A direct-forcing immersed boundary method (DFIB) with both virtual force and heat source is developed here to solve Navier-Stokes and the associated energy transport equations to study some thermal flow problems caused by a moving rigid solid object within. The key point of this novel numerical method is that the solid object, stationary or moving, is first treated as fluid governed by Navier-Stokes equations for velocity and pressure, and by energy transport equation for temperature in every time step. An additional virtual force term is then introduced on the right hand side of momentum equations in the solid object region to make it act exactly as if it were a solid rigid body immersed in the fluid. Likewise, an additional virtual heat source term is applied to the right hand side of energy equation at the solid object region to maintain the solid object at the prescribed temperature all the time. The current method was validated by some benchmark forced and natural convection problems such as a uniform flow past a heated circular cylinder, and a heated circular cylinder inside a square enclosure. We further demonstrated this method by studying a mixed convection problem involving a heated circular cylinder moving inside a square enclosure. Our current method avoids the otherwise requested dynamic grid generation in traditional method and shows great efficiency in the computation of thermal and flow fields caused by fluid-structure interaction.

This study presents the influence of heat and mass transfer on peristaltic transport of Finitely Extensible Nonlinear Elastic Peterlin (FENE-P) fluid in the presence of chemical reaction. It is assumed that all the fluid properties, except the density are constant. The Boussinesq approximation which relates density change to temperature and concentration changes is used in formulating buoyancy force terms in the momentum equation. Moreover, we neglect viscous dissipation and include diffusion-thermal (Dufour) and thermal-diffusion (Soret) effects in the present analysis. By the consideration of such important aspects the flow equations become highly nonlinear and coupled. In order to make the problem tractable we have adopted widely used assumptions of long wave length and low Reynolds number. An exact solution of the simplified coupled linear equations for the temperature and concentration has been obtained whereas numerical solution is obtained for dimensionless stream function and pressure gradient. The effects of different parameters on velocity field, temperature and concentration fields and trapping phenomenon are highlighted through various graphs. Numerical integration has been performed to analyze pressure rise per wavelength.

Solar radiation assisted mixed convection boundary layer flow of Newtonian fluid along a non- reflecting, non-absorbing and ideally transparent semi-infinite vertical plate is studied here. Beer's law is used to express the solar radiation term. It is convenient to transform the non-linear dimensionless parabolic partial differential equations into (i) primitive variable formulation (PVF) and (ii) stream function formulation (SFF) before applying the numerical schemes. Coupled equations thus obtained from PVF are integrated numerically through implicit finite difference method together with the Gaussian elimination technique whereas block tridiagonal Keller-box technique is adopted to simulate the system of equations obtained from SFF. Numerical results from these two methods are also compared graphically in order to test the validation of the two schemes. However, due to less computation time and accuracy numeric results of shear stress, local Nusselt number coefficient, velocity and temperature profiles are obtained via SFF. It is found that velocity as well as temperature of the non-absorbing fluid enhances owing to the increase in solar radiation parameter.

In this paper, mixed convection stagnation point flow of nanofluids over a stretching/shrinking surface is studied numerically in the presence of thermal radiation and viscous dissipation. The governing boundary layer equations are transformed into a system of nonlinear ordinary differential equations, by using a similarity transformation, which are then solved numerically using a fifth-order Runge-Kutta-Fehlberg method with shooting technique. The effects of various physical parameters are analyzed and discussed. Computed results are presented in graphical and tabular forms. It is found that the Richardson number, thermal radiation and internal heat generation/absorption have interesting and significant effects on skin-friction and local Nusselt number for all the three types of nanofluids.

This paper is concerned with the effect of thermally stratification on the steady, two-dimensional mixed convection flow of a micropolar fluid past a vertical stretching permeable surface saturated in porous medium taking into account the effect of thermal radiation. The governing system of partial differential equations describing the problem are converted into a system of non-linear ordinary differential equations using similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is solved numerically using the Chebyshev spectral method. The numerical results for the velocity, the micro-rotation and the temperature are displayed graphically showing the effects of various parameters like the buoyancy parameter, the radiation parameter, the stratification parameter, the permeability parameter and the suction/injection parameter. Moreover, the numerical values of the local skinfriction coefficient, the wall couple stress and the local Nusselt number for these parameters are also tabulated and discussed.

Enhancement of a heat transfer rate of mixed convection flow in a three-dimensional vertical channel with insertion of a moving slender block is investigated numerically. A slender block is installed along the direction of the channel flow, and the movement of the slender block is in periodic motion and transverse to the channel flow. The interaction between the moving block and the channel flow destroys and suppresses the velocity and thermal boundary layers on the heat surface periodically. Various ratios of the Richardson numbers (Gr/Re2) are simulated. The results show that under a higher velocity of the channel flow and a lower magnitude of Gr/Re2, the enhancement of heat transfer rate is better. Oppositely, under a lower velocity of the channel flow and a higher magnitude of Gr/Re2, the effect of natural convection driven by the buoyancy force is stronger and it is unfavorable to the heat transfer. A counter effect of the heat transfer rate is observed. These phenomena which are seldom analyzed before by numerical simulation are carried out in this study.

