Thermal Interaction between Two Forced‐Convection Boundary Layers across a Conductive Solid Wall

This paper presents an analytical model to the problem of thermal interaction between two forced convection layers of parallel flow on opposite wall sides. The problem is formulated in dimensionless terms to generalize the solution. The two convection layers are analyzed separately by employing the integral technique. The two analyses are then coupled by applying the solid–fluid interfacial conditions. The study indicates that the thermal interaction process is governed mainly by two dimensionless parameters relating the heat transfer effectiveness of two interactive convection modes and wall conduction. The effects of governing parameters on the flow and heat transfer characteristics of two coupled convection layers are documented. Results regarding mean conjugate Nusselt number are obtained for wide ranges of governing parameters.     

Mixed Convection Over a Vertical Plate in a Doubly Stratified Fluid‐Saturated Non‐Darcy Porous Medium with Cross‐Diffusion Effects

The present article investigates the influence of Dufour and Soret effects on mixed convection heat and mass transfer over a vertical plate in a doubly stratified fluid‐saturated porous medium. The plate is maintained at a uniform and constant wall heat and mass fluxes. The Darcy–Forchheimer model is employed to describe the flow in porous medium. The nonlinear governing equations and their associated boundary conditions are initially transformed into dimensionless forms. The resulting system of nonlinear partial differential equations is then solved numerically by the Keller‐box method. The variation of the dimensionless velocity, temperature, concentration, heat, and mass transfer rates for different values of governing parameters involved in the problem are analyzed and presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21114     

Numerical computation on Marangoni convective flow of two‐phase MHD dusty nanofluids under Brownian motion and thermophoresis effects

The current theoretical study describes the Marangoni thermal convective flow of magnetohydrodynamic dusty nanofluids along a wavy vertical surface. The two‐phase mathematical model is developed under the influence of thermal radiation and exponentially varying space‐dependent heat source. Pure and hybrid nanoparticles together with dust particle suspension in the base fluid are taken into consideration to characterize the behavior of the flow. Brownian motion and thermophoresis mechanisms are considered, since it enhances the convection features of dusty nanofluid. Appropriate transformations are adopted to modify the flow governing equations and boundary conditions to dimensionless form. The forward finite difference scheme is implemented to illustrate the resultant coupled partial differential equations. The Newton quasi‐linearization technique is utilized to reduce the nonlinear system into a linear form, which is solved thereafter by Thomas algorithm. The responses of velocity, temperature, concentration, friction factor, and heat and mass transfer rate profiles with various governing parameters are discussed and portrayed graphically. The study evidences that the radiation and space‐dependent heat generating parameters strengthen the temperature distribution. Also, the heat transfer rate appreciably rises with the increment in Marangoni convection. The solution methodology and accuracy of the model is validated by generating the earlier outcomes for nonradiating nanofluid flow without heat source/sink.     

Transient heat transfer in a heat‐generating fin with radiation and convection with temperature‐dependent heat transfer coefficient

The transient heat transfer in a heat‐generating fin with simultaneous surface convection and radiation is studied numerically for a step change in base temperature. The convection heat transfer coefficient is assumed to be a power law function of the local temperature difference between the fin and its surrounding fluid. The values of the power exponent n are chosen to include simulation of natural convection (laminar and turbulent) and nucleate boiling among other convective heat transfer modes. The fin is assumed to have uniform internal heat generation. The transient response of the fin depends on the convection‐conduction parameter, radiation‐conduction parameter, heat generation parameter, power exponent, and the dimensionless sink temperature. The instantaneous heat transfer characteristics such as the base heat transfer, surface heat loss, and energy stored are reported for a range of values of these parameters. When the internal heat generation exceeds a threshold the fin acts as a heat sink instead of a heat source. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21012     

Fluid‐to‐fluid scaling of heat transfer to mixed convection flow of supercritical pressure fluids

Fluid‐to‐fluid scaling for supercritical heat transfer can effectively reduce the difficulty and cost of heat transfer experiments in supercritical boilers and supercritical water reactors and can reduce the number of experiments by converting experimental data of the model fluid to the prototype fluid in organic Rankine cycles. Currently, most existing scaling methods are only suitable for forced convection, while few are developed for mixed convection where buoyancy significantly affects the heat transfer. This paper attempts to extend the applicability of scaling method to mixed convection with the aid of computational fluid dynamic simulations. The scaling parameters were analyzed first and then the shear‐stress transport k‐ω model was used to analyze the supercritical heat transfer characteristics of water and R134a to provide further information for developing a dimensionless number. The results show that significant variations of properties and flow parameters occur in the layer of y⁺ = 5 to 100 and the axial velocity gradient in this layer changes in quite a similar manner to the wall temperature. Based on numerical results, the axial velocity gradient was used with a thermal resistance analogy to derive a new dimensionless number, Re^?0.9π_A , to scale the mass flux. Then, a set of fluid‐to‐fluid scaling laws were developed to predict the heat transfer to supercritical fluids. To validate the newly proposed scaling laws, well‐developed correlations were used for forced convection flow and a direct validation method was developed for buoyancy‐influenced flow. Results show that this new scaling method exhibits reasonable accuracy for both forced and mixed convection heat transfer with supercritical fluids.     

