Magnetohydrodynamic mixed convection in a non-Newtonian third-grade fluid flowing through vertical parallel plates: A semianalytical study of flow and heat transfer

Buoyancy assisted and buoyancy opposed mixed convection of a third-grade fluid, which flows through vertically oriented parallel plates, subjected to uniform and constant wall heat fluxes, under the effect of an externally applied magnetic field, are investigated. The coupled, nonlinear conservation equations of momentum and energy are solved employing the collocation method (CM) and velocity and temperature distributions are solved semianalytically. The results produced by the CM and the results of exact solution are compared for the buoyancy assisted and buoyancy opposed flow of a Newtonian fluid through the vertically oriented parallel plates arrangement without the effect of the externally applied magnetic field. An excellent agreement is exhibited by demonstrating the efficacy of the CM. The effects of the third-grade fluid parameter, Hartmann number, and mixed convection parameter on the dimensionless velocity, temperature, and Nusselt number are studied. The results imply that in the case of buoyancy assisted flow, an increment in the non-Newtonian third-grade fluid parameter causes a decrease in the fluid velocity near the plate walls, which finally causes an increase in the velocity in the central core of the plates. In buoyancy opposed flow, the effect of the same parameter is to oppose the flow reversal near the walls and with higher values of this parameter, it can totally prevent the flow reversal near the walls. The results of the present study can be useful in the fields of flow and heat transfer of various grades of polymers, paints, and food processing.     

Assessment of heat transfer in large parallel plates with a narrow gap maintained at a constant temperature

Investigations are conducted on electromagnetohydrodynamic (EMHD) flow and heat transfer in a third-grade fluid flowing through large parallel plates, which are maintained at constant temperatures. The impact of convective heat transmission is disregarded since the space between the plates is small. The influence of viscous dissipation is considered. Despite being addressed for Newtonian fluids, the conduction problem with the viscous dissipation effect is not examined in third-grade fluids for EMHD flow and heat transfer behavior. The least-square method is adopted to solve nondimensional, nonlinear momentum and energy conservation equations to get the dimensionless velocity, temperature distribution, and heat flux. Temperature and heat flux are investigated in relation to the third-grade fluid parameter, the Hartmann number, the electric field parameter, and the Brinkman number. The findings show a rise in the Brinkman number dramatically increases heat transfer from both walls, necessitating cooling of both plates. The heat flow from both walls increases as the parameters of third-grade fluid increases.     

Laminar forced convection with viscous dissipation in a Couette–Poiseuille flow between parallel plates

In this study, analytical solutions are obtained to predict laminar heat-convection in a Couette–Poiseuille flow between two plane parallel plates with a simultaneous pressure gradient and an axial movement of the upper plate. A Newtonian fluid with constant properties is considered with an emphasis on the viscous-dissipation effect. Both hydrodynamically and thermally fully-developed flow cases are investigated. The axial heat-conduction in the fluid is neglected. Two different orientations of the thermal boundary-conditions are considered: the constant heat-flux at the upper plate with an adiabatic lower plate (Case A) and the constant heat-flux at the lower plate with an adiabatic upper plate (Case B). For different values of the relative velocity of the upper plate, the effect of the modified Brinkman number on the temperature distribution and the Nusselt number are discussed. Comparison of the present analytical results for a special case with those available in the literature indicates an excellent agreement.     

Free surface dynamics of MHD third-grade fluid model over a heated stretching sheet with variable fluid properties

