Search

Heat transfer is an important process in many engineering, industrial, residential, and commercial buildings. Thus, this study aims to analyse the effect of MHD and viscous dissipation on radiative heat transfer of Reiner–Philippoff fluid flow over a nonlinearly shrinking sheet. By adopting appropriate similarity transformations, the partial derivatives of multivariable differential equations are transformed into the similarity equations of a particular form. The resulting mathematical model is elucidated in MATLAB software using the bvp4c technique. To determine the impact of physical parameters supplied into the problem, the results are shown in the form of tables and graphs. The findings reveal that the heat transfer rate reduces as the Eckert number and radiation parameter are introduced in the operating fluid. However, increasing the magnetic parameter raises both the skin friction coefficient and the local Nusselt number, which impulsively improves the heat transfer performance. The suction effect has a noticeable influence on the Reiner–Philippoff fluid, since increasing the suction parameter's value is seen to enhance the skin friction coefficient and the heat transfer performance. The dual solutions are established, leading to the stability analysis that supports the first solution’s validity.

The viscoelastic fluid flow over a non linear stretching porous sheet is considered in this analysis. The case of suction and injection is also discuused. The effects of thermophoresis and brownain motion with viscous dissipation is taken into account. Under the flow assumptions, boundary layer approximation applied on the mathematical model and developed the partial differential equations. The similarity variable is applied on the partial differential equations which converted into ordinary differential equations. The dimensionless system further solved through numerical technique bvp4c method. The results of the current problem achieved after solving the problem which presented through graphs and table. Influence of numerous physical parameters on velocity function, concentration function and temperature function are manipulated through graphs. The tabular results are schemed to display skin friction and local Nusselt number. The higher values of N b which enhanced the velocity profile but declines velocity profile due to higher values of Ec . The thermal thickness enhances due larger values of γ and Pr but thermal thickness declines due to higher values of Ec and N t . The concentration profile enhances due to enhancing the values of Ec and Pr but concentration profile declines due to increasing the values of N t . Nusselt number enhaced due to higher values of Ec , S c and N t but declines of higher values of Pr .

This paper investigates the effect of slits within the arc-plug insert of the solar parabolic trough receiver (PTR). In order to predict the performance of the parabolic trough collector (PTC) with arc-plug slits within the absorber tube; two different variants of slits of 2 mm and 1 mm thicknesses are considered. Then, each of the variants of slits with different thicknesses are varied in terms of numbers of their occurrence in the arc-plug. The 2 mm thickness slits are varied in 5, 7, and 9 numbers with uniform space of separation between them in the arc-plug. While 1 mm thickness slits are varied from 11 to 13 in numbers and also maintaining uniform space of separation between them like in 2 mm thickness slits. The objective is to determine the effects of viscous dissipation within the slits of the arc-plug of PTR; and also, the optimized version of the slit with its numbers. It is found that 2 mm slits with 9 in numbers showed the highest value of thermal efficiency as compared to all other cases. The thermal efficiency (η) of the PTC with arc-plug slits are seen to be about 1.642 times of conventional PTC; whereas, 1.309 times of arc-plug without slits. Therefore, it is always beneficial to use slits within inserts of PTCs for its performance enhancement; but, the selection of slit’s thickness and its numbers plays a vital role in its application.

This research article is aimed to investigate the behavior of MHD two dimensional flow of Maxwell nanofluid. Non-Newtonian Maxwell nanofluid is considered in the present study to evaluate the phenomena of heat transfer of steady boundary layer flow. The flow of fluid is derived over a stretching melting surface. Observation are made for the concise and terse effect of viscous dissipation, magnetic field and Joule heating. Porous medium is taken into account to observe the flow. The entropy generation model for Maxwell nanofluid is analyzed against different parameters. The set of highly non linear PDE’s are generated. A pertinent and relevant similarity transformation is applied to alter the fundamental PDE’s of momentum and energy into set of ODE’s. The set of non-linear ODE’s are solved by using the homotopy analysis method. The flow features and the heat transfer characteristics prevailing this phenomena are investigated and argued for different engaging flow parameters. Tabulated and graphical results for the skin-friction coefficient and Nusselt number are presented for various values of the flow concerened parameters. Entropy generation get hightened increases against increasing values of porosity parameter, Reylond number, nanoparticle fraction, Brinkman number and Hartman number during the flow.

In current study, heat transfer and viscous dissipation effects in nanoliquid flow through a porous stretchable cylinder are examined. The upgraded heat transport rate in the base fluid with tiny-sized nanoparticles is investigated. Convective heating and non-linearly thermal radiation effects are investigated. In this analysis, solid particles M o S 2 & A g and base fluid engine-oil are used. Moreover, boundary layer approximations are used to model a set of PDEs. The structure model of PDEs is reduced into non-dimensional set of ODEs with the help of recommended similarity transformations. The converted equations jointly with specific boundary restrictions are solved numerically by using the bvp4c solver (shooting scheme) in computational software MATLAB. The behavior of prominent parameters against flow and thermal fields are analyzed. From the results, we observed that velocity enhances for larger solid volume fraction. Furthermore, temperature of fluid is increased via greater estimations of thermal Biot number. The nanofluid has improved heat transport rate and therefore the current analysis has many applications in nano-sized devices of cylindrical shapes.

