Unsteady mhd flow and heat transfer on a rotating disk in an ambient fluid

An unsteady flow and heat transfer of a viscous incompressible electrically conducting fluid over a rotating infinite disk in an otherwise ambient fluid are studied. The unsteadiness in the flow field is caused by the angular velocity of the disk which varies with time. The magnetic field is applied normal to the disk surface. The new self-similar solution of the Navier–Stokes and energy equations is obtained numerically. The solution obtained here is not only the solution of the Navier–Stokes equations, but also of the boundary layer equations. Also, for a simple scaling factor, it represents the solution of the flow and heat transfer in the forward stagnation-point region of a rotating sphere or over a rotating cone. The asymptotic behaviour of the solution for a large magnetic field or for a large independent variable is also examined. The surface shear stresses in the radial and tangential directions and the surface heat transfer increase as the acceleration parameter increases. Also the surface shear stress in the radial direction and the surface heat transfer decrease with increasing magnetic field, but the surface shear stress in the tangential direction increases.     

Subcooled flow boiling heat transfer and associated bubble characteristics of R-134a in a narrow annular duct

Experiments are conducted here to investigate how the channel size affects the subcooled flow boiling heat transfer and associated bubble characteristics of refrigerant R-134a in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm in this study. From the measured boiling curves, the temperature undershoot at ONB is found to be relatively significant for the subcooled flow boiling of R-134a in the duct. The R-134a subcooled flow boiling heat transfer coefficient increases with a reduction in the gap size, but decreases with an increase in the inlet liquid subcooling. Besides, raising the imposed heat flux can cause a substantial increase in the subcooled boiling heat transfer coefficient. However, the effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient are small in the narrow duct. Visualization of the subcooled flow boiling processes reveals that the bubbles are suppressed to become smaller and less dense by raising the refrigerant mass flux and inlet subcooling. Moreover, raising the imposed heat flux significantly increases the bubble population, coalescence and departure frequency. The increase in the bubble departure frequency by reducing the duct size is due to the rising wall shear stress of the liquid flow, and at a high imposed heat flux many bubbles generated from the cavities on the heating surface tend to merge together to form big bubbles. Correlation for the present subcooled flow boiling heat transfer data of R-134a in the narrow annular duct is proposed. Additionally, the present data for some quantitative bubble characteristics such as the mean bubble departure diameter and frequency and the active nucleation site density are also correlated.     

The effect of upper surface conditions on convection in a shallow cavity with differentially heated end-walls

The effect of upper surface boundary conditions on the flow structure in shallow cavities with differentially heated end-walls is examined. Matched asymptotic solutions, valid for small cavity aspect ratios are presented for the following cases; uniform shear stress with zero heat flux, uniform heat flux with zero shear stress, and heat flux linearly dependent on surface temperature with zero shear stress. It is shown that these changes in surface boundary conditions have an important influence on the temperature and flow structure within the cavity.     

Embedded converging surface microchannels for minimized friction and thermal irreversibilities

Embedded converging surface microchannels are developed as effective new ways of reducing entropy production in boundary layer flow with convective heat transfer. A similarity solution with slip-flow boundary conditions is developed to find the spatial distributions of velocity, temperature, wall shear stress and wall heat flux. Mixed Knudsen number conditions along the surface require both slip-flow and no-slip formulations to be combined in an integral solution. Predicted results from the method of EBSM (entropy based surface micro-profiling) are presented for the optimized microchannel aspect ratio, spacing between adjacent microchannels and the angles characterizing the converging microchannels.     

Saturated flow boiling heat transfer and associated bubble characteristics of R-134a in a narrow annular duct

Experiments are conducted here to investigate how the channel size affects the saturated flow boiling heat transfer and associated bubble characteristics of refrigerant R-134a in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm in this study. The measured heat transfer data indicate that the saturated flow boiling heat transfer coefficient increases with a decrease in the gap of the duct. Besides, raising the imposed heat flux can cause a significant increase in the boiling heat transfer coefficients. However, the effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient are milder. The results from the flow visualization show that the mean diameter of the bubbles departing from the heating surface decreases slightly at increasing R-134a mass flux. Moreover, the bubble departure frequency increases at reducing duct size mainly due to the rising shear stress of the liquid flow, and at a high imposed heat flux many bubbles generated from the cavities in the heating surface tend to merge together to form big bubbles. Correlation for the present saturated flow boiling heat transfer data of R-134a in the narrow annular duct is proposed. Additionally, data for some quantitative bubble characteristics such as the mean bubble departure diameter and frequency and the active nucleation site density are also correlated.     

Heat transfer in a viscoelastic boundary layer flow over a stretching sheet

Studies are made on the viscoelastic fluid flow and heat transfer characteristics over a stretching sheet with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for the cases of prescribed surface temperature (PST) and prescribed surface heat flux (PHF). The momentum equation is decoupled from the energy equation for the present incompressible boundary layer flow problem with constant physical parameters. Exact solution for the velocity field and the skin-friction are obtained. Also, the solutions for the temperature and heat transfer characteristics are obtained in terms of Kummer’s function. The work due to deformation in energy equation, which is essential while formulating the viscoelastic boundary layer flow problems, is considered. This paper examines the effect of viscoelastic parameter, Eckert number, Prandtl number and non-uniform heat source/sink parameter on temperature distribution, wall temperature gradient for PST-case and wall temperature for PHF-case.     

