Expressions For Nusselt Number Research Articles

MHD flow of water-based Brinkman type nanofluid over a vertical plate embedded in a porous medium with variable surface velocity, temperature and concentration

The aim of this paper is to investigate the unsteady magnetohydrodynamic (MHD) flow of Brinkman type nanofluid over a vertical plate embedded in a porous medium with variable surface velocity, temperature and concentration. The thermal radiation effect in the energy equation and chemical reaction in the concentration are also considered. Four different types of nanoparticles of spherical shape namely Silver (Ag), Copper (Cu), Titanium oxide (TiO2) and Aluminum oxide (Al2O3) are suspended in water taken as conventional base fluid. The problem is modeled in terms of partial differential equations with physical boundary conditions. Closed form solutions are obtained for velocity, temperature and concentration, using the Laplace transform technique. Graphical results for different physical parameters such as Brinkman parameter, volume fraction and radiation parameter are presented. Corresponding expressions for skin-friction, Nusselt number and Sherwood number are also evaluated. The present solutions are reduced to some well-known results in the published literature and are found in an excellent agreement.

The impact silver nanoparticles on MHD free convection flow of Jeffrey fluid over an oscillating vertical plate embedded in a porous medium

This article studies the influence of copper nanoparticles (CuNPs) and silver nanoparticles (AgNPs) on the unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid over an oscillating vertical plate embedded in a saturated porous medium. Nanoparticles (CuNPs and AgNPs) are suspended in Kerosene oil which is chosen as a conventional base fluid. Appropriate dimensionless variables are employed to the governing equations and the exact solutions are obtained for velocity and temperature fields using the Laplace transform technique. The results for various controlling parameters for both CuNPs and AgNPs are shown graphically and discussed in details. Expressions for skin friction and Nusselt number are also evaluated and presented in tabular forms. It has been observed that, an increase of volume fraction leads to the enhancement of velocity and temperature distributions. On the other hand, Hartmann number tends to resist the fluid flow due to the Lorentz force. A comparative study of the present results with the results from the earlier works provides an excellent agreement.

Hydromagnetic boundary layer flow of Williamson fluid in the presence of thermal radiation and Ohmic dissipation

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.

Heat transfer in ferrofluid with cylindrical shape nanoparticles past a vertical plate with ramped wall temperature embedded in a porous medium

This paper studies magnetogydrodynamic (MHD) and porosity effects on ferrofluid over an oscillating plate with time dependent wall temperature. Nanoparticles of cylindrical shape are contained inside the base fluids. Kerosene oil is chosen as conventional base fluids. Two types of nanoparticles, magnetite (Fe3O4) and non-magnetic (Al2O3) are added to the base fluid. The flow is unsteady and the ferrofluid is considered as an electrically conducting due to a uniform magnetic field applied in a perpendicular direction to the plate. The problem is modelled in terms of partial differential equation with some physical conditions and solved by using the Laplace transform technique. Exact solutions are obtained for velocity and temperature for both cases of time dependent and isothermal wall temperatures. Graphs of velocity and temperature for time dependent and isothermal wall temperatures are plotted and compared. It is found that under time dependent wall temperature condition, velocity and temperature are smaller in magnitudes than those obtained under isothermal wall temperature condition. Moreover, effects of porosity and Hartmann number are studied graphically and discussed. A comparison is also made between magnetite (Fe3O4) and non-magnetic (Al2O3) nanoparticles. Expressions for skin-friction and Nusselt number are computed in tables. Excellent agreement of the present results is found with existing results in the literature. In this work, cylindrical nanoparticles are chosen because of their abundant applications in biology and medicine. For instance, cylindrical nanoparticles are seven times more deadly than traditional spherical nanoparticles when delivering drugs to breast cancer cells.

Entropy Generation on Nanofluid Flow through a Horizontal Riga Plate

In this article, entropy generation on viscous nanofluid through a horizontal Riga plate has been examined. The present flow problem consists of continuity, linear momentum, thermal energy, and nanoparticle concentration equation which are simplified with the help of Oberbeck-Boussinesq approximation. The resulting highly nonlinear coupled partial differential equations are solved numerically by means of the shooting method (SM). The expression of local Nusselt number and local Sherwood number are also taken into account and discussed with the help of table. The physical influence of all the emerging parameters such as Brownian motion parameter, thermophoresis parameter, Brinkmann number, Richardson number, nanoparticle flux parameter, Lewis number and suction parameter are demonstrated graphically. In particular, we conferred their influence on velocity profile, temperature profile, nanoparticle concentration profile and Entropy profile.