The impact of Joule heating due to electric double layer (EDL) and viscous dissipation on electroosmotic mixed convection flow in a vertical microchannel with asymmetric heat fluxes is established in this article. The Poisson-Boltzmann, momentum and energy equations representing the electric potential, velocity profile and temperature distribution in the microchannel are obtained in dimensionless forms. Using the Debye-Huckel linearization, exact solutions are obtained for electric potential, velocity profile and temperature distributions by method of undetermined coefficients in the absence of viscous dissipation and Joule heating while an inbuilt Matlab function called pdepe is employed to solve the coupled nonlinear momentum and energy equations in the presence of Joule heating and viscous dissipation. Results show that the presence of Joule heating and viscous dissipation lead to decrease in velocity profile and temperature distributions throughout the microchannel.

The aerodynamic performance of compressor airfoil is significantly affected by the surface roughness at low Reynolds number (Re). In the present study, numerical simulations have been conducted to investigate the impact of surface roughness on the profile loss of a high subsonic compressor airfoil at Re = 1.5 × 105. Four roughness locations, covering 10%, 30%, 50% and 100% of the suction surface from the leading edge and seven roughness magnitudes (Ra) ranging from 52 to 525 μm were selected. Results showed that the surface roughness mainly determined the loss generation process by influencing the structure of the Laminar Separation Bubble (LSB) and the turbulence level near the wall. For all the roughness locations, the variation trend for the profile loss with the roughness magnitude was similar. In the transitionally rough region, the negative displacement effect of the LSB was suppressed with the increase of roughness magnitude, leading to a maximum decrease of 14.6%, 16.04%, 16.45% and 10.20% in the profile loss at Ra = 157 μm for the four roughness locations, respectively. However, with a further increase of the roughness magnitude in the fully rough region, the stronger turbulent dissipation enhanced the growth rate of the turbulent boundary layer and increased the profile loss instead. By comparison, the leading edge roughness played a dominant role in the boundary layer development and performance variation. To take fully advantage of the surface roughness reducing profile loss at low Re, the effects of roughness on suppressing LSB and inducing strong turbulent dissipation should be balanced effectively.

Rayleigh convection is an interfacial transport phenomenon in the CO2 capture and storage processes. In the present paper, we proposed a mesoscale model to capture the convection structure caused by Rayleigh convection in a 20 mm × 10 mm CO2 absorption cell with low mesh density. To close this mesoscale model, we analyzed the relationship between entropy generation caused by mass transfer and viscous dissipation, and raised a criterion. This criterion was also verified by a PIV/LIF quantitative experiment in CO2 absorption cell with R a = 1.15 ∼ 2.3 × 10 7 . The proposed mesoscale method can prediction the concentration and velocity distributions of Rayleigh convection effectively. The relative error of total mass transfer flux can be decreased from 43% to 6.3%. The idea of this mesoscale method is promising for solving complicated transport problem that is difficult to find the conservation model.

This research article elaborates the salient attributes of sundry variables i.e., Darcy-Forchheimer number, mixed convection parameter, porosity parameter, Weissenberg number, slip parameter, Prandtl number, activation energy parameter and chemical reaction parameter on the forced convective Darcy-forchheimer flow of non-Newtonian fluid (Carreau-Yasuda fluid) subject to stretchable and flat surface of the sheet. A general mathematical form of the entropy generation rate for Carreau-Yasuda fluid is derived in the presence of porosity irreversibility, fluid friction irreversibility, heat transfer irreversibility and Joule heating irreversibility through second law of thermodynamics. The fluid flow is saturated and magnetized through Darcy-Forchheimer porous medium and applied magnetic field. The energy equation is modeled in the presence of viscous dissipation. Series solutions are calculated by semi analytical method HAM. The behavior of pertinent flow parameters is discussed graphically. The main interest in giving to the engineering curiosity like velocity gradient and Nusselt number. The main theme of this research communication is to enhance the information of entropy optimized flow and heat and mass transport, and to inspire the investigators and analysts to scrutinize gradually innovative attributes that can take improvement on the entropy generation minimization.

Here entropy optimized magnetohydrodynamic flow of second-grade fluid is addressed. The energy equation is developed through Joule heating and dissipation effects. Mass transportation along with an interface between two liquids due to surface tension gradient is called Gibbs–Marangoni effect (Marangoni effect). On the other hand, if there is thermal dependence case, then the phenomenon is called Benard–Marangoni convection (thermo-capillary convection). Marangoni convection depends upon the difference of surface pressure computed by the gradient of temperature, magnetic effect, and concentration gradients. The basic concept of mass and heat transportation phenomenon in Marangoni boundary layer flow are comprehensively discussed. The physical feature of irreversibility exploration is developed with the help of thermodynamics second law. Here we discussed both first and second laws of thermodynamics. Nonlinear ODE's are obtained through adequate variables. Optimal homotopy analysis method (OHAM) is employed to construct the convergent solutions. Entropy optimization, temperature, Bejan number, concentration, and velocity variations for various secondary parameters are deliberated. Velocity enhances via the Marangoni ratio parameter. For larger Hartmann number the temperature and velocity have a reverse effect. The velocity field is amplifying against second grade fluid variable. A similar effect is noticed versus a larger fluid parameter and Eckert number. For a higher approximation of the Marangoni ratio variable, the concentration reduces. Larger fluid parameter rises the entropy generation rate.