A thorough investigation of MHD third-grade differential-type fluid flow over a heated stretching sheet is performed in this work. In particular, we analyze the film thinning process, when the thermal sensitive fluid parameters vary due to the effect of heat supplied to the stretching sheet. Starting with a two-dimensional (2D) free surface boundary value problem of non-Newtonian third-grade fluid, we present a systematic derivation of a 1D transient thin-film height equation using longwave analysis with respect to the small aspect ratio of the fluid domain. The derived model is used to study the impact of Newtonian and non-Newtonian parameters with variable fluid properties on the thin film height. The model is discretized using an upwind discretization in space and implicit time integration to guarantee first-order convergence. The model is analyzed thoroughly with the help of numeric computing software MATLAB. The existing findings for a Newtonian fluid are in excellent agreement with derived evidence. In comparison to Newtonian fluid, the study finds that the third-grade parameter causes thinning under different parametric restrictions. Simulations on the coupling effect explain that, the film thickness can be reduced with a high Marangoni number for highly viscous fluids. Also, since the effect of the conductivity parameter can be reduced at a low Prandtl number, the fluid shows a thinning effect. The film thinning rate, on the other hand, is reduced by the magnetic field.     

Entropy generation through combined non-grey gas radiation and forced convection between two parallel plates

The current study presents a numerical computation of combined gas radiation and forced convection through two parallel plates. A laminar flow of a temperature-dependent and non-grey gas in the entrance region of the channel was investigated. Over-heated water vapor was chosen as a gas because of its large absorption bands. Some special attention was given to entropy generation and its dependence on geometrical and thermodynamic parameters. The radiative part of the study was solved using the “Ray Tracing” method through S₄ directions, associated with the “statistical narrow band correlated-k” (SNBCK) model. The temperature fields were used to calculate the distributions of local and global entropy generation.     

Mixed convective flow of immiscible viscous fluids in a vertical channel

Combined free and forced convection flow in a parallel‐plate vertical channel is analyzed for immiscible viscous fluids taking into account the effect of viscous dissipation. Three types of thermal boundary conditions are described. These thermal boundary conditions are isothermal‐isothermal, isoflux‐isothermal, and isothermal‐isoflux for the left–right walls of the channel. The coupled nonlinear governing equations are solved analytically using the regular perturbation method. Separate solutions are matched at the interface using suitable matching conditions. The results are represented graphically for various governing parameters such as the ratio of Grashof number to Reynolds number, viscosity ratio, width ratio, and conductivity ratio for equal and different wall temperatures. It is found that the viscous dissipation enhances the flow reversal in the case of a downward flow while it counters the flow in the case of an upward flow. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20324     

Magnetohydrodynamic forced convection in bidisperse porous medium: Analysis of flow and temperature distributions in a parallel-plate channel

This study aims to explore magnetohydrodynamic forced convection in a parallel-plate channel filled with a bidisperse porous medium, while emphasizing the significance of viscous dissipation. The study utilizes the two-velocity two-temperature model to analyze the flow and temperature distributions in both the fluid phase and solid phase. Convective boundary conditions at the channel walls are considered, and momentum slip is incorporated into the analysis. By nondimensionalizing the governing equations and employing the Homotopy Analysis Method, the velocity and temperature profiles for both phases are determined. Notably, the findings of the study highlight a notable discrepancy in the temperature increase between the solid phase and the fluid phase. Furthermore, the study investigates the impact of various parameters, such as the Darcy number, Biot number, slip parameter, Hartmann number, and Brinkman number, on velocity, temperature, Nusselt number, and skin friction.     

The flow of non-Newtonian fluid in an inclined channel through variable permeability

A non-Newtonian fluid's Poiseuille flow in a porous medium with variable inclination and permeability is investigated. Let us assume for the sake of simplification that permeability varies as a quadratic parabolic function form. The porous medium is used by the Brinkman methodology to control the flow. The equations for velocity distribution and mass flow that result from this are evaluated using different input values. This problem describes the effect of inclination, Jeffrey parameter, and variable permeability on the classical Poiseuille flow between parallel plates. This problem can also be treated as an extension of the work of Hamdan and Kamel for non-Newtonian fluid flow in an inclined channel. Also, the effects of these variables on the variation of mass flux with Jeffrey parameter λ₁ is analyzed through graphs, and the skin friction coefficient is analyzed through table values. It is observed that the maximum permeability of the porous medium affects both the mass flow rate and the velocity, which increase with rising λ₁ and decrease with rising H_a, respectively.     

