Investigation of transient conduction–radiation heat transfer in a square cavity using combination of LBM and FVM

In this paper, the effect of surface radiation in a square cavity containing an absorbing, emitting and scattering medium with four heated boundaries is investigated, numerically. Lattice Boltzmann method (LBM) is used to solve the energy equation of a transient conduction–radiation heat transfer problem and the radiative heat transfer equation is solved using finite-volume method (FVM). In this work, two different heat flux boundary conditions are considered for the east wall: a uniform and a sinusoidally varying heat flux profile. The results show that as the value of conduction–radiation decreases, the dimensionless temperature in the medium increases. Also, it is clarified that, for an arbitrary value of the conduction–radiation parameter, the temperature decreases with decreasing scattering albedo. It is observed that when the boundaries reflect more, a higher temperature is achieved in the medium and on boundaries.     

Heat Transfer in a Micropolar Fluid along a Non-linear Stretching Sheet with a Temperature-Dependent Viscosity and Variable Surface Temperature

In this paper, heat transfer characteristics of a two-dimensional steady hydromagnetic natural convection flow of a micropolar fluid passed a non-linear stretching sheet taking into account the effects of a temperature-dependent viscosity and variable wall temperature are studied numerically for local similarity solutions by applying the Nachtsheim-Swigert iteration method. The results corresponding to the dimensionless temperature profiles and the local rate of heat transfer are displayed graphically for important material parameters. The results show that in modeling the thermal boundary layer flow with a temperature-dependent viscosity, consideration of the Prandtl number as a constant within the boundary layer produces unrealistic results and therefore it must be treated as a variable rather than a constant within the boundary layer. The results also show that the local rate of heat transfer strongly depends on the non-linear stretching index and temperature index.     

Hydromagnetic stagnation point flow by a perturbation technique

An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow and heat generating/absorbing fluid at the stagnation point of an isothermal two-dimensional porous body immersed in a fluid saturated porous medium. The results are obtained by solving the coupled non-linear partial differential equations describing the conservation of mass, momentum and energy by a perturbation technique [A. Aziz, T.Y. Na, Perturbation Methods in Heat Transfer, Springer-Verlag, Berlin, 1984 (pp. 1–184), R. Kenneth Cramer, Shih-I Pai, Magnetofluid Dynamics for Engineers and Applied Physicists, McGraw-Hill Book Company, New York, 1973 (pp. 164–171).]. These results are presented to illustrate the influence of the Hartmann number, Prandtl number, and dimensionless heat generation/absorption coefficient and suction injection parameter. Numerical results for the dimensionless velocity profiles, the temperature profiles, the local friction coefficient and the local Nusselt number are presented for various parameters. These effects of the different parameters on the velocity and temperature as well as the skin friction and wall heat transfer are presented graphically.     

Heat transfer in boundary layer flow of a micropolar fluid past a curved surface with suction and injection

Van Dyke's singular perturbation technique has been used to study the heat transfer in the flow of a micropolar fluid past a curved surface with suction and injection. The conditions for similar solutions of the thermal boundary layer equations have been obtained. In addition to the usual “no slip” condition for velocity, the two types of boundary conditions used for microrotation are: (i) no relative spin on the boundary; (ii) the anti-symmetric part of the stress tensor vanishes at the boundary. The effect of suction or injection on velocity, microrotation, temperature, skin friction coefficient, wall couple stress coefficient, displacement and momentum thicknesses, rate of heat transfer and adiabatic wall temperature have been studied. It is observed that with the increase of injection velocity, the thickness of the boundary layer is increased and the local drag is reduced. A comparison with the results obtained for a Newtonian fluid reveals that the microelements present in the fluid reduce the velocity and frictional drag, and cool the boundary.     

Effects of tangential and radial velocity on fluid flow and heat transfer for flow through a pipe with twisted tape insert—laminar flow

The present study reports the numerical analysis of fluid flow and heat transfer in a pipe with full length twisted tape insert. The investigation is carried out for five different twist ratios of 4, 5, 6, 8 and 10 at 100 ≤ Re ≤ 1000. The velocity field in terms of streamwise, tangential and radial velocity and temperature field are studied as a function of Reynolds number and twist ratio. The variation of friction factor and Nusselt number with Reynolds number for different twist ratios is also presented. The heat transfer enhancement due to insertion of twisted tape mainly comes from the tangential and radial components of velocities, which are regarded as secondary fluid motion. It is evident from the results that with increase in Reynolds number the axial convection increases. However, with the decrease in the twist ratio, the tangential and radial convection increases, leading to increased heat transfer. The secondary flow affects the thermal boundary layer inside the tube and increases the cross-flow mixing, which increases the heat transfer. The correlations for prediction of friction factor and Nusselt number based on the numerical data are also proposed.     