Electroviscous effect and convective heat transfer of pressure-driven flow through microtubes with surface charge-dependent slip

Although electroviscous effect and convective heat transfer of pressure-driven flow in a microtube have been widely studied, the effect of surface charge on the boundary slip is less considered in previous studies in these fields. This present work develops closed form expressions of velocity distribution, temperature distribution and Nusselt number for hydrodynamically and thermally fully developed pressure-driven flow in a microtube considering the dependence of slip on the surface charge. On basis of these, the combined effect of surface charge and surface charge-dependent slip on the electroviscous effect and convective heat transfer of the pressure-driven flow are studied. The results show that slip length decreases with increasing magnitude of zeta potential of the solid–liquid interface, and this dependence of slip on surface charge inevitably affect the fluidic behavior and convective heat transfer. The slip can increase the Nusselt number by increasing the velocity of the pressure-driven flow, however, the zeta potential leads to a decrease in the Nusselt number by decreasing the velocity. When considering the dependence of slip on surface charge, there is a further reduction on the Nusselt number due to a further decreasing velocity induced by the decreasing slip length. Both a larger magnitude of zeta potential and a larger slip length lead to a larger misestimate of the flow rate and Nusselt number without considering the surface charge-dependent slip. The underlying mechanisms of these phenomena are analyzed.

Effect of magnetic field on the Nusselt number of a multi-plate thermoacoustic system

This paper presents the results of heat transfer of a multi-plate thermoacoustic system using complex Nusselt number in the presence of magnetic field. Assuming the applied magnetic field is perpendicular to the direction of the oscillating fluid flow, we derive the expressions for the fluctuating velocity and temperature from the governing unsteady-compressible-viscous forms of the continuity, momentum, and energy equations. These equations are simplified assuming small amplitude oscillations, a long wave, and a short stack. The hydrodynamic and thermal boundary layers are considered to be very small compared to the acoustic wavelength, and the longitudinal conduction heat transfer inside the boundary layers is assumed to be negligible. Both bulk mean and space averaged temperatures are considered as reference temperatures in the analytical solution. The complex Nusselt number equations are simplified and expressed as a function of the Hartmann number (Haδ), the Swift number (Sw), the modified Swift number (S¯w) and Rott’s functions (fν and fk). The effect of Haδ, Sw, and S¯w on the Nusselt number is analyzed and presented graphically for both viscous and inviscid fluids. The value of Nusselt number in the boundary layer limit for the inviscid fluid is also analyzed. In the absence of a magnetic field, the simplified complex Nusselt number expression that is obtained by using the space averaged temperature as a reference temperature is compared with the data available in the literature and an excellent agreement is observed. This study will offer insight into ways to increase convection heat transfer rate, consequently help the thermoacoustic system designer to design a more power dense thermoacoustic system.

Numerical solutions for magnetohydrodynamic flow of nanofluid over a bidirectional non-linear stretching surface with prescribed surface heat flux boundary

Numerical solutions of three-dimensional flow over a non-linear stretching surface are developed in this article. An electrically conducting flow of viscous nanoliquid is considered. Heat transfer phenomenon is accounted under thermal radiation, Joule heating and viscous dissipation effects. We considered the variable heat flux condition at the surface of sheet. The governing mathematical equations are reduced to nonlinear ordinary differential systems through suitable dimensionless variables. A well-known shooting technique is implemented to obtain the results of dimensionless velocities and temperature. The obtained results are plotted for multiple values of pertinent parameters to discuss the salient features of these parameters on fluid velocity and temperature. The expressions of skin-friction coefficient and Nusselt number are computed and analyzed comprehensively through numerical values. A comparison of present results with the previous results in absence of nanoparticle volume fraction, mixed convection and magnetic field is computed and an excellent agreement noticed. We also computed the results for both linear and non-linear stretching sheet cases.

Natural Convection Boundary Layer Flow of a Double Diffusive and Rotating Fluid Past a Vertical Porous Plate

An investigation is carried out for a fully developed unsteady magnetohydrodynamic free convection flow of a viscous incompressible and electrically conducting Newtonian fluid through porous medium bounded by an infinite vertical porous plate, in a rotating system in the presence of heat source and thermal diffusion. The porous plane and the porous medium are assumed to rotate in a solid body rotation. Whereas the vertical surface is subject to variable suction perpendicular to it and the temperature at this surface varies with respect to time about a nonzero constant mean. Analytical solutions for the distributions of velocity, temperature and concentration fields are obtained by using a regular perturbation technique. The effects of pertinent parameters on these distributions are studied numerically with the help of graphs. With the aid of the above flow quantities the expressions for skin friction, Nusselt number and Sherwood number are derived. Variations in these distributions are presented in tables. It is noticed that the velocity boundary layer condenses with the increasing values of Schmidt number. Flow reversal is prevented for low speed of rotation, high value of chemical reacting species and high value of magnetic parameter.