This study investigates the characteristics of flow parameters like Brinkman number, magnetic parameter, diffusion parameter, Weissenberg number and ratio of temperature and concentration parameters for the entropy generation in reactive dissipative flow of Carreau-Yasuda fluid over a stretched surface. A total entropy expression is derived for the Carreau-Yasuda fluid using the second law of thermodynamics. Electrical conducting slip flow is considered. Furthermore, Joule heating, heat generation/absorption and dissipation effects are accounted for the development of the energy equation. Appropriate transformations and semi-analytical technique (homotopy analysis method) are utilized to obtain the series solutions for nonlinear flow expressions. Our obtain results show that an increase in magnetic parameter, Brinkman number, diffusion parameter and concentration ratio parameter causes an enhancement in the entropy generation rate. The engineering curiosity like skin friction coefficient and heat transfer rate (Nusselt number) are discussed numerically in the presence of magnetic parameter, Weissenberg number, Prandtl number, Eckert number and heat generation/absorption parameter. The main theme of this research article is to increase the knowledge of the effects flow behavior and heat transfer on the entropy generation, and to motivate the engineers and researchers to investigate progressively novel characteristics that can take development on the entropy generation minimization.

In the field of engineering, Biologically-inspired propulsion systems are getting the utmost importance. The theoretical analysis explores the effect of heterogeneous-homogeneous reactions on heat and thermal transfer analysis for incompressible Sutterby fluid. Using low Reynolds number and long wavelength assumptions, the governing system of equations of fluid transport problem is abridged and solved using the perturbation technique. The Nusselt number and skin friction coefficient are also incorporated in this contemplation. Particular attention is given to elastic parameters and Brinkman number and plotted their graph for velocity profile, temperature distribution, and concentration profile. It is initiated that momentum distribution profile is enhanced for higher values of elastic parameters, which is because less resistance occurs at the channel walls. The impact of heterogeneous and homogeneous reactions shows reverse bearing on the concentration field. Brinkman number (viscous dissipation effects) contributes to boosts the thermal profile for all the cases. Moreover, augmentation in skin friction is noticed by escalating the parametric values of damping and rigidity. The present study has a wide range of applications in biomedical engineering and biological functions i.e. electromagnetic peristaltic micro pumps.

The steady magnetohydrodynamic stagnation point flow and heat transfer over a stretching/shrinking surface in a hybrid nanofluid with partial slip and viscous dissipation were theoretically/numerically studied. The governing equations of the problem were turned into ODEs by using appropriate transformations. The plots of most important parameters were presented for both surfaces. It was found that on increasing the magnetic parameter, the hybrid nanofluid is better as a heater rather than nanofluid, however, it is better as a cooler on rising Eckert number, the stretching and slip parameters. For shrinking sheet, critical regions of unique/dual solution have been introduced. Further, stability of the unique/dual solution was studied where three regions of stability were noticed. It was deduced that the velocity and temperature are sensitively available close to the terminated line in the dual solution region. It was also proved that their behavior is absolutely different over the three regions of stability.

Here magnetohydrodynamics (MHD) nanomaterial slip flow of Williamson fluid is addressed. The flow is discussed over a porous medium and generated via nonlinear stretching phenomenon. The behavior of heat and mass transport are discussed subject to Cattaneo-Christov double diffusions (CCDD). Mathematical modeling for both CCDD is performed under the basic concept of Fourier's and Fick's laws. The energy equation for the consider flow problem is developed using Brownian motion, dissipation and thermophoretic diffusion. Relevant transformations variables are utilized to convert the partial differential equations into ordinary ones. Flow parameters are discussed on the velocity, temperature and concentration through built-in-Shooting method. Skin friction is computed and discussed through bar chart versus Weissenberg number and slip parameter. It is concluded that the skin friction coefficient is decreased for higher values of Weissenberg number and slip parameter. Furthermore, velocity field decays against Weissenberg number, slip parameter and porosity parameter.

Different approaches to model the cleaning of (i) very thin and (ii) thin soil layers by impinging water jets are compared to evaluate their predictive capabilities. Cleaning experiments were performed with coherent 2 mm and 3 mm diameter water jets (Re > 10,000) impinging on flat layers of an insoluble, viscoplastic petroleum jelly. The jelly exhibited creep below the yield stress and Herschel-Bulkley behaviour above it. A two-film shear-driven model for case (i) gave very poor predictive capability, partly due to the complex soil rheology. Case (ii) data were compared to modified versions of the phenomenological model of Fernandes and Wilson (2020), and a fully-coupled CFD model of the liquid and soil motion using the volume of fluid method. The modifications to the former did not improve its accuracy. The latter gave a good prediction of the initial cleaning behaviour for the case considered: the high computational cost precluded extensive testing.