Numerical analysis of convective heat transport in a porous semi‐trapezoidal enclosure with radiation effect

A theoretical and numerical study of natural convection of two‐dimensional laminar incompressible flow in a semi‐trapezoidal porous enclosure in the presence of thermal radiation is conducted. The semi‐trapezoidal enclosure has an inclined left wall that in addition to the right vertical wall is maintained at a constant temperature, whereas the remaining (horizontal) walls are adiabatic. The Darcy‐Brinkman isotropic model is utilized. The governing partial differential equations are transformed using a vorticity stream function and nondimensional quantities and the resulting governing nonlinear dimensionless equations are solved using the finite difference method with incremental steps. The impacts of the different model parameters (Rayleigh number [Ra], Darcy number [Da], and radiation parameter [Rd]) on the thermofluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with the greater Darcy parameter (permeability). The flow is accelerated with the increasing buoyancy effect (Rayleigh number) and heat transfer is also increased with a greater radiative flux. The present numerical simulations are more relevant to hybrid porous media solar collectors.     

Optimal design with entropy generation minimization approach in combined natural convection with surface radiation in a two‐dimensional enclosure

Analysis of combined natural convection with surface radiation in a two‐dimensional enclosure is carried out. To search the optimal location of the heat source, the entropy generation minimization approach and conventional heat transfer parameters are used and compared. Air is considered as an incompressible fluid and transparent media filling the enclosure with a steady and laminar regime. The enclosure internal surfaces are also gray, opaque, and diffused. The governing equations are solved using the finite difference approach. The results show that with increase in emissivity, entropy generation decreases, and as the Rayleigh number increases, the rate of entropy generation increases. Furthermore, optimum design with the maximum dimensionless temperature and convective Nusselt number confirms the applicability of the second law for optimal design.     

Nonsimilar solutions for mixed convection of water at 4°C over a vertical surface with a convection boundary condition in a porous medium

A boundary layer analysis has been presented for the mixed convection of water at 4°C over a vertical plate embedded in a porous medium. The Robin or convective boundary condition at the surface has been considered where the heat lost from the surface is the product of a heat transfer coefficient and the temperature difference between the surface and the free stream. The governing non‐similar boundary layer equations for both the forced and free convection dominated regimes were solved numerically by means of an implicit finite difference method. The friction factor and dimensionless heat transfer rate (Nusselt number) are presented for several values of the dimensionless heat transfer coefficient and buoyancy parameter. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21022     

Nonlinear convection in an elasticoviscous fluid‐saturated anisotropic porous layer using a local thermal nonequilibrium model

By adopting a perturbation method and a local thermal nonequilibrium model, nonlinear thermal convection in an anisotropic porous layer saturated by an elasticoviscous fluid is investigated. An elasticoviscous fluid is modeled by a modified Darcy‐Oldroyd‐B model, and the fluid and solid phase temperatures are represented using a two‐field model for the heat transport equation. Anisotropy in permeability and fluid and solid thermal conductivities are considered. A cubic Landau equation is derived separately to study the stability of bifurcating solution of both stationary and oscillatory convection, and the results of linear instability theory are delineated. The boundary between stationary and oscillatory convection is demarcated by identifying codimension‐two points in the viscoelastic parameters plane. It is found that the subcritical instability is not possible, and the linear instability analysis itself completely captures the behavior of the onset of convection. Heat transfer is obtained in terms of Nusselt number, and the effect of governing parameters on the same is discussed. The results of the Maxwell fluid are obtained as a particular case from the present study.     

Numerical investigation on mixed convection in a non-Newtonian fluid inside a vertical duct

This paper reports a numerical study of the thermal and fluid-dynamic behaviour of laminar mixed convection in a non-Newtonian fluid inside a vertical duct enclosed within two vertical plates that are plane and parallel, having linearly varying wall temperatures. The other inlet conditions consist of a parabolic distribution of the velocity field and a constant fluid temperature. The problem is assumed to be steady and two-dimensional. The formulation of a mathematical model in dimensionless co-ordinates and the discretisation of the governing equations by means of the finite difference method, have made it possible to create a numerical code developed in Matlab environment. The study was focused on the simultaneous presence and on the mutual interaction of natural and forced convection, starting from the effects of the re-circulation on the heat transfer. The quantitative results of the analysis, which are strongly affected by the variation of the Grashof number and of the exponent of the power law, are given in terms of graphic visualisations of the fluid velocity profiles and, when the governing parameters vary, of the various geometries characterising the heat transfer.     

