Application of multiple magnetic coils to drive the air flow in a long pipe

The laminar air flow in a pipe is studied with application of multiple magnetic fields at the point of uniform heat flux heating from the wall as the first boundary conditions. As the second boundary condition, after a coil, uniform heat flux heating and then uniform heat flux cooling from the wall is applied. Numerical computations are successfully carried out by solving transient 2-D equations with pressure gradient boundary condition for three lengths of pipe and two boundary conditions. The first one is for a ratio of pipe length and diameter L = 10 with a single electric coil. The second one is for L = 20 with two electric coils and the third one is for L = 30 with three electric coils to generate the magnetic field. A parameter ξ is from 0 to 2 × 10⁷, which represents the strength of the magnetic field and the uniform heat flux from the pipe wall. The results show that the volume flow rate increases with the strength of magnetic field. Magnetic fields generated by the multi-coils can drive the air flow in the corresponding longer pipe almost equally to the shorter one with a single coil. From the distributions of the cross-sectional magnetic force along the pipe length, the effect of pressure, pressure gradient distribution along the pipe length, and the effect of gradient magnetic field and temperature field on the overall air flow rate can be analyzed and compared on the effect of wall cooling.     

Magnetic field effect on the unsteady free convection flow in a square cavity filled with a porous medium with a constant heat generation

The effects of an inclined magnetic field and heat generation on unsteady free convection within a square cavity filled with a fluid-saturated porous medium have been investigated numerically. The top and bottom horizontal walls of the enclosure are adiabatic whereas the vertical walls are kept at constant but different temperatures. The physical problems are represented mathematically by a set of partial differential equations along with the corresponding boundary conditions. By using an implicit finite-difference scheme, namely the ADI method (Alternative Direction Implicit), the non-dimensional governing equations are numerically solved. The influential parameters are the Rayleigh number Ra, the inclination angle γ of the magnetic field relative to the gravity vector g, the Hartmann number Ha and the heat generation parameter Q. In the present study, the obtained results are presented in terms of streamlines, isotherms and average Nusselt number along the hot wall. The result shows that with increasing Ha, the diffusive heat transfer become prominent even though the Rayleigh number increases.     

The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer

The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer rates, as given by the Nusselt number, is numerically evaluated subject to constant wall heat flux (H2) and constant wall temperature (T) thermal boundary conditions. Numerical results are obtained using a continuum based, three-dimensional, compressible, unsteady computational fluid dynamics algorithm with slip velocity and temperature jump boundary conditions applied to the momentum and energy equations, respectively. For the limiting case of parallel plate channels, analytic solutions for the thermally and hydrodynamically fully developed momentum and energy equations are derived, subject to both first- and second-order slip velocity and temperature jump boundary conditions, from which analytic Nusselt number solutions are then obtained. Excellent agreement between the analytical and numerical results verifies the accuracy of the numerical algorithm, which is then employed to obtain three-dimensional rectangular channel and thermally/hydrodynamically developing Nusselt numbers. Nusselt number data are presented as functions of Knudsen number, Brinkman number, Peclet number, momentum and thermal accommodation coefficients, and aspect ratio. Rarefaction and viscous dissipation effects are shown to significantly affect the convective heat transfer rate in the slip flow regime.     

Heat transfer for Herschel–Bulkley fluids in the entrance region of a rectangular duct

In this study, we present a numerical solution for combined laminar fluid flow and heat transfer of Herschel–Bulkley non-Newtonian fluids in the entrance region of a rectangular duct. The governing equations are solved iteratively by using finite difference method to obtain temperature, bulk temperature, and Nusselt number. Two cases of the thermal boundary conditions are considered; (i) T thermal boundary condition “constant temperature at the wall” and (ii) H2 thermal boundary condition “constant heat flux at the wall”. The results are presented in tables and figures for different parameters for the fluid and the duct geometry.     

Development of free convection flow of a gas in a heated vertical open tube

The system is a vertical tube open at both ends and heated at the wall. An ambient gas (Pr = 0.7) enters the bottom of the tube with uniform velocity and temperature and flows up through the tube due to natural convection. The flow is assumed to be both stable and laminar. The incompressible thermal boundary layer equations for this situation were solved by a finite difference method for conditions of constant wall temperature and constant wall heat flux.     