Effects of Combined Heat and Mass Transfer on Entropy Generation due to MHD Nanofluid Flow over a Rotating Frame

The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe3O4 based Brinkmann type nanofluid flow over a vertical rotating frame. The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers, including Grashof, Eckert, and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles, Hall current, magnetic field, viscous dissipation, and the chemical reaction on the physical quantities. The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg (RKF-45) method. The variation of dimensionless velocity, temperature, concentration, skin friction, heat, and mass transfer rate, as well as for entropy generation and Bejan number with governing parameters, are presented graphically and are provided in tabular form. The results reveal that the Nusselt number increases with an increase in the solid volume fraction of nanoparticles. Furthermore, the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number.     

Non-linear radiation effects on magnetic/non-magnetic nanoparticles with different base fluids over a flat plate

This work investigates the two-dimensional steady convective boundary layer flow and heat transfer of Newtonian/non-Newtonian base fluids with magnetic/non-magnetic nanoparticles over a flat plate which incorporates non-linear thermal radiation and slip effects. We considered magnetite and aluminium oxide as magnetic and non-magnetic nanoparticles suspending inside the two sorts of base fluids specifically Water and Sodium Alginate. For physical significance we analyzed the behavior on non-Newtonian profiles by employing Casson model individually. The particular intrigue lies in looking the impacts of non-linear thermal radiation on the behavior of the flow. The solution of wide class of boundary value problems are facilitated by the change of the partial differential equations administering the flow utilizing similarity transformations into ordinary differential equations. The ODE’s are numerically handled by applying fourth order Runge-Kutta integration scheme in association with shooting procedure. The novel results for the dimensionless velocity and temperature inside the boundary layer are exhibited graphically for various parameters that describe the flow. A graphical demonstration is given for the skin friction coefficient and the local Nusselt number.     

Thermal boundary layers over a shrinking sheet: an analytical solution

In this paper, the heat transfer over a shrinking sheet with mass transfer is studied. The flow is induced by a sheet shrinking with a linear velocity distribution from the slot. The fluid flow solution given by previous researchers is an exact solution of the whole Navier–Stokes equations. By ignoring the viscous dissipation terms, exact analytical solutions of the boundary layer energy equation were obtained for two cases including a prescribed power-law wall temperature case and a prescribed power-law wall heat flux case. The solutions were expressed by Kummer’s function. Closed-form solutions were found and presented for some special parameters. The effects of the Prandtl number, the wall mass transfer parameter, the power index on the wall heat flux, the wall temperature, and the temperature distribution in the fluids were investigated. The heat transfer problem for the algebraically decaying flow over a shrinking sheet was also studied and compared with the exponentially decaying flow profiles. It was found that the heat transfer over a shrinking sheet was significantly different from that of a stretching surface. Interesting and complicated heat transfer characteristics were observed for a positive power index value for both power-law wall temperature and power-law wall heat flux cases. Some solutions involving negative temperature values were observed and these solutions may not physically exist in a real word.     

液滴与壁面撞击流动及传热特性研究

采用Level Set-VOF模拟单液滴撞击壁面的铺展行为及液滴初速度、初始直径及液膜厚度对液滴撞壁传热特性的影响。研究表明:液滴初始速度较大,撞击壁面后发生强烈反弹,液滴在表面回缩破碎及铺展破碎能力加强,导致表面传热系数随之增大;随着液滴初始直径增大,液滴铺展破碎的发生,将对表面传热起促进作用;初始液膜越厚,撞击后液滴溅射能力被削弱且在表面铺展趋势延缓,因此不利于热量迅速传递。     

Heat transfer in micropolar boundary layer flow over a flat plate

Boundary layer solutions are presented to study the steady state heat transfer from a semi-infinite flat plate to a micropolar fluid. The boundary conditions of isothermal wall, constant surface heat flux and insulated wall with viscous dissipation effects have been treated in this paper. Numerical results for the temperature distribution and the missing wall values of the thermal functions have been given. The range of Prandtl numbers investigated was from 10 to 1000 while the dimensionless grouping of the material properties was allowed to vary over a wide range.     