Unsteady MHD Heat And Mass Transfer Flow Of A Radiating Fluid Past An Accelerated Inclined Porous Plate With hall Current

An analysis has been carried out to study the effects of Hall current and radiation of MHD free convective heat and mass transfer flow past an accelerated inclined plate with temperature and concentration in a porous medium in presence of thermal diffusion and heat source. The solutions for velocity field, temperature field and concentration distribution are obtained using Laplace transform technique. The expressions for skin friction, Nusselt number and Sherwood number are also derived. The variations in fluid velocity, fluid temperature and species concentration are shown graphically, whereas numerical values of skin friction, Nusselt number and Sherwood number are presented in tabular form for various values of physical parameters.

Flow of ReinerPhilippoff based nano-fluid past a stretching sheet

In this article flow of a classical non-Newtonian fluid, Reiner–Philippoff fluid, in the presence of nano-particles over a non-linear stretching sheet is studied numerically. The mathematical model incorporates the non-linear stress-deformation behavior for Reiner–Philippoff fluid and Brownian motion and thermophoresis effects due to nanoparticles. The correlation expressions for skin friction, Nusselt number and Sherwood number are developed by performing linear regression on the obtained numerical data. The effects of nano-particles and Reiner–Philippoff fluid are discussed on the skin friction, Nusselt number and Sherwood number. It is observed that skin friction for dilatant fluids is higher than pseudoplastic fluids and temperature and nanoparticles concentration fluxes at the surface increase with an increase in Reiner–Philippoff fluid parameter.

Heat and mass transfer analysis for MHD flow of nanofluid inconvergent/divergent channels with stretchable walls using Buongiorno’s model

The present article investigates the flow, heat, and mass transfer in the convergent and divergent channels under the influence of magnetic field. The walls of the channel are also considered to be stretching/shrinking. Buongiorno’s model is used to formulate the problem for nanofluids. The equations governing the flow are transformed to a set of nonlinear ordinary differential equations by employing appropriate similarity transformations. Solution of the equations is obtained with the help of a useful and efficient numerical technique called the Runge–Kutta–Fehlberg method. Influence of the various emerging parameters on velocity, temperature and concentration profiles is described pictorially. Comprehensive discussions on the results obtained are provided. Backflow phenomena are observed for the stretching of divergent channel when angle opening and Re are increasing. This backflow can be controlled in two ways: one is by applying a strong magnetic field and other by shrinking the walls of the divergent channels. These results can be useful in various practical situations. Furthermore, expressions for skin friction coefficient, Nusselt and Sherwood numbers are obtained, and the variations in these quantities are analyzed graphically. Comparison of the results obtained here with the ones already existed in the literature confirms our solutions.

Entropy Generation on MHD Casson Nanofluid Flow over a Porous Stretching/Shrinking Surface

In this article, entropy generation on MHD Casson nanofluid over a porous Stretching/Shrinking surface has been investigated. The influences of nonlinear thermal radiation and chemical reaction have also taken into account. The governing Casson nanofluid flow problem consists of momentum equation, energy equation and nanoparticle concentration. Similarity transformation variables have been used to transform the governing coupled partial differential equations into ordinary differential equations. The resulting highly nonlinear coupled ordinary differential equations have been solved numerically with the help of Successive linearization method (SLM) and Chebyshev spectral collocation method. The impacts of various pertinent parameters of interest are discussed for velocity profile, temperature profile, concentration profile and entropy profile. The expression for local Nusselt number and local Sherwood number are also analyzed and discussed with the help of tables. Furthermore, comparison with the existing is also made as a special case of our study.

EXPERIMENTAL FORCED SOLAR THIN LAYER GINGER DRYING

In this research paper, the convective and the evaporative heat transfer coefficients of ginger (zingiber officinale) drying in an indirect solar cabinet dryer under the induced forced convection mode is presented. Experiments were conducted during the month of March 2015 under the climatic conditions of Hisar, India (29°5’5”N latitude and 75°45’55”E longitude). The experimental data obtained for solar drying of a constant ginger mass of 150 g has been used to determine constants ‘C’ and ‘n’ in the Nusselt number expression using linear regression analysis; consequently, the convective and the evaporative heat transfer coefficients have been evaluated. The average value of constants ‘C’ and ‘n’ were evaluated as 0.999 and 0.318, respectively. The average values of the convective and the evaporative heat transfer coefficients were found to be 3.95 W/m2 °C and 160.47 W/m2 °C, respectively, for the given mass samples of ginger. The average collector efficiency was observed to be 14.5%. The experimental error in terms of percentage uncertainty was found to be 20.87%.

