Convective Type Boundary Condition Research Articles

Thin film flow of chemically reactive nonlinear thermally radiative magnetized variable viscosity fluid over a stretchable surface with non-uniform heat source/sink and Fick’s mass flux theory

The study of thin film flow over a stretching sheet holds significant importance from an industrial perspective due to its relevance in various manufacturing and engineering processes. In the present investigation, we delved into the combined influence of non-uniform heat source/sink on the governing heat and mass transfer equations in a thin liquid film on a permeable stretching surface. We have considered the nonlinear thermal radiation and implemented convective-type boundary conditions. Our analysis examined the effects of crucial physical parameters, including non-uniform heat source/sink, thermal radiation, chemical reaction, magnetic parameter , Prandtl number, Schmidt number, and unsteadiness parameter in the range [−3.5, 2.0], [−2, 5], [0, 1], [0.3, 4.0], [1, 7], [0.8, 1.7], [0.7, 2.0], respectively. It is found that a non-uniform heat source/sink mitigated the temperature gradient, while an elevation in the Schmidt number intensified the mass transfer rate. The validation process enhanced the robustness and reliability of our numerical simulations.

Linear stability analysis of a solidification process with convection in a bounded region of space

The morphological/dynamic instability of crystallization process in a bounded region in the presence of intense convection in liquid is studied. The paper considers a linear theory of morphological instability with a flat solid-liquid interface on the example of molten metal and magma. The mathematical model includes heat transfer equations and convective type boundary conditions at the interface. The equations for perturbations of the temperature field and interfacial boundary are found, allowing to obtain the dispersion relation. Its analysis has shown the existence of morphological instability of the flat interfacial boundary for a wide range of wavenumbers. Dynamic perturbations (perturbations of the quasi-stationary crystallization velocity) were also analyzed and two solutions for the perturbation frequency were obtained. One of them is stable and the other one is unstable. The system selects one of them depending on the action of convection. The result of morphological and dynamic instability is the appearance of a two-phase region in front of a flat solid-liquid interface. Therefore, the paper also considers the dynamic instability of stationary crystallization with a two-phase region replaced by a discontinuity surface. In this case, the dynamic instability was also found for a wide range of crystallization velocities.

Rheology of hydromagnetic viscoelastic fluid subjected to dissipation aspect

PurposeThe purpose of this paper is to address the impact of gravity induced stretching flow of second grade liquid subject to thermal radiation. The flow is generated by the stretching of an impermeable cylinder. Stagnation point flow is considered. Convective type boundary conditions are applied on temperature and concentration. The present investigation further includes the aspects of magnetohydrodynamics, Joule heating, chemical reaction and viscous dissipation and heat generation/absorption.Design/methodology/approachThe ordinary differential expressions are formed using suitable similarity transformations from the governing partial differential expressions. The subsequent nonlinear ordinary differential expressions are solved analytically using homotopy concept to report the consequences of different dimensionless physical parameters in graphical and tabular forms.FindingsThe results witnessed that increasing values of curvature parameter corresponds to higher temperature and concentration. Besides this, the impacts of destructive and constructive chemical processes on the concentration distribution are noted opposite.Originality/No such analysis has yet been reported.

Heat transport on steady MHD flow of copper and alumina nanofluids past a stretching porous surface

AbstractAn attempt is made to investigate the steady magnetohydrodynamic convective flow of the viscous nanofluid due to a permeable exponentially stretching porous surface. Water is used as a traditional fluid while nanoparticles include copper and alumina. The fluid is electrically conducting, subject to an applied magnetic field with a constant strength. Convective type boundary conditions are employed in modeling the heat transfer process. The nonlinear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations and then solved using the Runge‐Kutta fourth‐order method. A parametric study of the physical parameters is made, and a representative set of numerical results for the velocity and temperature, as well as local shear stress and local Nusselt number, is presented graphically. Hartman number increase diminishes the velocity and has the contrary result in the subjective sense for the mass transfer parameter. An increase in the Prandtl number Pr lessens the temperature and thickness of the thermal boundary layer. The main conclusions have been indicated.

Analysis of active and passive control of nanoparticles in viscoelastic nanomaterial inspired by activation energy and chemical reaction

Activation energy is an important role in chemical reaction because the factor is very useful in the application of geothermal reservoir engineering, oil emulsions and water mechanics. Based on this observation investigated the role of activation energy and chemical reaction in viscoelastic liquid past a stretching surface. Buongiorno’s model is used in this study. Nonlinear thermal radiation is incorporated in the energy equation. Convective type boundary condition is implemented. Mass transport performance is analyzed through zero normal flux condition. Solution of the nonlinear equations is obtained by adopting RKF method of fourth and fifth order. The dimensionless numbers on velocity curve, temperature curve and nanoparticle volume concentration curve is elaborated. Further engineering curiosity of drag coefficient, local Nusselt and Sherwood numbers are tabulated, depicted and interpreted. It is noted that rise of reaction rate and activation energy decelerates the local Nusselt number and accelerates the local Sherwood number.