There is increasing evidence of altered tissue mechanics in neurodegeneration. However, due to difficulties in mechanical testing procedures and the complexity of the brain, there is still little consensus on the role of mechanics in the onset and progression of neurodegenerative diseases. In the case of Alzheimer’s disease (AD), magnetic resonance elastography (MRE) studies have indicated viscoelastic differences in the brain tissue of AD and healthy patients. However, there is a lack of viscoelastic data from contact mechanical testing at higher spatial resolution. Therefore, we report viscoelastic maps of the hippocampus obtained by a dynamic indentation on brain slices from the APP/PS1 mouse model where individual brain regions are resolved. A comparison of viscoelastic parameters shows that regions in the hippocampus of the APP/PS1 mice are significantly stiffer than wild-type (WT) mice and have increased viscous dissipation. Furthermore, indentation mapping at the cellular scale directly on the plaques and their surroundings did not show local alterations in stiffness although overall mechanical heterogeneity of the tissue was high (SD~40%). Therefore, reported mechanical alterations at a tissue scale indicates global remodeling of the brain tissue structure.

We study the spreading dynamics of a sessile viscoelastic drop on a horizontal surface, where a simplified Phan–Thien–Tanner (sPTT) model is considered to represent the rheology of viscoelastic drop. We have adopted a macroscopic approach to obtain the temporal evolution of the spreading drop, while to establish the efficacy of the theoretical model, we have validated the results obtained from the mathematical formulation with the experimental results for both the Newtonian (Si-oil) and viscoelastic (PDMS and aqueous solution of CMC and glycerin) drops. Following the framework of Seaver–Berg approximation, the spherical shape of the drop is assumed as a cylindrical disk here. We observe from this study that an increment in the elasticity of the fluid enhances the velocity gradient and increases the viscous dissipation in the drop volume, leading to a reduction in the spreading rate.

The study examines the thermal explosion branched-chain and entropy generation as a result of irreversibility of hydromagnetic reactive couple stress liquid with viscous heating and Navier slips. The reactive fluid flow is enhanced by heat dependent pre-exponential factor and axial pressure gradient in a porous wall. The flow equations for the non-Newtonian couple stress fluid model and heat transfer are solved by employing a semi-analytical collocation weighted residual method (CWRM). The efficiency and validity of the obtained results was verified with the existing results. The results reveal that at low hysteresis magnetic and viscous dissipation the irreversibility process is minimized and thermodynamic equilibrium is improved. The results from this study can assist in understanding the relationship between thermal and thermal explosions branched-chain. Keywords: Thermal criticality, Entropy generation, Viscous heating, Non-Newtonian fluid

Magnetic field plays a significant role in innumerable fields like mechanical, chemical, biological and medical research. Few examples include power generation systems, magnetohydrodynamic (MHD) accelerators, liquid metal fluids, cooling of nuclear reactors, high-temperature plasmas, chemical processing equipment and electronic components. In view of these facts, the current investigation discusses the fundamental flows of a Casson fluid in horizontal parallel plates (three fundamental situations considered such as the plate walls progresses in the conflicting directions, the progress of lower plate in the flow direction and other is in fixed position, and the progress of the plates in the flow direction respectively). Influences of radiation, velocity slip, porous medium and Joule heating are considered into account. The flow situation is assumed in Cartesian coordinate system. The momentum and energy equations are transformed into non-dimensional system utilizing appropriate non-dimensional parameters. The exact solutions of the non-dimensional differential equations have been obtained. The pictorial representations are provided for the velocity as well as temperature characteristics in all the mentioned cases. It is concluded by graphical approach that velocity is enhanced in the case of increasing Darcy's parameter and boundary slip while reduced for the large magnetic field. On the other hand, it is found that slip factor is reducing the heat transfer rate while magnetic field is giving rise to it.

The aim of present investigation was to study the effects of thermal radiation, viscous dissipation, ohmic dissipation and mass transfer effects on unsteady hydromagnetic boundary layer flow over a stretching surface. The governing equations of momentum, thermal and concentration boundary layers are reduced to a set of ordinary differential equations by means of suitable similarity transformations. Those equations are solved numerically for some arbitrary values of the governing physical parameters such as the Unsteadiness parameter (A), Magnetic interaction parameter (M2), Prandtl number (Pr), Radiation parameter (Rd), Eckert number (Ec) and Schmidt number (Sc) using Runge Kutta method of fourth order along with an efficient shooting method called Nachtsheim Swigert integration technique for the satisfaction of asymptotic boundary conditions. The results obtained are discussed with the help of graphical illustrations. Important physical concepts such as skin friction coefficient, Nusselt number and Sherwood number are also obtained and are discussed in detail. Keywords: Unsteady stretching surface, Radiation heat transfer, Mass transfer, MHD, Viscous dissipation, Ohmic dissipation

Double stratification in stagnation point flow of magneto Williamson nanoliquid towards nonlinear stretching sheet of variable thickness is explored. Flow is stretched in non-linear way since the sheet is assumed not flat. Aspects of viscous dissipation and radiation are accounted. First order chemical reaction is also present. Proper transformations lead to dimensionless the problems. Resultant problems is analytically solved via homotopic technique. Convergent solutions are obtained. Graphs and table are arranged to manifest the behavior of various influential variables. Our analysis pointed out that stratification variables diminishes the temperature and concentration. Moreover skin friction is decayed for larger magnetic parameter. Finally, conclusion of current investigations are listed in the last section.