Entropy Generation for Flow and Heat Transfer of Sisko-Fluid Over an Exponentially Stretching Surface

In the present study, the effects of the magnetic field on the entropy generation during fluid flow and heat transfer of a Sisko-fluid over an exponentially stretching surface are considered. The similarity transformations are used to transfer the governing partial differential equations into a set of nonlinear-coupled ordinary differential equations. Runge-Kutta-Fehlberg method is used to solve the governing problem. The effects of magnetic field parameter M, local slip parameter λ, generalized Biot number γ, Sisko fluid material parameter A, Eckert number Ec, Prandtl number Pr and Brinkman number Br at two values of power law index on the velocity, temperature, local entropy generation number N_G and Bejan number Be are inspected. Moreover, the tabular forms for local skin friction coefficient and local Nusselt number under the effects of the physical parameters are exhibited. The current results are helpful in checking the entropy generation for Sisko-fluid. It is found that, an extra magnetic field parameter makes higher Lorentz force that suppresses the velocity. For shear thinning fluids (n < 1), the temperature dominates and the velocity rises. Local entropy generation number is more for larger generalized Biot number, magnetic field parameter and Brinkman number. The local skin friction coefficient increases as magnetic field parameter and material parameter are increase and it decreases as local slip parameter increases. The local Nusselt number decreases as magnetic field parameter, local slip parameter and Eckert number are increase, while it increases as material parameter, generalized Biot number and Prandtl number are increase.     

开槽对管内填充金属泡沫对流换热的影响

采用数值模拟方法建立计算机CPU翅片散热器相同尺寸的金属泡沫模型,研究了矩形管内插入金属泡沫后的流动和换热性能。研究表明,数值模拟结果与文献实验结果吻合较好;开槽深度对金属泡沫换热性能具有明显影响,在低雷诺数下,努塞尔数随着无因次高度H/D(开槽深度和迎风面水力直径比值)的增加而减小;在高雷诺数下,努塞尔数随着H/D的增加先增大后减小,H/D在0.146~0.438范围内,努塞尔数比不开槽金属泡沫的大。引入基于渗透率的雷诺数整理数据得到了管内填充开槽金属泡沫的强制对流换热准则方程。     

Three-dimensional wall-bounded laminar boundary layer with span-wise cross free stream and moving boundary

In the current work, the 3D boundary layers of wall-bounded flow configurations were extended to the situations with span-wise cross moving boundary and free stream. The unsteady boundary layer is also addressed for the Falkner–Skan wedge flow with a span-wise oscillating wall or oscillating free stream. The span-wise secondary boundary layer equation is obtained using similarity transformation technique and solved analytically in terms of the primary stream-wise boundary layer flow solutions. Different fluid motion behaviors are found for these new solutions. It is found that for the span-wise secondary boundary layer flow there is no flow separation for any wall cross moving velocity, which is different from the primary stream-wise boundary layers with a reverse flow. For the unsteady boundary layer with an oscillating wall or free stream, it is seen that the solution is different from the Stokes oscillating plate or free stream problem. The unsteady wall drag increases with the increase in the oscillating frequency and decreases with increasing the primary span-wise free stream magnitude. The velocity overshooting near the wall is also seen for an oscillating free stream for a large oscillating frequency or a lower primary stream-wise free stream magnitude.     

Viscous flow due to an exponentially shrinking permeable sheet in nanofluid in presence of slip

Classical problem of steady boundary layer flow of nanofluid over an exponentially permeable shrinking sheet in presence of slip is investigated. The model used for nanofluid includes Brownian motion and thermophoresis effects. The governing equations for momentum, energy, and nanofluid solid volume fraction are transformed to ordinary differential equations with the help of similarity transformations and then solved numerically using fourth order Runge–Kutta method with shooting technique. It is found that the governing parameters, viz. the suction/blowing parameter, velocity slip, thermal and mass slip parameters, Brownian motion parameter, thermophoresis parameter, Prandtl number, and Lewis number significantly affect the flow field, heat, and mass transfer. The results obtained indicate that the dual solutions exist for certain values of the mass suction parameter. Velocity increases whereas the temperature and nanoparticle volume fraction decrease due to suction through the porous sheet. It is noted that with the increase in velocity slip fluid velocity increases whereas temperature and concentration decrease. Due to increase in thermal slip and mass slip both temperature and concentration decrease.     