A non‐Fourier heat flux model for magnetohydrodynamic micropolar liquid flow across a coagulated sheet

In this analysis, a heat transfer extrusion system was made by using a modified heat flux model, namely, the Cattaneo‐Christov heat flux. In the present study, we examined the effect of Arrhenius activation energy on magnetohydrodynamic mixed convection stagnation point flow of a micropolar fluid over a variable thickened surface in the attendance of Brownian motion. The fluid motion is assumed to be steady and laminar. The combined influence of heat and mass transfer aspects are scrutinized. First, suitable transformations are considered to modify the governing partial differential equations as ordinary differential equations and revealed by the consecutive application of numerical procedures like shooting and Runge‐Kutta‐Fehlberg. Graphs are delineated to scrutinize the effects of sundry dimensionless parameters on the flow fields. We found that, the present results made a good agreement with the existing results. We observed that there is an enhancement in the fields of concentration with thermophoresis and activation energy parameters but an opposite trend is noticed for the Brownian motion parameter. Also, it is interesting to note that the buoyancy and the primary slip parameters are increasing functions of velocity fields.     

Two‐phase natural convection analysis and hybrid nanoparticle migration around micromixer blades

In this paper, numerical investigations are presented for hybrid nanoparticle migration and free convection heat transfer of two kinds of nanofluids in a micromixer at the fixed propeller condition. The inner blades and outer crust of the micromixer are kept at constant hot and cold temperatures, respectively. Two kinds of hybrid nanofluids, TiO₂‐CuO water and ethylene glycol‐(MoS₂‐SiO₂), are considered. The governing equations including velocity, pressure, temperature formulation, and nanoparticle concentrations are solved by a partial differential equation solver based on the Galerkin finite element method. The results are discussed based on the governing parameters, such as nanoparticle volume fraction, thermal and solutal Rayleigh numbers. The average Nusselt number was found to increase with the increasing nanoparticle volume fractions. Also, increasing the thermal Rayleigh number enhanced heat transfer while the solutal Rayleigh number has an insignificant effect on it. More importantly, increasing the thermal Rayleigh number assisted avoiding the agglomeration of nanoparticles around the blades and ensured more uniform nanoparticle distribution.     

g‐Jitter–Induced Electrothermoconvection in a Dielectric Fluid Saturated Porous Layer

This paper presents linear and nonlinear stability analyses of thermal convection in a dielectric fluid saturated sparsely packed porous layer subject to the combined effect of time‐periodic gravity modulation (GM) and an AC electric field. In the domain of linear theory, the critical stability parameters are computed by the regular perturbation method in the form of a perturbation series in powers of frequency of modulation. The local nonlinear theory based on the truncated Fourier series method gives information on convection amplitudes and heat transfer. The principle of the exchange of stabilities is found to be valid and subcritical instability is ruled out. Based on the governing linear autonomous system, several qualitative results on stability are discussed. The sensitive dependence of the solution of a Lorenz system of electrothermal convection subject to the choice of initial conditions points to the possibility of chaos. Low‐frequency g‐jitter is found to have a significant stabilizing influence, which is in turn diminished by an imposed AC electric field. The role of sparseness of the porous layer, viscosity ratio, and normalized porosity on the stability criterion and on heat transport is determined.     

Free Convective Flow of Pseudo‐Plastic and Newtonian Fluid Past a Convectively Heated Vertical Plate in a Darcian Porous Medium with Heat Generation/Absorption

We study the effect of thermal convective boundary condition and yield stress on free convection heat transfer for a pseudo‐plastic and Newtonian fluid past a permeable vertical flat plate which is embedded in a Darcian porous medium in the presence of heat generation/absorption numerically. Instead of using similarity transformations available in the literature, we have developed them by one point transformation and hence transform the governing boundary layer equations into corresponding similarity equations. The resulting similarity equations were solved using Runge–Kutta–Fehlberg fourth fifth (RKF45) order numerical method. The effect of the governing parameters, namely the power index of pseudo‐plastic fluids n, the rheological parameter Ω, heat generation/absorption parameter Q, suction/injection parameter , and the convective heat parameter B on the dimensionless velocity, the temperature and the heat transfer rates were investigated. A close agreement is found between our results and published results. Our present study finds application in printing and polymer industries and fluid phenomena associated with concentrated suspensions.     