This paper investigates upper-convected Oldroyd-B fluid thin film flow over an unsteady stretching sheet considering modified viscous dissipation and chemical reaction. With Cattaneo-Christov double diffusion theory, the governing equations are obtained. Meanwhile, unlike the viscous dissipation of Newtonian fluid, depending on the constitutive relation of Oldroyd-B fluid, the relaxation-retardation viscous dissipation is developed. Furthermore, the chemical reaction with relaxation-time characteristic has been discussed firstly. The governing equations are solved by a new efficient analytical method known as double-parameter transformation expansion method (DPTEM). Some interesting results can be revealed. Increasing unsteadiness parameter causes a rise in film thickness for β2 > β1, but a decline as β2 β1. Furthermore, unsteadiness parameter has the opposite influences on the concentration in the cases of β2 > β1 and β2

In this paper, we apply a new modification of the Adomian decomposition method for solving the problem of boundary layer convective heat transfer with viscous dissipation and low pressure gradient over a at plate. The technique is based on the standard Adomian decomposition method and the Chebyshev pseudospectral method. Comparisons are made between the pro-posed technique, the standard Adomian decomposition method, and the numerical solutions to demonstrate the applicability, validity, and high accuracy of the present approach. The results demonstrate that the new modification is more efficient and converges faster than the Adomian decomposition method. Keywords: Adomian decomposition method, Chebyshev spectral method, Boundary layer convective

We report detailed measurements of the rate-dependent fracture energy Γ of poroelastic gelatin gels for two distinct boundary conditions on the crack faces. When the crack tip is in contact with a reservoir of solvent, Γ increases linearly with the crack velocity V . When the tip is exposed to air, Γ ( V ) exhibits a marked departure from linearity at low enough velocities. We show that viscous dissipation associated with poroelastic flow in the tip vicinity plays a minor role in this phenomenon. We interpret the previously overlooked, peculiar behavior of dry cracks as resulting from the rate-dependent hydration state of the gelatin chains in the cohesive zone, where they are pulled-out. At large velocities, the cohesive zone is fully dry and Γ is larger than in the wet tip case. At velocities low enough for solvent to flow from the bulk of the gel, partial rehydration occurs and reduces the difference between the dry and wet fracture energies.

This paper presents an experimental study of heat transfer in a slightly rarefied gas flowing in a circular tube with constant wall temperature boundary condition. Local temperature measurements are carried out for the first time in rarefied gas flows to investigate into the anomalous values of Nusselt number (Nu) obtained by a previous experimental study (Demsis et al., 2009). The present measurements agree well with the low Nu reported by Demsis et al. (2009) when the Nu is obtained using their procedure; additionally, the measurements reveal the importance of end effects in determining the Nusselt number in rarefied gases. The Nusselt number obtained in the present experiments tends to zero with increasing axial conduction. Nu shows a weak dependence on Knudsen number for the range investigated here (0.001 < Kn < 0.012).

The goal of current research is to peruse the influences of magnetic field and nonlinear radiation on stagnation-point flow of nanofluid past a stretching surface. The Joule heating and viscous dissipation properties are considered for analysis in present work. The spectral relaxation numerical approach is implemented to solve the principal equations of the problem. Also, the influences of nanoparticles thermophoretic diffusion and Brownian motion, as well as Prandtl, Eckert, Lewis, and Biot numbers are analyzed and discussed in details. As a main result, it can be concluded that by increasing Prandtl number the temperature profile reduces for different values of radiation parameter. Furthermore, the results show that the nanofluid temperature profile rises with increase of Lewis number. In addition, the findings reveal that increasing the strength of the magnetic field affects the temperature and concentration of nanofluid.

This is corrigendum of the study reported in Ahmed et al. (2017). In the analysis, magnetization effects of magnets are missing in the constitutive relation which is an important characteristic of riga plates. Therefore, said effects are incorporated in the model. The solution code is updated accordingly and reproduced the results with comprehensive discussion.

Solar thermal absorption has an important role in the solar power plant to store the energy and usually, the solar systems face the problem to store and control the energy at high temperatures. The research aims to study the hybrid nanofluids which is used as the solar energy absorber and tends to store the thermal energy. In the this study, the authors focus on response of the inclined plate solar collector when the base fluid of water is substituted by the Hybrid nanofluid containing MgO (Magnesium oxide), CuO (Copper Oxide) with MWCNTs (Multiple wall carbon nanotubes), and water is used as a base solvent. The inclined plate is embedded in the permeable medium in the existence of solar radiation. The solution to the problem has been tackled through analytical techniques. The essential physical features are observed for heat transfer, absorption, and omission rate of the solar radiations.

Present study accords exploration of double diffusion in an axisymmetric flow of chemically reacting viscous fluid which impulsively starts flowing over a cylinder due to stretched surface. Non-Fourier law is employed to explain the heat flow whereas non-Fick's law of mass flux is employed to delve into the diffusion of mass. Activation energy is also taken into account. Transformed governing equations are solved using efficient mathematical technique called Homotopy Analysis Method (HAM). For the validity of the solution technique convergence table and h curves are plotted. Numerical solution has also been computed by using Shooting method for comparison with HAM. Entropy generation of the system has been investigated. Significant impact of pertinent flow parameters on thermal profile, concentration and velocity distribution are examined graphically. Velocity and thickness of momentum boundary layer increase by increasing curvature. Thermal profile is inversely related with Prandtl number and thermal relaxation time. Concentration profile trickles down by an increase in Schmidt number, mass relaxation parameter, Fitted rate constant and temperature ratio parameter. Most of the studies available in the literature focused on the double diffusion using generalized Fourier and Fick's laws neglecting activation energy and entropy generation which is an inevitable aspect in practical problems now a days. These features have been considered in the present article and it is the novelty of the present research.