Free convection in the laminar boundary layer flow of a thermomicropolar fluid past a vertical flat plate with suction/injection

Summary The effect of suction/injection in the laminar free convection flow of a thermomicropolar fluid past a nonuniformly heated vertical flat plate has been considered. The conditions under which similarity exists have been examined. The resulting system of non-linear ordinary differential equations has been solved numerically after transforming the infinite domain of boundary layer coordinate into a finite domain. The effects of variation of the boundary condition parameter and suction/injection parameter on the velocity, microrotation and temperature fields and the heat transfer coefficient have been studied graphically. The skin-friction parameter and the gradient of microrotation on the wall have been tabulated. It is found that there is significant increase in velocity, skin-friction and the heat transfer coefficient with the decreasing concentration of microelements.With 4 Figures     

Influences of fluid property variation on the boundary layers of a stretching surface

Summary. In this work, the influences of temperature-dependent fluid properties on the boundary layers over a continuously stretching surface with constant temperature are investigated. Based on the boundary layer assumptions, the coupled similarity equations are obtained for special situations, in which the fluid density and heat capacity are assumed without dependence on the temperature. Those similarity equations are solved numerically. The influences of property variation on wall stresses and heat fluxes are discussed. It is found that the property variation can influence the distributions of both fluid velocity and temperature across the boundary layers. For the thermal boundary layer, using mean properties evaluated at the average temperature of wall and ambient fluid can give good results for the temperature distribution. However, for the momentum boundary layer, the difference of velocity distributions can be large.     

Heat transfer in a viscoelastic boundary layer flow through a porous medium

This paper examines the viscoelastic fluid flow and heat transfer characteristics in a saturated porous medium over an impermeable stretching surface with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for two different heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). The governing equations for the boundary layer flow problem result similar solutions. For the specified five boundary conditions, it is not possible to solve directly the resulting sixth-order nonlinear ordinary differential equation. For the present incompressible boundary layer flow problem with constant physical parameters, the momentum equation is decoupled from the energy equation. Two closed–form solutions for the momentum equation are obtained and identified the realistic solution of the physical problem. Exact solution for the velocity field and the skin-friction are obtained. Also, the solution for the temperature and the heat transfer characteristics are obtained in terms of Kummers function. Asymptotic results for the temperature function for large Prandtl numbers are presented. The work due to deformation in the energy equation, which is essential and escaped from the attention of researchers while formulating the visco-elastic boundary layer flow problems, is considered. Drastic variation in the values of heat transfer coefficient is observed when the work due to deformation is ignored.The authors would like to thank the reviewers for their valuable comments/ suggestions to improve the clarity of the paper.     

Compressible turbulent boundary layer on a permeable plate with injection of foreign gas

A numerical solution is obtained for equations of motion, diffusion, and energy using a three-parameter model of turbulence for boundary layer with different thermal boundary conditions on a permeable plate with injection of foreign gas. For an ideal gas with constant values of Prandtl and Schmidt numbers, the numerical solution is compared with limiting dependences for dimensionless temperature and enthalpy of gas on the wall. For helium/xenon mixtures with a low value of Prandtl number, the effect of intensity of injection and of the values of Reynolds and Mach numbers on the integral and local characteristics of flow and heat and mass transfer is investigated.     

The thermal state of a porous wall under conditions of transpiration cooling

Results of numerical experiment are used for analysis of fields of temperature in a laminar boundary layer, in a porous wall, and in a cooling gas delivery chamber, as well as for analysis of heat transfer and of distribution of the temperature difference between the cooling gas and the porous wall frame and cooling efficiency. It is demonstrated that heat transfer between a porous wall of finite thickness and a high-temperature gas flow differs significantly from heat transfer with preassignment of the same intensity of injection and of the homogeneous thermal boundary condition directly on the surface subjected to flow. One of the reasons for this is the formation of wall temperature variable along the boundary layer.     

Unsteady incompressible boundary layer flow of a micropolar fluid at a stagnation point

The flow, heat and mass transfer on the unsteady laminar incompressible boundary layer in micropolar fluid at the stagnation point of a 2-dimensional and an axisymmetric body have been studied when the free stream velocity and the wall temperature vary arbitrarily with time. The partial defferential equations governing the flow have been solved numerically using a quasilinear finite-difference scheme. The skin friction, microrotation gradient and heat transfer parameters are found to be strongly dependent on the coupling parameter, mass transfer and time, whereas the effect of the microrotation parameter on the skin friction and heat transfer is rather weak, but microrotation gradient is strongly affected by it. The Prandtl number and the variation of the wall temperature with time affect the heat-transfer very significantly but the skin friction and micrortation gradient are unaffected by them.