Uncoupled thermoelastic problem of a functionally graded thermosensitive rectangular plate with convective heating

The main objective of the present paper is to study the temperature and thermal stress analysis of a functionally graded rectangular plate with temperature-dependent thermophysical characteristics of materials under convective heating. The nonlinear heat conduction equation is reduced to linear form using Kirchhoff’s variable transformation. Analytic solution of the heat conduction equation is obtained in the transform domain by developing an integral transform technique for convective-type boundary conditions. Goodier’s displacement function and Boussinesq harmonic functions are used to obtain the displacement profile and its associated thermal stresses. A mathematical model is prepared for functionally graded ceramic–metal-based material. The results are illustrated numerically and depicted graphically for both thermosensitive and nonthermosensitive functionally graded plate. During this study, one observed that notable variations are seen in the temperature and stress profile, due to the variation in the material parameters.

Combined effects of variable thermal conductivity and induced magnetic field on convective Jeffrey fluid flow with nth order chemical reaction

AbstractThis study addresses the impact of variable thermal conductivity and induced magnetic field on an unsteady two‐dimensional channel flow of an incompressible laminar mixed convective and chemically reacted Jeffrey fluid embedded in a non‐Darcy porous medium with an appropriate convective type boundary conditions. The suction/injection velocity distribution has been assumed to be in an exponential form. The set of transport equations is reduced into coupled ordinary differential equations by using appropriate similar variables, which are solved by shooting technique with Runge‐Kutta fourth‐order algorithm. The investigation is carried out for various emerging nondimensional parameters on the axial, radial velocities, temperature distribution, concentration, and induced magnetic fields and also with skin friction coefficient are discussed through graphs. The value of the local Sherwood and Nusselt numbers are analyzed numerically. We noticed that the effect of the induced magnetic field is increased with Strommer's number while it decreases for high magnetic Reynolds number.

Magnetohydrodynamic nanoliquid due to unsteady contracting cylinder with uniform heat generation/absorption and convective condition

In this article, the flow of an incompressible nanoliquid induced due to unsteady contracting cylinder is investigated. Analysis of heat transport phenomenon is reported under uniform heat absorption/generation and convective type boundary condition. A set of transformations is implemented to reduce PDEs to ODEs. The obtained coupled nonlinear equations are treated numerically through the help of RKF 45 technique. Physical evaluation of convective condition and heat absorption/generation on thermal analysis is discussed through graphs. Output shows that both the parameters of convective condition and heat absorption/generation give an increment in liquid temperature and its related thickness of boundary layer.

Magnetohydrodynamic flow of nanofluid over permeable stretching sheet with convective boundary conditions

Analysis has been carried out for the magnetohydrodynamic (MHD) boundary layer flow of nanofluid. The flow is caused by a permeable stretching sheet. Convective type boundary conditions are employed in modeling the heat and mass transfer process. Appropriate transformations reduce the nonlinear partial differential equations to ordinary differential equations. The convergent series solutions are constructed. Graphical results of different parameters are discussed. The behaviors of Brownian motion and thermophoretic diffusion of nanoparticles have been examined. The dimensionless expressions of local Nusselt and local Sherwood numbers have been evaluated and discussed.

MHD flow of Jeffrey nanofluid with convective boundary conditions

This article investigates the effects of convective heat and concentration conditions in magnetohydrodynamic flow of non-Newtonian fluid with nanoparticles. Convective type boundary conditions are utilized for heat and nanoparticles concentration. The nonlinear partial differential equations are reduced into the nonlinear ordinary differential equations by suitable similarity variables. Homotopy analysis method is employed to obtain the dimensionless velocity, temperature and nanoparticles concentration expressions. Graphical results for temperature and nanoparticles concentration are plotted and examined. Numerical values of skin friction coefficient are computed and discussed. Heat transfer and nanoparticles concentration transfer rates at the wall are examined by plotting the graphs of different governing physical parameters. We noticed that the temperature and nanoparticles concentration profiles are enhanced when the values of Biot numbers are increased. An increase in thermophoresis parameter leads to an enhancement in the temperature and nanoparticles concentration. On the other hand the increasing values of Brownian motion parameter has reverse effects on the temperature and nanoparticles concentration fields.

MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions

This article concentrates on the steady magnetohydrodynamic (MHD) flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper (Cu), Silver (Ag), Alumina (Al2O3) and Titanium Oxide (TiO2). Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.

Analysis to a critical state of thermal field in microwave ablation of liver cancer influenced by large vessels

To study the effect of large blood vessels on the temperature field in invasive microwave ablation, a finite element method was applied based on the convective-type boundary condition on the interface between tissues and blood flow. Whether a large blood vessel is outside of or involved in the lesion area will affect the 54°C effective therapeutic area in different critical conditions. This paper drew the function diagraph on the distance between blood vessel and antenna with the diameter of the blood vessel and put forward the concept of effective therapy radius. It can be used to study the influence of large vessels on the external boundary of the coagulation area and can be used as a theoretical basis to help to decide whether to occlude the large vessels before microwave ablation therapy.