While a microchannel heat sink is known to regulate the temperatures of microelectronics devices, viscous dissipation that originates from work done by viscous forces, might have an impact on the heat convection coefficient from a heated boundary. In this study, the exact solution of the temperature field is established for a fully developed forced convection in a parallel plate channel saturated with a porous medium, subjected to uniform heating at one boundary. Applying the new temperature field in a microchannel heat sink, modelled as a porous medium, this study gauges the effect of viscous dissipation on the electronics cooling device; utilizing a 4% volume fraction CuO-Water nanofluid as a coolant. Assuming a homogeneous model whereby the concentration of the nanofluid is taken as uniform spatially, the two-dimensional temperature field, computed based on the effective thermophysical properties of the nanofluid, reveals that viscous dissipation affects the heat convection at the heated boundary adversely, lowering the heat transfer coefficient by 15.3%, for Reynolds number, R e = 1500 and elevates the temperature gradient in the vicinity of the insulated boundary.

Results of theoretical study and numeric simulation of propagation of plane acoustic unipolar pulses and periodic waves in media with quadratic hysteretic nonlinearity and linear viscous dissipation are presented. The exact analytical solution is derived for self-similar pulses. Numerical simulation of propagation of initially triangular pulses and harmonic waves was carried out using spectral method. Agreement between analytical and numeric calculations is discussed.

This paper investigates the effects of viscous dissipation, pressure work, shear work, rarefaction and axial heat diffusion on convective heat transfer in a microtube gaseous flow. The problem is investigated numerically for the whole flow region using a finite difference scheme and the line Gauss-Seidel iterative technique. Exact solutions of the problem in terms of temperature distribution and Nusselt number variations are also derived under fully developed flow conditions. The microtube is assumed to be sufficiently long, so that fully developed conditions are established. The analysis presented demonstrate that the effect of the boundary shear work is significant and its contribution to heat transfer can be as high as that due to heat conduction close to the upper limit of the slip flow regime. As the shear work is a result of the combined effects of viscous dissipation and pressure work at the boundary, including these effects in the analysis leads to better predictions of heat transfer phenomena. Axial heat diffusion effect on Nusselt number and the thermal entrance length are also quantified.

Objective This paper addresses numerical investigation of steady, magneto-hydrodynamic boundary-layer slip flow of a nanofluid past a permeable stretching/shrinking sheet with thermal radiation using RKF45 with shooting technique. The effect of viscous dissipation, suction/injection, Brownian motion, thermophoresis, partial velocity slip and thermal slip is taken into account and controlled by the non-dimensional parameters. Results and conclusions The dual solutions are obtained for the skin friction, Nusselt number, temperature and nanoparticle volume fraction with pertinent parameters in the domain χ c , ∞ and s c , ∞ . The study shows that the Nusselt number decreases with an increase in thermophoresis parameter Nt and thermal slip parameter δ but increases with thermal radiation R and Prandtl number Pr. Practice implications The present problem has numerous applications in engineering and petroleum industries such as glass blowing, annealing and thinning of copper wires. The study of radiation heat transfer plays an important role in the industrial applications at high temperature.

This paper describes a novel model developed for a priori prediction of the maximal spread of a liquid drop on a surface. As a first step, a series of experiments were conducted under precise control of the initial drop diameter, its falling height, roughness, and wettability of dry surfaces. The transient liquid spreading was recorded by a high-speed camera to obtain its maximum spreading under various conditions. Eight preexisting models were tested for accurate prediction of the maximum spread; however, most of the model predictions were not satisfactory except one, in comparison with our experimental data. A comparative scaling analysis of the literature models was conducted to elucidate the condition-dependent prediction characteristics of the models. The conditioned bias in the predictions was mainly attributed to the inappropriate formulations of viscous dissipation or interfacial energy of liquid on the surface. Hence, a novel model based on energy balance during liquid impact was developed to overcome the limitations of the previous models. As a result, the present model was quite successful in predicting the liquid spread in all the conditions.

Annular flow of a viscoelastic fluid described by the Giesekus model has received some attention over the years, both concerning the fluid mechanical and thermal aspects, yet no investigation has been carried out using the analytical solution for the velocity profile in the energy equation to determine temperature distribution and heat transfer characteristics. Moreover, viscous dissipation, when accounted for, is usually defined by a formulation of the Brinkman number which proves inconsistent when applied to non-Newtonian fluids. In this work the purely tangential flow of a Giesekus fluid in an annulus with rotating inner wall subject to thermal boundary conditions of the first kind (imposed temperature) at the walls is investigated employing the analytical solution for the velocity profile. Viscous dissipation is accounted for by first deriving a consistent Brinkman number which is easily related to the one usually employed in previous studies and the temperature profiles are obtained for different values of the Deborah number and the non-dimensional mobility factor. Results for the Nusselt numbers at the inner and outer wall are also discussed.