Free convective MHD flow of visco-elastic fluid past a vertical porous plate in the presence of heat source and chemical reaction

Magnetohydrodynamics flow of a visco-elastic incompressible fluid (Walter’s B′ model) past an infinite porous plate in porous medium under the action of transverse uniform magnetic field in the presence of heat source and chemical reaction is investigated. The governing equations of the motion, energy and concentration are solved by a successive perturbation technique. The flow phenomenon is characterized by suction parameter, magnetic parameter, porosity parameter, Grashoff number, modified Grashoff number, Prandtl number, heat source parameter, chemical reaction parameter and Schmidt number. The expressions for skin friction coefficient, Nusselt number, and Sherwood number on the surface are also discussed.

Impact of velocity slip and joule heating on MHD peristaltic flow through a porous medium with chemical reaction

The present study investigates the effect of joule heating and velocity slip on MHD peristaltic flow in a porous medium with chemical reaction. The relevant equations on the fluid flow have been developed. Analytic solution is carried out under long-wavelength and low-Reynolds number approximations. Exact solution is evaluated for the stream function, which is used to find the velocity of the fluid flow, temperature, concentration. Numerical computations have been performed for the influence of various emerging parameters on the flow characteristics velocity, temperature, concentration are shown and discussed with the help of graphs. Also, the expressions for skin friction coefficient, Nusselt number and Sherwood number at the channel wall are obtained and analyzed. It is found that a generative chemical reaction is greater than the destructive chemical reaction on the concentration. The size of the trapping bolus increases with increasing velocity slip parameterβ.

Magneto Convective Flow of a Non-Newtonian Fluid through Non-Homogeneous Porous Medium past a Vertical Porous Plate with Variable Suction

Radiation absorption and chemical reaction effects on unsteady MHD free convective flow of a viscoelastic fluid past a vertical porous plate in the presence of variable suction and heat source is considered. A uniform magnetic field is assumed to be applied in the transverse direction of the flow. The set of non-linear partial differential equations is transformed into a set of ordinary differential equations by super imposing a solution with steady and unsteady part. The set of ordinary differential equations is solved by using regular perturbation scheme. The expressions for velocity, temperature and species concentration fields are obtained and the expressions for Skin friction, Nusselt number and Sherwood number are also derived. The effects of numerous physical parameters on the above flow quantities are studied with the help of graphs and tables.

Influence of Thermal Radiation on Unsteady MHD Free Convection Flow of Jeffrey Fluid over a Vertical Plate with Ramped Wall Temperature

Influence of thermal radiation on unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid over a vertical plate with ramped wall temperature is studied. The Laplace transform technique is used to obtain the analytical solutions. Expressions for skin friction and Nusselt number are also obtained. Results of velocity and temperature distributions are shown graphically for embedded parameters such as Jeffrey fluid parameterλ, Prandtl numberPr, Grashof numberGr, Hartmann numberHa, radiation parameterRd, and dimensionless timeτ. It is observed that the amplitude of velocity and temperature profile for isothermal are always higher than ramped wall temperature.

A Study of Mixed Convection Flow over Stretching Cylinder in Presence of Slip Flow and Thermal Jump Boundary Conditions

The present work focuses on the study of flow and heat transfer in the axisymmetric flow of a viscous incompressible fluid over a permeable vertical stretching cylinder. The flow model is studied for the second order slip flow and first order thermal jump boundary condition. The governing equations of continuity, momentum and energy are transformed into system of non-linear ordinary differential equations and solved numerically. The velocity and temperature distributions are discussed and shown through graphs. The effects of various physical parameters are examined and discussed in detail. The expressions of skin-friction coefficient and Nusselt number at the cylinder are discussed and their variations are presented through tables. It is found that the increase in first and second order slip parameters increases the fluid velocity while temperature distribution is not considerably affected. Further, the increase in thermal jump parameter tends to increase fluid velocity and temperature.

Effects of Time Dependent Variable Temperature and Concentration Boundary Layer on MHD Free Convection Flow Past a Vertical Porous Plate in the Presence of Thermal Radiation and Chemical Reaction

An analytical solution is presented for the case of time dependent variable temperature and variable concentration boundary layer on unsteady MHD free convection flow past a vertical porous plate in the presence of thermal radiation, thermal diffusion and first order chemical reaction. The dimension less governing equations are solved analytically and the expressions for temperature, concentration and velocity fields are determined using the Laplace transform technique. Finally, the influence of various physical parameters on the temperature, concentration and velocity fields is graphically studied and discussed. The expressions for local skin friction, Nusselt number and Sherwood number are derived and discussed with the help of tables. It noticed that Skin friction increase with an increase in magnetic parameter, Prandtl number, radiation parameter and chemical reaction parameter while it decrease with an increase in Grashof number, modified Grashof number, permeability parameter, heat source and Schmidt number. The rate of heat transfer increase with increasing values of Prandtl number and radiation parameter while it decreases with increasing value of heat source. The rate of mass transfer increases with increasing values of Schmidt number and chemical reaction parameter.