Similarity solutions for flows and heat transfer in microchannels between two parallel plates

In this paper we give analytical similarity solutions of the Navier–Stokes equations coupled with energy equation of Newtonian fluid in a microchannel between two parallel plates taking into account the effects of viscous dissipation, the velocity slip and the temperature jump at the wall. Two different thermal boundary conditions are considered: the constant heat flux (CHF) and the constant wall temperature (CWT). We provide new similarity transformations for the governing equations and derive the expressions of Poiseuille number (Po) and Nusselt number (Nu). Then, the homotopy analysis method (HAM) is employed to solve the nonlinear differential equations with related boundary conditions. Both the dimensionless analytical expressions of velocity and temperature are obtained. The rarefaction effects on velocity distribution and flow friction are exhibited. The interactive effects of the Brinkman number (Br) and the Knudsen number (Kn) on Nu are analytically studied for both the CHF and CWT cases.     

Effects of viscous dissipation on the heat transfer in a forced pipe flow. Part 2: Thermally developing flow

In this part of the study, consideration is given to thermally developing laminar forced convection in a pipe including viscous dissipation. The axial heat conduction in the fluid is neglected. Two different thermal boundary conditions are considered: the constant heat flux (CHF) and the constant wall temperature (CWT). Both the wall heating (the fluid is heated) case and the wall cooling (the fluid is cooled) case are considered. The distributions for the developing temperature and local Nusselt number in the entrance region are obtained. Results show that the temperature profiles and local Nusselt number are influenced by the Brinkman number (Br) and the thermal boundary condition used for the wall. Significant viscous dissipation effects have been observed for large Br.     

Numerical investigation of natural convection in an inclined enclosure filled with porous medium under magnetic field

In the present study, natural convection of fluid in an inclined enclosure filled with porous medium is numerically investigated in a strong magnetic field. The physical model is heated from left-hand side vertical wall and cooled from opposing wall. Above this enclosure an electric coil is set to generate a magnetic field. The Brinkman–Forchheimer extended Darcy model is used to solve the momentum equations, and the energy equations for fluid and solid are solved with the local thermal non-equilibrium (LTNE) models. Computations are performed for a range of the Darcy number from 10⁻⁵ to 10⁻¹, the inclination angle from 0 to π/2, and magnetic force parameter γ from 0 to 100. The results show that both the magnetic force and the inclination angle have significant effect on the flow field and heat transfer in porous medium.     

Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition

Non-Newtonian boundary layer flow and heat transfer over an exponentially stretching sheet with partial slip boundary condition has been studied in this paper. The flow is subject to a uniform transverse magnetic field. The heat transfer analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST), and (ii) prescribed heat flux (PHF). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. An effective second order numerical scheme has been adopted to solve the obtained differential equations. The important finding in this communication is the combined effects of the partial slip and the third grade fluid parameters on the velocity, skin-friction coefficient and the temperature boundary layer. It is found that the third grade fluid parameter β increases the momentum boundary layer thickness and decreases the thermal boundary layer thickness.     

MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition

A numerical approach has been used to study the heat and mass transfer from a vertical plate embedded in a porous medium experiencing a first-order chemical reaction and exposed to a transverse magnetic field. Instead of the commonly used conditions of constant surface temperature or constant heat flux, a convective boundary condition is employed which makes this study unique and the results more realistic and practically useful. The momentum, energy, and concentration equations derived as coupled second-order, ordinary differential equations are solved numerically using a highly accurate and thoroughly tested finite difference algorithm. The effects of Biot number, thermal Grashof number, mass transfer Grashof number, permeability parameter, Hartmann number, Eckert number, Sherwood number and Schmidt number on the velocity, temperature, and concentration profiles are illustrated graphically. A table containing the numerical data for the plate surface temperature, the wall shear stress, and the local Nusselt and Sherwood numbers is also provided. The discussion focuses on the physical interpretation of the results as well their comparison with the results of previous studies.     

Investigation effect of nanoparticle mean diameter on mixed convection Al2O3-water nanofluid flow in an annulus by two phase mixture model

In this paper, laminar mixed convection of nanofluid (Al₂O₃–water) in horizontal concentric annulus with constant heat flux boundary condition has been studied. Two thermal boundary conditions were investigated, one in which a uniform heat flux at the inner wall and an adiabatic at the other wall, and the other inner and outer walls were heated in a same heat flux. Two phase mixture model employed to investigate effect of mean diameter of nanoparticle on the hydrodynamics and thermal characteristic. The fluid flow properties are assumed constant except for the density in the body force, which varies linearly with the temperature (Boussinesq's hypothesis), thus the fluid flow characteristics are affected by the buoyancy force. Three dimensional elliptical governing equations have been discretized using the finite volume approach (FVM) using SIMPELC algorithm to investigate fluid flow throughout of an annulus duct. Numerical simulations have been carried out for the nanoparticle volume fraction (ϕ = 0.02) and various mean diameters of nanoparticles (d_p) between 13 and 72 nm and different values of the Grashof and Reynolds numbers. The calculated results demonstrate that Nusselt number decreases with increasing nanoparticle mean diameter while it does not influence significantly the hydrodynamic parameters. Also this results show that nanoparticle distribution at the annuluses cross section is non-uniformity.     