Impinging liquid jets are widely used to clean unwanted soil layers from the walls of structures and vessels. When the soil is a thin layer of an immiscible viscoplastic material, removal involves the growth of a cleared area (which is circular for a jet impinging normally) bounded by a berm of displaced material. Glover et al. [1] presented a semi-empirical model relating the rate of removal to the momentum flow rate in the liquid film. We present a first-order model for cleaning thin layers of these materials based on the rate of rate of viscous dissipation in a shallow wedge of material at the cleaning front. This yields a result of the form of the model in [1], with expressions linking the kinetic parameters to measurable quantities including the rheology of the soil. The fully coupled problem is not solved: the wedge angle and residual layer thickness need to be specified and were obtained here by fitting to the data. The model is compared with experimental results obtained for three soft solids two petroleum jellies and a soft paraffin which exhibited Bingham plastic behaviour and creep, for jet Reynolds numbers between 10,000-37,000, and 0.1 < < 1.5, where is the average film depth and the layer thickness. The data show reasonable agreement with the model.

This study analyses current density and thermodynamics second law of double reaction of a magneto-Oldroyd 8-constant liquid in a convective asymmetric cooling medium. The viscoelastic properties of the liquid are prevented from distortion by convective cooling of the flow media device which is taken to satisfy Newton’s law of cooling. The flow momentum is motivated by exothermic reaction, chemical kinetics and energized by pressure gradient in the absence of material consumption. The dimensionless leading flow equations are solved using partition weighted residual analytical technique to reveal the parameters sensitivity and impacts on the viscoelastic flow liquid, exothermic combustible heat diffusion, entropy generation and current density. The solution results are presented in tables and graphs for clear understanding of the thermophysical parameters implication on the double reaction fluid considered. As observed, the second step reaction enhances exothermic reaction that in turn support complete combustion process in an engine. An improvement of thermodynamic equilibrium through reducing material terms and Frank-Kamenetskii will minimize the entropy generation and promote thermal engineering machine performance. Current density is augmented by rising second step reaction, electric field loading and activation energy ratio.

In this paper a numerical and asymptotic analysis to the Graetz problem with viscous dissipation is carried out, based on a series expansion of the temperature field, the Nusselt number is reported for different values of the Brinkman number. The range of Brinkman numbers considered has been extended to larger values. Numerical results are compared with an asymptotic analysis to larger values of Brinkman number.

Outcome of entropy generation in peristalsis of Casson fluid in a rotating frame is intended. Formulation is based upon thermal radiation, viscous dissipation and slip conditions of velocity and temperature. Lubrication approach is followed. The velocity components, temperature and trapping are examined. Specifically the outcomes of Taylor number, fluid parameter, slip parameters, Brinkman, radiation and compliant wall effects are focused. In addition entropy generation and Bejan numbers are examined. It is observed that entropy is controlled through slip effects. Keywords: Casson fluid, Radiative heat flux, Entropy generation, Rotating frame, Slip conditions, Wall properties

Multiple slips are most significant in many biological processes such as blood pumping from heart to various parts of body, endoscopy treatment, distribution of food and controlling the heat transport phenomena. By considering this, in the present investigation we analysed the multiple slips and joule's dissipation on magnetic Casson fluid over a stretching surface. To control the heat and mass transport phenomena we also included the heat source or sink, chemical reaction and thermal radiation. The arising physical governing systems of partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs). The transformed governing equations are solved numerically by using Runge-Kutta-Fehlberg method. We presented the numerical solutions for various governing parameters (Eckert number, Joule heating parameter, velocity, thermal and mass slip parameters etc) on velocity, temperature and concentration profiles. Graphical and numerical results are described for the various parameters of attention entering into the modelled problems. The present numerical results are compared with published results. It is found that the slip have propensity to control the boundary layer flow.

The purpose of present study is to identify the effects of viscous dissipation and suction/injection on MHD flow of a nanofluid past a wedge with convective surface in the appearance of slip flow and porous medium. The basic non-linear PDEs of flow and energy are altered into a set of non-linear ODEs using auxiliary similarity transformations. The system of equations together with coupled boundary conditions have been solved numerically by applying Runge-Kutta-Fehlberg procedure via shooting scheme. The influence of relevant parameters on non-dimensional velocity and temperature profiles are depicted graphically and investigated in detail. The results elucidate that as enhance in the Eckert number, the skin friction coefficient increases, while heat transfer rate decreases. The outcomes also specify that thermal boundary layer thickness declines with an increase in suction parameter. Moreover, it is accelerated with augment in injection parameter. The results are analogized with the study published earlier and it creates a fine concord.