Unsteady Mixed Convection Flow of a Rotating Second‐Grade Fluid on a Rotating Cone

In the present article, we have investigated the unsteady mixed convection flow of a rotating second‐grade fluid in a rotating cone with time‐dependent angular velocities. Two cases of heat transfer are presented which are known as (i) prescribed wall temperature (PWT) and (ii) prescribed heat flux (PHF). The governing coupled nonlinear partial differential equations are simplified with the help of transformations and non‐dimensional similar and non‐similar variables, and solved analytically with the help of the homotopy analysis method (HAM). The effects of pertinent parameters on the velocity, temperature, concentration, skin friction coefficients, Nusselt number, and Sherwood number have been examined through graphs. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 204–220, 2014; Published online 30 August 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21072     

Thermophoretic Deposition Effect on Transient Free Convection Hydromagnetic Flow Along an Accelerated Inclined Permeable Surface with Time‐Dependent Temperature and Concentration

This work investigates the thermophoretic deposition effect on a transient free convection hydromagnetic flow along an accelerated infinite inclined permeable surface in the presence of heat generation, suction (or injection), thermal diffusion, and diffusion‐thermo taking into account that the surface temperature and concentration are time dependent. The governing partial differential equations are transformed into a set of nonlinear coupled ordinary differential equations, which are then solved numerically by applying the shooting method with a sixth‐order Runge–Kutta integration scheme. Graphical results for the dimensionless velocity, temperature, concentration distributions as well as wall thermophoretic velocity are reported and examined for the pertinent parameters showing the interesting aspects of the obtained solutions. The local skin‐friction coefficient, the local Nusselt number, and the local Sherwood number are also computed. The results show that higher flow rates can be obtained when the temperature and concentration are time independent. Smaller buoyancy is observed for higher temperature indexes. Wall thermophoretic velocity is decreased with the increasing values of the Prandtl number, the thermophoretic parameter, as well as heat generation parameter. The results further show that the presence of thermal diffusion and diffusion‐thermo intensify the shear stress but reduce the rate of heat as well as mass transfer. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(4): 352–367, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21081     

Entropy analysis of a flow past a heat‐generated bluff body

Cooling of a bluff body is a topic of interest for many engineers and scientists. Forced convection over the bluff body generates flow separation, which in turn affects the heat transfer characteristics and increases the irreversibilities involved in the system. In the present study, flow over a rectangular solid body with constant heat flux is considered. The governing flow and energy equations are solved in two‐dimensional space numerically using a control volume approach. In order to investigate the effect of the fluid properties on the heating process, three different fluids are taken into account. These are air, ethylene glycol and therminol. To determine the irreversibilities involved in the system, entropy analysis is carried out. It is found that fluid properties have considerable effect on the entropy generation. The entropy generation due to heat transfer well exceeds the entropy generation due to fluid friction. The surface temperature of the solid body highly depends on the cooling fluid employed. Copyright © 1999 John Wiley & Sons, Ltd.     

Coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes

The coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes is investigated numerically. The medium flows in a laminar and fully developed state with a Poiseuille velocity distribution, but the thermal status is developing. By the discrete ordinate method, the nonlinear integrodifferential radiative transfer equation in a cylindrical coordinate form is solved to give the radiative source term in the energy equation of coupled heat transfer. The energy equation is solved by the control volume method. The local Nusselt number and wall heat flux of convection as well as the total wall heat flux are employed to evaluate the influence of radiation heat transfer on convection. The analysis shows that the radiation heat transfer weakens the convection effect, promotes the temperature development, and significantly shortens the tube length with obvious heated/cooled effect. There is an obvious difference between the coupled heat transfer in a heated tube and that in a cooled tube, even though the medium properties are kept constant. The wall emissivity, the medium thermal conductivity and scattering albedo have significant influences on the coupled heat transfer, but the effect of medium scattering phase function is small. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(1): 64–72, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10137     

Three‐dimensional turbulent forced convection around a hot cubic block exposed to a cross‐flow and an impinging jet

A numerical study of a three‐dimensional, turbulent, forced convection flow around a hot cubic block exposed to cross‐flow and an impinging jet is carried out. The standard k‐ε turbulence model is used to study the effects of Reynolds number ratio on the flow and heat transfer. For each value of the Reynolds number of the jet, the Reynolds number ratio is equal to 1, 1.5, and 2. The influence of the channel height and the jet axis location are also examined. The governing equations are solved by using Ansys Fluent software 14.5. Results show that the heat transfer increases with the increase in the Reynolds number ratio. At the top of the cube, better cooling occurs with an increase in the speed of the impinging jet. A reduction in the height of the channel and the displacement of the axis of the jet toward the channel inlet improve the heat transfer. Our simulations are compared with experimental data found in the literature, using different turbulence models.     

Mixed convection heat and mass transfer over a vertical plate in a power‐law fluid‐saturated porous medium with radiation and chemical reaction effects

Mixed convection heat and mass transfer from a vertical plate embedded in a power‐law fluid‐saturated Darcy porous medium with chemical reaction and radiation effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using the shooting method. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21058