Investigation of a multiple piezoelectric–magnetic fan system embedded in a heat sink

Previous studies have investigated the thermal performance of embedding a single piezoelectric fan in a heat sink. Based on this work, a multiple piezoelectric–magnetic fan system (“MPMF”) has been successfully developed that exhibits lower fan power consumption, optimum fan pitch and an optimum fan gap between the fan tips and the heat sink. In this study, the cooling performance and heat convection improvement for the MPMF system embedded in a heat sink are evaluated at different fan tip locations. The results indicate that the fan tip location of the MPMF system at x/S_l = 0.5 and y/S_h = 0 is an optimum configuration, improving the thermal resistance by 53.2% over natural convection condition for the fan input power of 0.1 W. The MPMF system breaks the thermal boundary layer and causes fluctuations inside the fins of the heat sink to enhance the overall heat transfer coefficient. Moreover, the relationship between the convection improvement and the Reynolds number for the MPMF system has been investigated and transformed into a correlation line for nine different fan tip locations to provide a means of predicting the cooling performance for the MPMF system embedded in a heat sink.     

An exact analysis of radiative heat transfer and unsteady MHD convective flow of a second‐grade fluid with ramped wall motion and temperature

The influence of simultaneously applied ramped boundary conditions on unsteady magnetohydrodynamic natural convective motion of a second‐grade fluid is investigated and analyzed in this study. The motion of the fluid is considered near an infinite upright plate that is nested in a porous medium subject to nonlinear thermal radiation effects. The Laplace transformation technique is utilized to acquire the exact solutions of momentum and energy equations. To effectively examine the rate of heat transfer and shear stress, the Nusselt number and skin friction coefficient are also established. The outcomes of mathematical computations are elucidated through tables and figures to highlight some physical aspects of the problem. Some limiting models of the present problem are also deduced and presented. On comparison, it is observed that the fluid exhibits lower temperature and velocity profiles under ramped boundary conditions. It is also found that wall shear stress can be controlled by choosing large values of the magnetic parameter (M) and Prandtl number (Pr). In addition, the heat transfer rate specifies inverse trends for growing values of radiation parameter (Nr) and Prandtl number (Pr), while it increases rapidly under a ramped surface condition and decreases slowly under a constant surface condition.     

MHD Flow and Heat Transfer of a Dusty Fluid Over a Stretching Hollow Cylinder with a Convective Boundary Condition

In this study, we deal with the problem of a steady two‐dimensional magnetohydrodynamic (MHD) flow of a dusty fluid over a stretching hollow cylinder. Unlike the commonly employed thermal conditions of constant temperature or constant heat flux, the present study uses a convective heating boundary condition. The multi‐step differential transform method (multi‐step DTM), one of the most effective methods, is employed to find an approximate solution of the system of highly nonlinear differential equations governing the problem. Comparisons are made between the results of the proposed method and the numerical method in solving this problem and excellent agreement has been observed. The influence of important parameters on the flow field and heat transfer characteristics are presented and discussed in detail. The results show that both the thermal boundary layer thickness and the heat transfer rate at the wall increases with increasing Biot number Bi, while it has no effect on the skin friction coefficient. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 221–232, 2014; Published online 30 August 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21073     

Three-dimensional laminar slip-flow and heat transfer in a rectangular microchannel with constant wall temperature

Three-dimensional laminar slip-flow and heat transfer in rectangular microchannels having constant temperature walls are studied numerically using the finite-volume method for thermally and simultaneously developing flows. The Navier–Stokes and energy equations are solved with velocity slip and temperature jump at the wall. A modified convection–diffusion coefficient at the wall–fluid interface is defined to incorporate the temperature-jump boundary condition. Validity of the numerical simulation procedure is established and the effect of rarefaction on hydrodynamicaly developing flow field, pressure gradient and entrance length is analyzed. A correlation for the fully developed friction factor is presented as a function of Knudsen number (Kn) and aspect ratio (α). The influence of rarefaction on the Nusselt (Nu) number is investigated for thermally and simultaneously developing flows. The effect of velocity slip is found to increase the Nu number, while the temperature-jump tends to decrease it, and the combined effect could result in an increase or a decrease in the Nu number. In the fully developed region, there could be high as 15% increase or low as 50% decrease in Nu number is plausible for the range of parameters considered in this work.     