Impact of Soret and Dufour on MHD mixed convective flow of non-Newtonian fluid over a coagulated surface

In the present study, we investigated the steady, two-dimensional mixed convective stagnation point flow of an electrically conducting micropolar fluid due to stretching of a variable thicked surface in the attendance of viscous dissipation. The flow is incompressible and laminar. The combined heat and mass transfer features are investigated. Convective and diffusion conditions are considered. The nonlinear thermal radiation, thermo-diffusion, and diffusion thermal effects are considered. The governing partial differential equations are converted to ordinary differential equations by using the appropriate similarity transformations. The obtained nonlinear and coupled ordinary differential equations are elucidated numerically using the fourth-order Runge–Kutta based shooting technique. The influence of various nondimensional parameters on the flow field like velocity, microrotation, temperature, and concentration is examined with the assistance of graphs. Results indicate that the Dufour number has a proclivity to increase the distributions of concentration and temperature correspondingly. Also, fluid temperature and concentration enhance for increasing values of the wall thickness parameter.     

Numerical investigation of mixed convection of non-Newtonian fluid in a vented square cavity with fixed baffle

This paper numerically investigates mixed convective heat transfer in a vented square cavity incorporated with a baffle that is subjected to external non-Newtonian fluids (NNFs). Adiabatic conditions are imposed on the top and bottom walls, while cold temperature conditions are applied to the right and left solid boundaries. Heated NNF enters the cavity through the inlet and goes out through the outlet at three different locations, and it passes on a vertical baffle fixed at the base placed at different lengths. To examine the impact of the inlet and outlet positions, three different shapes of the outlet port located on the right wall and the inlet port on the left bottom wall were investigated. The impacts of Reynolds number (Re) of 100 ≤ Re ≤ 1000, Richardson number (Ri) of 0.1 ≤ Ri ≤ 3, power law index (n) of 0.6 ≤ n ≤ 1.4, length of baffle (L_b) of 0.2 ≤ L_b ≤ 0.6 and the outlet hole positions (S) of $0\le S\le 0.9$ on the thermal and flow distributions in the cavity are taken into consideration in this paper. The results demonstrated that the flow's intensity and heat transfer increase with improvement in the Re and n at any baffle length. When the Ri increased from 0.1 to 3, $N{u}_{\mathrm{avg}}$ increased by 23.3% at $n=0.6$, and 13.8% at $n=1.2$. Also, the Ri increment results in the augmentation of the average heat transfer.     

A review of heat and fluid flow characteristics in microchannel heat sinks

Heat transfer and flow characteristic in microchannel heat sinks (MCHS) are extensively studied in the literature due to high heat transfer rate capability by increased heat transfer surface area relative to the macroscale heat sinks. However, heat transfer and fluid flow characteristics in MCHS differ from conventional ones because of the scaling effects. This review summarizes the studies that are mainly based on heat transfer and fluid flow characteristic in MCHS. There is no consistency among the published results; however, everyone agrees on that there is no new physical phenomenon in microscale that does not exist at macroscale. Only difference between them is that the effect of some physical phenomena such as viscous dissipation, axial heat conduction, entrance effect, rarefaction, and so forth, is negligibly small at macroscale, whereas it is not at microscale. The effect of these physical phenomena on the heat transfer and flow characteristics becomes significant with respect to specified conditions such as Reynolds number, Peclet number, hydraulic diameter, and heat transfer boundary conditions. Here, the literature was reviewed to document when these physical phenomena become significant and insignificant.     