A fully higher-order compact (HOC) finite difference scheme on the 9-point two-dimensional (2D) stencil is formulated for solving the steady-state laminar mixed convection flow in a lid-driven inclined square enclosure filled with water-Al2O3 nanofluid. Two cases are considered depending on the direction of temperature gradient imposed (Case I, top and bottom; Case II, left and right). The developed equations are given in terms of the stream function-vorticity formulation and are non-dimensionalized and then solved numerically by a fourth-order accurate compact finite difference method. Unlike other compact solution procedure in literature for this physical configuration, the present method is fully compact and fully higher-order accurate. The fluid flow, heat transfer and heat transport characteristics were illustrated by streamlines, isotherms and averaged Nusselt number. Comparisons with previously published work are performed and found to be in excellent agreement. A parametric study is conducted and a set of graphical results is presented and discussed to elucidate that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by inclination of the enclosure at moderate and large Richardson numbers.

A mathematical model for the steady, mixed convection heat and mass transfer along a semi-infinite vertical plate embedded in a micropolar fluid in the presence of Soret and Dufour effects is presented. The non-linear governing equations and their associated boundary conditions are initially cast into dimensionless forms using local similarity transformations. The resulting system of equations is then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The non-dimensional velocity, microrotation, temperature and concentration profiles are displayed graphically for different values of coupling number, Soret and Dufour numbers. In addition, the skin-friction coefficient, the Nusselt number and Sherwood number are shown in a tabular form.

Fluids engineering is extremely important in a wide variety of materials processing systems, such as soldering, welding, extrusion of plastics and other polymeric materials, Chemical Vapor Deposition (CVD), composite materials manufacturing. In particular, mixed convection due to moving surfaces is very important in these applications. Mixed convection in a channel, as a result of buoyancy and motion of one of its walls has received little research attention and few guidelines are available for choosing the best performing channel configuration, particularly when radiative effects are significant. In this study a numerical investigation of the effect of radiation on mixed convection in air due to the interaction between a buoyancy flow and an unheated moving plate induced flow in a uniformly heated convergent vertical channel is carried out. The moving plate has a constant velocity and moves in the buoyancy force direction. The principal walls of the channel are heated at uniform heat flux. The numerical analysis is accomplished by means of the commercial code Fluent. The effects of the wall emissivity, the minimum channel spacing, the converging angle and the moving plate velocity are investigated and results in terms of air velocity and temperature fields inside the channel and wall temperature profiles, both of the moving and the heated plates, are given. Nusselt numbers, both accounting and not for the radiative contribution to heat removal, are also presented.

This study investigates the problem of non-Newtonian liquid evaporation from an impermeable vertical plate in a porous medium under mixed convection conditions. The analysis examines the effects of non-Darcian flow phenomena on the evaporation process and investigates the heat and mass transfer characteristics under a range of flow conditions in the aiding and opposing flow types. The parameters of interest include Rak,non, Pex,non, Pr and Sc. The data required for the calculations include a fixed wall temperature of Tw = 45°C, a free flow temperature of T∞ = 20°C and an air free flow rate of u∞ = 4m/sec and the corresponding humidity of 50% flows over fixed temperature and moist wall.

The results indicate that an increasing buoyancy force enhances the mixing effect and therefore improves the rate of heat transfer, the latent heat flux is the primary mode of heat transfer in evaporation processes and the velocity gradient at the wall increases with an increasing buoyancy effect. Furthermore, the evaporation rate increases with a reducing flow index and an increasing buoyancy effect.

The objective of the present study is to investigate the buoyancy effects induced by various body forces in non-isothermal rotating fluids. The buoyancy effects stemmed from the gravity, the centrifugal and Coriolis forces generated by system rotation, and the curvilinear motion of the fluids are all taken into account. Mixed convection between two disks rotating at different rates is employed as the physical model. The present work is the first study for detailed investigation of the various buoyancy forces in the class of non-isothermal flows. Complete system of axially-symmetric thermal flow model with assumption of Boussinesq fluids is formulated. By a scaling analysis and the solutions of a novel similarity model developed in this work, the relative importance of the buoyancy effects induced by various body forces is explored. The present work discloses the significance of the rotation-induced buoyancy effects under various conditions and is useful in understanding the mechanisms as well as modeling the mixed convection heat transfer in the class of rotating thermal flows.