Thermal response of a heat pipe with axially “Ω”-shaped microgrooves

A transient model of capillary flow and heat transfer in a heat pipe with axially “Ω”-shaped microgrooves is developed and numerically analyzed to predict the thermal response characteristics. The transient distributions of the axial capillary radius and solid wall temperature, the evaporating mass rate, the time constant and instantaneous effective thermal conductivity are all investigated and discussed. The results indicate that the rise rate of wall temperature during the initial period is relatively larger, and the coordination of solid wall temperature response among the evaporator, adiabatic and condenser section is realized during the whole startup process. When the input power is increased/decreased, the evaporator temperatures start rising/dropping immediately. In particular, the time constant and instantaneous effective thermal conductivity in the startup process are larger than those in the shutdown process. Additionally, the accuracy of the present model is verified by experimental data obtained in this paper.     

Hydrothermal Behavior of a Ferrofluid in a Corrugated Channel in the Presence of a Magnetic Field

In this paper, results of applying a non‐uniform magnetic field on a dilute ferrofluid (water and 3% vol. Fe₃O₄) flow in a corrugated channel under a constant heat flux boundary condition have been reported. The thermal behavior of the flow is investigated numerically using a two‐phase mixture model and control volume technique. It is concluded that using a magnetic field with a negative gradient on a nanofluid flow in corrugated channels can be proposed as a suitable method to achieve higher heat transfer performance and augment the heat transfer coefficient and also reduces the wall temperature. This method can lead to the design of more compact heat exchangers. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(1): 80–92, 2014; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21060     

Numerical study of heat transfer over banks of rods in small Reynolds number cross-flow

This work presents numerical computations of heat transfer over banks of square rods in aligned and staggered arrangements with porosity in the range 0.44–0.98. It is focused on low Reynolds number flows (0.05–40). Two thermal boundary conditions were investigated, namely constant wall temperature and constant volumetric heat source. The effects of bank arrangements and porosity as well as the effects of Prandtl and Reynolds numbers on the Nusselt number are examined. In the case of constant volumetric heat source, the results are approximated with a power equation adapted for the case of low Re number flows. This study shows that the thermal boundary condition on the solid surface influences heat transfer when thermal equilibrium is reached in the bank of rods.     

Laminar free-convection in glycerol with variable physical properties adjacent to a vertical plate with uniform heat flux

The steady laminar boundary layer flow of glycerol along a vertical stationary plate with uniform heat flux is studied in this paper. The density, thermal conductivity and heat capacity of this liquid are linear functions of temperature but dynamic viscosity is a strong, almost exponential, function of temperature. The results are obtained with the numerical solution of the boundary layer equations. Both upward flow (plate heating) and downward flow (plate cooling) is considered. The variation of μ with temperature has significant influence on wall heat transfer and much stronger influence on wall shear stress. It was also found that the similarity exponent, which is equal to 0.20 for the classical problem with constant properties, is lower than 0.20 in the upward flow and higher than 0.20 in the downward flow.     

Exploration of radiative heat on magnetohydrodynamic rotating fluid flow through a vertical sheet

An analysis is built up for the exploration of radiative heat transport on the magnetohydrodynamic flow of rotating fluid over a vertical sheet. The inclusion of thermal radiation in conjunction with the reacting species enhances the energy as well as the solutal profiles respectively. In an advance, external heat source and applied magnetic field effects are considered for further improvement. As the magnetic Reynolds number is low, the influence of the induced magnetic field is neglected. The transformation of governing nonlinear partial differential equations into coupled nonlinear ordinary differential equations is attained with a proper supposition of similarity variables. Moreover, the solution of these transformed equations is scheduled using the “Runge–Kutta fourth-order” method numerically in association with the “shooting technique.” The simulation or various illustrating parameters affecting the flow phenomena are obtained and displayed through graphs and for numerical validation with earlier published work shows the convergence process of the methodology applied. The main findings of the study are; the Dufour number is favorable to enhance the fluid temperature throughout the domain and the destructive chemical reaction also encourages the solutal profile significantly.