A numerical study of mixed convection in a two-sided lid-driven tall cavity containing a heated triangular block for non-Newtonian power-law fluids

The study of hydrodynamics and thermal characteristics inside a lid-driven cavity has been one of the most captivating problems in computational fluid dynamics. In this numerical work, the mixed convection phenomenon inside a two-dimensional, tall lid-driven cavity with top and bottom lids moving in opposite directions, +x and –x, respectively, has been explored for non-Newtonian power-law fluids. The cavity contains a uniformly heated equilateral triangular obstacle at its geometric center.  Numerical experimentation is performed for a range of flow governing parameters, such as aspect ratio (0.25, 0.5, and 0.75), Prandtl number (1, 50, and 100) Richardson number (0.1, 1, and 10), power-law index (0.6–1.4) and Grashof number of 10⁴. The physical perceptions of the cavity are explained by using streamline and isotherm contours. The fluid movement is limited adjacent to the moving wall concerning the Richardson number at the lower Prandtl number. With a rise in the aspect ratio of the cavity, the flow-pattern becomes more dispersed inside the cavity. Heat transfer enhancement is observed at a lower aspect ratio equal to 0.25.     

Heat transfer and fluid flow analysis of non-Newtonian fluid in a microchannel with electromagnetohydrodynamics and thermal radiation

The study of electromagnetohydrodynamics (EMHD) of non-Newtonian fluid plays a significant role for optical design, thermal management of electronic components, and various operations of microfluidic devices. The use of parallel geometry is seen in the circulatory system, extrusion process, and respiratory system. By considering various practical applications, in the current study, the Poiseuille flow of an incompressible Casson liquid between the plates is investigated. The effects of MHD, Joule heating, thermal radiation, modified Darcy's law, and chemical reaction have been taken into account. The dimensional governing equations have been converted into dimensionless equations with pertinent nondimensional quantities. The resulting system of nondimensional system of equations has been analytically solved with nondimensional slip boundary conditions. The graphical results have been displayed with various fluid flow parameters. From the current study, it is concluded that the influence of Darcy number and Casson fluid parameter enhances the velocity profile, but the concentration declines with the enhancement of Casson fluid parameter. The radiation parameter and Prandtl number suppress the temperature profile.     

Effects of viscous dissipation on forced convective heat transfer in a channel embedded in a power-law fluid saturated porous medium

The convective heat transfer analysis in a channel embedded in a power-law fluid saturated porous medium subject to uniform heat flux is presented and compared with a Newtonian fluid concerning the effects of viscous dissipation. Governing momentum and energy equations for non-Newtonian fluids which accounts for the viscous dissipation effects are solved numerically. The temperature profiles of the non-Newtonian fluids are found to relate closely to the velocity profiles. When viscous dissipation is taken account of, Nusselt numbers for non-Newtonian fluid are found to deviate more from Newtonian fluid with increasing Brinkman number for a certain range of the Darcy number.     

Adomian decomposition solution for propulsion of dissipative magnetic Jeffrey biofluid in a ciliated channel containing a porous medium with forced convection heat transfer

Physiological transport phenomena often feature ciliated internal walls. Heat, momentum, and multispecies mass transfer may arise and additionally non‐Newtonian biofluid characteristics are common in smaller vessels. Blood (containing hemoglobin) or other physiological fluids containing ionic constituents in the human body respond to magnetic body forces when subjected to external (extracorporeal) magnetic fields. Inspired by such applications, in the present work we have considered the forced convective flow of an electrically conducting viscoelastic physiological fluid through a ciliated channel under the action of a transverse magnetic field. The presence of deposits (fats, cholesterol, etc.) in the channel is mimicked with a Darcy porous medium drag force model. The effect of energy loss is simulated via the inclusion of viscous dissipation in the energy conservation (heat) equation. The velocity, temperature, and pressure distribution are computed in the form of infinite series constructed by Adomian decomposition method and numerically evaluated in a symbolic software (Mathematica). The influence of Hartmann number (magnetic parameter), Jeffrey first and second viscoelastic parameters, permeability parameter (modified Darcy number), and Brinkman number (viscous heating parameter) on velocity, temperature, pressure gradient, and bolus dynamics is visualized graphically.     

