflow. Using a combination of Galerkin and shooting techniques the critical eigenvalues are obtained for stationary mode. The effect of Prandtl number (Pr > 1) on onset is insignificant and nonlinearity of non-buoyancy magnetic parameter M3 is found to have no influence on the onset of ferroconvection. The magnetic buoyancy number, M1 and variable viscosity parameter, V have destabilizing influences on the system. The effect of throughflow Peclet number, Pe is to delay the onset of ferroconvection and this effect is independent of the direction of flow.

Effects of Viscous Dissipation and Concentration Based Internal Heat Source on Convective Instability in a Porous Medium with Throughflow

Linear stability analysis of double diffusive convection in a horizontal porous layer saturated with fluid is examined by considering the effects of viscous dissipation, concentration based internal heat source and vertical throughflow. The basic steady state solution for Governing equations is derived. Linear stability analysis has been implemented numerically by using shooting and Runge-kutta methods. Critical thermal Rayleigh number Rac is obtained for various values of solutal Rayleigh number Sa, vertical Peclet number Pe, Gebhart number Ge, Lewis number Le and measure of concentration based internal heat source γ. It is observed that Ge has destabilizing effect for upward throughflow and stabilizing effect for downward throughflow. And γ has considerable destabilizing effect for upward throughflow and insignificant destabilizing effect for downward throughflow.

A Thermodynamic Solution for the Static and Dynamic Characteristics of a Two-Lobe Journal Bearing

The work described in this paper is an investigation of the static and dynamic characteristics of two-lobe journal bearings taking into consideration the thermal effects. A thermo-hydrodynamic solution of a finite two-lobe journal bearing is performed by solving the generalized form Reynolds equation with the energy equation, taking into consideration viscosity variation across the film thickness. The static and dynamic characteristics were numerically obtained. The results are evaluated for different values of viscosity-temperature coefficient and Peclet number. The results show that considering the thermal effects in the solution of the two-lobe journal bearing has a marked on the study of its stability.

Subcritical Water Extraction of Mannitol from Olive Leaves

Subcritical water extraction was investigated as a novel and alternative technology in the food and pharmaceutical industry for the separation of Mannitol from olive leaves and its results was compared with those of Soxhlet extraction. The effects of temperature, pressure, and flow rate of water and also momentum and mass transfer dimensionless variables such as Reynolds and Peclet Numbers on extraction yield and equilibrium partition coefficient were investigated. The 30-110 bars, 60-150°C, and flow rates of 0.2-2 mL/min were the water operating conditions. The results revealed that the highest Mannitol yield was obtained at 100°C and 50 bars. However, extraction of Mannitol was not influenced by the variations of flow rate. The mathematical modeling of experimental measurements was also investigated and the model is capable of predicting the experimental measurements very well. In addition, the results indicated higher extraction yield for the subcritical water extraction in contrast to Soxhlet method.

Influence of Heat Transfer on Stability of Newtonian and Non-Newtonian Extending Films

The stability of Newtonian and Non-Newtonian extending films under local or global heating or cooling conditions are considered. The thickness-averaged mass, momentum and energy equations with convective and radiative heat transfer are derived, both for Newtonian and non-Newtonian fluids (Maxwell, PTT and Giesekus models considered). The stability of the system is explored using either eigenvalue analysis or transient simulations. The results showed that the influence of heating and cooling on stability strongly depends on the magnitude of the Peclet number. Examples of stabilization or destabilization of heating or cooling are shown for Pe

Streamwise Conduction of Nanofluidic Flow in Microchannels

The effect of streamwise conduction on the thermal characteristics of forced convection for nanofluidic flow in rectangular microchannel heat sinks under isothermal wall has been investigated. By applying the fin approach, models with and without streamwise conduction term in the energy equation were developed for hydrodynamically and thermally fully-developed flow. These two models were solved to obtain closed form analytical solutions for the nanofluid and solid wall temperature distributions and the analysis emphasized details of the variations induced by the streamwise conduction on the nanofluid heat transport characteristics. The effects of the Peclet number, nanoparticle volume fraction, thermal conductivity ratio on the thermal characteristics of forced convection in microchannel heat sinks are analyzed. Due to the anomalous increase in the effective thermal conductivity of nanofluid compared to its base fluid, the effect of streamwise conduction is expected to be more significant. This study reveals the significance of the effect of streamwise conduction under certain conditions of which the streamwise conduction should not be neglected in the forced convective heat transfer analysis of microchannel heat sinks.