Natural convection from an inclined plate embedded in a variable porosity porous medium due to solar radiation

Natural convection boundary-layer flow of an absorbing and electrically-conducting fluid over a semi-infinite, ideally transparent, inclined flat plate embedded in a porous medium with variable porosity due to solar radiation is considered. The governing equations are derived using the usual boundary-layer and Boussinesq approximations and accounting for the presence of an applied magnetic field and an applied incident radiation flux. To account for the heat loss from the plate surface, a convective-type boundary condition is employed there. These equations and boundary conditions are non-dimensionalized and transformed using a non-similarity transformation. The resulting non-linear partial differential equations are then solved numerically subject to the transformed boundary conditions by an implicit iterative finite-difference scheme. Graphical results for the velocity and temperature fields as well as the boundary friction and Nusselt number are presented and discussed for various parametric conditions.

Natural Convection Due to Solar Radiation from a Vertical Plate Embedded in a Porous Medium with Variable Porosity

Natural convection boundary-layer due to solar radiation flow of a Newtonian absorbing fluid over a semi-infinite, ideally transparent, vertical flat plate embedded in a porous medium having a variable porosity distribution is considered. Continuum equations governing this boundary-layer flow and heat transfer situation are derived taking into consideration the Boussinesq approximation and the presence of an applied incident radiation flux. To account for the heat loss from the plate surface, a convective-type boundary condition is employed there. The obtained equations and boundary conditions are transformed using a nonsimilarity transformation and solved numerically by an implicit iterative finite-difference scheme. Selected graphical results for the velocity and temperature fields as well as the boundary friction and Nusselt number are presented and discussed.

Perturbations in hyperthermia temperature distributions associated with counter-current flow: numerical simulations and empirical verification.

Two numerical techniques are used to calculate the effect of large vessel counter-current flow on hyperthermic temperature distributions. One is based on the Navier-Stokes equation for steady-state flow, and the second employs a convective-type boundary condition at the interface of the vessel walls. Steady-state temperature fields were calculated for two energy absorption rate distributions (ARD) in a cylindrical tissue model having two pairs of counter-current vessels (one pair with equal diameter vessels and another pair with unequal diameters). The first assumed a uniform ARD throughout cylinder; the second ARD was calculated for a tissue cylinder inside an existing four antenna Radiofrequency (RF) array. A tissue equivalent phantom was constructed to verify the numerical calculations. Temperatures induced with the RF array were measured using a noninvasive magnetic resonance imaging technique based on the chemical shift of water. Temperatures calculated using the two numerical techniques are in good agreement with the measured data. The results show: 1) the convective-type boundary condition technique reduces computation time by a factor of ten when compared to the fully conjugated method with little quantitative difference (approximately 0.3 degree C) in the numerical accuracy and 2) the use of noninvasive magnetic resonance imaging (thermal imaging) to quantitatively access the temperature perturbations near large vessels is feasible using the chemical shift technique.

Temperature and moisture distributions in a moist spherical capillary-porous body?a new approach

A novel technique, which is a combination of the Laplace transform and matrix calculus, is employed to obtain the exact solutions of the linearized Luikov system of coupled heat and moisture transport equations in a spherical capillary porous body addressed to specified initial and boundary conditions. It is shown that under certain restrictions, in the case of convective-type boundary conditions, the transcendental equation yields a countable number of complex conjugate roots. Here, a new computational scheme is employed, which evaluates real as well as a countable number of pairs of complex conjugate roots. A set of benchmark results is generated for the Luikov drying model, and in a way better than the alternative solutions proposed by Lobo et al. [19] for linear problems. Copyright © 1999 John Wiley & Sons, Ltd.

Simultaneous gas diffusion and chemical reaction in foods stored in modified atmospheres

A mathematical model based on simultaneous gas diffusion and chemical reaction was developed to represent the gas exchange in foods stored in modified atmospheres. The respiration process was modeled as a first order chemical reaction and the gas transfer process was modeled as ordinary diffusion. The resistance of the skin to gas transfer was modeled as a convective type boundary condition. A steady state solution of the model was obtained. Respiration rate, average internal gas concentration, and gas concentration under the skin were measured using Golden Delicious apples. The experimental methods were analyzed based on the model to determine the properties of apples. The experimentally determined values of the properties were diffusivity of the flesh to oxygen 2·67 × 10 −9 m 2/s and to carbon dioxide 3·28 × 10 −9 m 2/s, conductance of the skin to oxygen 290 × 10 −9 m/s and to carbon dioxide 220 × 10 −9 m/s, and first-order reaction rate constant 7·71 × 10 −6 s −1. These parameters were used in the model to simulate the internal gas concentration profiles.

On the Solution of Linear Diffusion Problems With Variable Boundary Condition Parameters

A method of solution is presented for the treatment of a class of boundary value problems of linear diffusion theory for finite homogeneous media which have applications in transient heat conduction (or mass diffusion) in a finite medium subjected to convective type boundary condition with time and space dependent coefficient, in the processes of neutron slowing in a finite medium with absorbing boundaries that exhibit energy-dependent cross sections, and in many related areas.