Application of heat transfer on MHD shear thickening fluid flow past a stretched surface with variable heat source/sink

The purpose of this study is to explore the viscous dissipation stimulus on the steady convective magnetohydrodynamic shear thickening liquid stream across a vertically stretched sheet. The impact of thermic heat, first-order velocity slip, and variable heat generation/absorption are considered and also ignored the effect of magnetic Reynold's number. We converted flow controlling equations into the set of dimensionless nonlinear ordinary differential equations by employing similarity variables to solve these coupled equations by R–K and shooting technique. The effect of different dimensionless variables on velocity, heat, friction factor, and local Nusselt numbers are presented through graphs and tables. Depreciation in velocity and growth in temperature distribution is detected when the Casson fluid parameter is increased. Temperature is the increasing function of the Eckert number.     

Genetic algorithm-assisted artificial neural network for retrieval of a parameter in a third grade fluid flow through two parallel and heated plates

Genetic algorithm (GA) has been used to determine important attributes of artificial neural network (ANN), such as number of neurons in different hidden layers and division of data for training, validation, and testing. The GA-assisted ANN (GAAANN) model was used to retrieve third grade fluid (TGF) parameter (A) in a TGF flow problem. The TGF was allowed to flow through two parallel plates, which were subjected to uniform heat flux. The least square method (LSM) was used to solve the governing equations, for specified boundary conditions. In this way, temperature profiles for different values of A were computed by LSM, constituting the direct part of the problem. In the inverse part, the GAAANN model was fed with a temperature profile as input and the corresponding value of A was obtained as output. Four different GAAANN model were developed, and a detailed analysis was done in retrieving the value of A by different GAAANN models. Two very important and commonly used algorithms: Levenberg-Marquardt (LM) and scaled conjugate gradient are explored for training of the neurons. The entire four GAAANN model were able to retrieve the value of A with different levels of accuracy.     

Simultaneous effects of viscous and Darcy dissipation on mixed convection flow in an annulus partially filled with porous material: Analytical approach

The effect of thermal dissipation on a steady, fully developed, mixed convection viscous, incompressible fluid in an annulus partially filled with porous materials has been thoroughly examined in this work. Fluid flow begins within the annulus when a pressure gradient is applied abruptly in the flow direction. The fluid flow in the porous zone is characterized by the Brinkmann-extended Darcy model. The fluid is divided into transparent and porous parts by a minimal interface. By matching their velocities and considering the shear stress jump conditions at the interface, the clear fluid and the porous region are connected. Additionally, the viscous dissipation effect is considered while determining the energy equation in the clear fluid zone. However, in the porous area, the Darcy dissipation effects are considered in addition to the viscous dissipation influence. In the model, the results of various fluid parameters in the problem were addressed using line graphs and the homotopy perturbation method. The study found that when the porous region's thickness grows, heat transmission on the annular surface enclosing the clear fluid region increases while it decreases on the border surface close to the porous region. In addition, a thicker porous region requires a greater pressure gradient to propel the flow.     

Thermal diffusion and diffusion thermoeffects on the peristaltic motion of a non-Newtonian micropolar fluid inside a nonuniform vertical channel

In this paper, the effects of Dufour and Soret numbers on the peristaltic motion of a non-Newtonian micropolar fluid are discussed. The motion inside a nonuniform vertical channel under the effect of the uniform magnetic field is considered. The Ohmic and elastic dissipations, as well as heat generation and chemical reaction, are taken into account. The problem is modulated mathematically by using continuity, momentum, angular momentum, and heat and mass transfer equations. The nonlinear partial differential equations describing these equations are written in terms of the physical parameters of the problem. The equations are transformed from the laboratory frame to the wave frame and then written in dimensionless form. The approximations of long wavelength and small Reynolds number are applied, then the equations are solved by using the homotopy perturbation method. The velocities, stream function, temperature, and concentration distributions are obtained as functions of the physical parameters of the problem. The effect of these parameters on the obtained solutions are computed mathematically and illustrated graphically through a set of figures. It is found that the parameters play an important role in controlling the solutions. It is found that the stream function decreases by increasing both non-Newtonian and micropolar parameters on the left side of the channel and vice versa occurs on the right side.