In order to support the recent MEMS and Lab-on-a-chip technologies, we studied heat transport in micro-scale slit channel gas flows. Since the micro convection transport phenomena diverges from conventional macro-scale transport due to rarefaction, axial conduction and viscous heating, an accurate understanding requires a complete coupling of these effects. For such cases, we studied heat transfer in hydrodynamically developed, thermally developing gas flows in micro-slits at various flow conditions. The analytical solution of the energy equation considered both the heat conduction in the axial direction and heat dissipation of viscous forces. Furthermore, updated boundary conditions of velocity slip and temperature jump were applied based on Knudsen number of flow in order to account for the non-equilibrium gas dynamics. Local Nusselt number (Nu) values were calculated as a function of Peclet (Pe), Knudsen (Kn) and Brinkman (Br) numbers which were selected carefully according to possible micro-flow cases. Strong variation of Nu in thermal development length was found to dominate heat transfer behavior of micro-slits with short heating lengths for early slip flow regime. For this instance, influence of axial conduction and viscous dissipation was equally important. On the other hand, high Kn slip flow suppressed the axial conduction while viscous heating in a small surface-gas temperature difference case mostly determined the fully developed Nu and average heat transfer behavior as a function of Kn value., Marie Curie Actions under FP7 (TUBITAK 115C026)

Numerical solutions are carried out for steady state two dimensional electrically conducting mixed convection flow of Casson fluid along non-isothermal moving wedge through porous medium in the presence of viscous dissipation and heat generation/absorption. The governing partial differential equations, subject to boundary conditions are transformed into ordinary differential equations using similarity transformations. The transformed equations are then solved numerically by Keller-box method. To check the validity of present method, numerical results for dimensionless local skin friction coefficient and rate of heat transfer are compared with results of available literature as special cases and revealed in good agreement. The influence of pertinent parameters on velocity, temperature profiles, as well as wall shear stress and heat transfer rate is displayed in graphical form and discussed. It is found that fluid velocity increases with increase of Eckert number in case of assisting flow, while it decreases in case of opposing flow. It is also noticed that heat generation/absorption parameter influence fluid velocity and temperature significantly. A significant result obtained from this study is that heat transfer rate reduces with increase of Prandtl number in the presence of viscous dissipation effect. Also, increasing values of Eckert number have no effects on force convection flow.

The influence of the viscous dissipation and radiation effects on the natural convection heat transfer in a square cavity filled with porous media saturated with a nanofluid is studied. The vertical walls of the cavity are subject to finite temperature difference while the top and bottom walls of the cavity are insulated. The Buongiorno's nanofluid model, incorporating the Brownian motion and thermophoresis effects, is employed. The governing equations, in nondimensional form, are written in the weak form and solved using the finite element method. The influences of viscous dissipation and radiation effects on the concentration distribution of nanoparticles are discussed. The average and local Nusselt numbers are reported for various values of viscous dissipation (Eckert number) and radiation effects. The results show that the Nusselt numbers at the hot and cold walls are not equal due to the presence of viscous dissipation effects. The raise of Eckert number decreases the Nusselt number at hot wall, but it increases the Nusselt number at the cold wall. It is also found that the increase of Lewis number enhances the heat transfer in the cavity.

This paper is concerned with the unsteady two-dimensional boundary layer flow of an incompressible Williamson fluid over an unsteady permeable stretching surface with thermal radiation. Effects of electric and magnetic fields are considered. The nonlinear boundary layer partial differential equations are first converted into the system of ordinary differential equations and then solved analytically. Effects of physical parameters such as Weissenberg number, unsteadiness parameter, suction parameter, magnetic parameter, electric parameter, radiation parameter, Prandtl number and Eckert number on the velocity and temperature are graphically analyzed. The expressions of skin friction coefficient and local Nusselt number are presented and examined numerically.

This article deals with the exact solutions regarding heat transfer of viscous fluid over a non-linear radially stretching sheet. The effects of viscous dissipation on the heat transfer characteristics are considered in account in the presence of a transverse magnetic field for two types of boundary heating process namely prescribed power law surface temperature (PST) and prescribed heat flux (PHF). Similarity transformations are used to reduce the governing non-linear momentum and thermal boundary layer equations into a set of ordinary differential equations. The exact solutions of the reduced ordinary differential equations are developed in the form of confluent hypergeometric function and graphically sketched to see the influence of pertinent parameters on the temperature profiles. In addition the results for the wall temperature gradient (Nusselt number) are also presented in graphical form and discussed in detail. It is found that Prandtl number decelerates the temperature profiles in both PST and PHF cases. Thermal boundary layer thickness increases by increasing the Eckert number.

In this paper, we show the global well-posedness for the 2 1 2 D Benard equations with partial viscosity terms, i.e. (1)?µ > 0 and ? = 0 ; (2)? µ = 0 and ? > 0, which mean the zero thermal diffusivity and the zero viscous dissipation, respectively.

In this paper, the influence of some thermo-physical properties of fluid on heat and mass transfer flow past semi-infinite moving vertical plate is considered. The fluid considered is optically thin such that the thermal radiative heat loss on the fluid is modeled using Rosseland approximation. The governing equations representing the physical model is a system of partial differential equations which are transformed into systems of coupled non-linear partial differential equation by introducing non-dimensional variables. The resulting equations are solved using the spectral relaxation method (SRM). The result shows that an increase in Eckert number of the fluid actually increases the velocity and temperature profiles of the flow. Whereas an increase in thermal radiation parameter reduces the temperature distribution when the plate is being cooled. The computational results for velocity, temperature and the concentration profiles are displayed graphically for various flow pertinent parameters.