Natural convection heat transfer of non-Newtonian fluids in porous media from a vertical cone under mixed thermal boundary conditions

This work studies the problem of the steady natural convection boundary layer flow over a downward-pointing vertical cone in porous media saturated with non-Newtonian power-law fluids under mixed thermal boundary conditions. A similarity analysis is performed, and the obtained similar equations are solved by cubic spline collocation method. The effects of the power-law viscosity index and the similarity exponent on the heat transfer characteristics under mixed thermal boundary conditions have been studied. Under mixed thermal boundary conditions, both the surface heat flux and the surface temperature are found to decrease when the power-law viscosity index of the non-Newtonian power-law fluid in porous media is increased. Moreover, an increase in the similarity exponent tends to increase the boundary layer thickness and thus decreases the surface heat flux under mixed thermal conditions. The generalized governing equations derived in this work can be applied to the cases of prescribed surface temperature and prescribed heat flux.     

Forced convection heat transfer of Williamson fluid flow in porous media over horizontal plate with constant heat flux

Forced convection of Williamson fluid flow in porous media under constant surface heat flux conditions is investigated numerically. A model of Darcy–Forchheimer–Brinkman is used and the corresponding governing equations are expressed in dimensionless forms and solved numerically using bvp4c with MATLAB package. Boundary layer velocity, shear stress, and temperature profiles, in addition to the local Nusselt number parameter over a horizontal plate, are found. The effects of the Forchheimer parameter, Nusselt number, Darcy parameter, porous inertia, and Williamson parameter on the velocity profiles, temperature profiles, coefficient of friction, and coefficient of heat transfer are investigated. The results showed that as the Darcy parameter increases, boundary layer velocity and shear stress increase, while the temperature and Nusselt number decrease. In addition, as Williamson's parameter increases, velocity within the boundary layer, shear stress, and Nusselt number decrease while the temperature profile increases. Also, with larger values of the Forchheimer parameter, the velocity of the boundary layer, shear stress, temperature, and Nusselt number increase. Furthermore, the Nusselt number and the coefficient of friction are obtained on the surface of the horizontal plate.     

Numerical analysis for forced convection over a flat plate in power law fluids

The analysis of forced convective heat transfer of power-law non-Newtonian fluids from a flat plate is studied. The cases of prescribed surface temperature and prescribed wall heat flux are considered. The results of local heat transfer are obtained by using implicit finite difference scheme to solve the nonsimilarity solution. It was found that local similarity solution is given the low accuracy results for the study of boundary layer heat transfer of power-law fluids.     

Heat transfer in a viscoelastic boundary layer flow over a stretching sheet with viscous dissipation and non-uniform heat source

In this paper, visco-elastic boundary layer flow and heat transfer over a stretching sheet in presence of viscous dissipation and non-uniform heat source have been discussed. Analytical solutions of highly non-linear momentum equation and confluent hypergeometric similarity solution of heat transfer equations are obtained. Here two types of different heating processes are considered namely (i) prescribed surface temperature (PST) and (ii) prescribed wall heat flux (PHF). The effect of various parameters like visco-elastic parameter, Eckert number, Prandtl number, and non-uniform heat source/sink parameter on temperature distribution are analyzed and effect of all these parameters on wall temperature gradient and wall temperature are tabulated and discussed.     

Heat transfer in the thermal entrance region for flow through rectangular porous passages

The study of heat transfer in rectangular passages with prescribed wall heat flux is of practical interest. These passages could be open or filled with saturated porous materials. A solution that uses the Green’s function can accommodate the inclusion of heat flux over the entire surface area or over isolated sections of the boundary. Also, this solution permits the inclusion of frictional heating. Two different boundary conditions are considered: constant wall temperature and constant wall heat flux. The computed heat transfer coefficients show that the thermally fully developed condition may not be attainable in practical applications for very narrow passages with prescribed wall heat flux.     

Hydromagnetic flow and heat transfer of a non-Newtonian power law fluid over a vertical stretching sheet

We consider the steady state, viscous, incompressible two-dimensional magneto hydrodynamic flow of an electrically conducting power law fluid over a vertical stretching sheet. The stretching of the surface velocity and the prescribed surface temperature are assumed to vary linearly with the distance from the slit. The coupled partial differential equations governing the flow and heat transfer are transformed into non-linear coupled ordinary differential equations by a similarity transformation. The transformed boundary layer equations are solved numerically by Keller-Box method for several sets of values of the parameters governing the flow and heat transfer. The flow and heat transfer characteristics are analysed and discussed for different values of the parameters. We observe that the local skin friction coefficient and the local Nusselt number decrease as the magnetic parameter Mn increase for fixed value of the buoyancy parameter λ. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.     

Viscoelastic boundary layer flow and heat transfer over an exponential stretching sheet

Viscoelastic boundary layer flow and heat transfer over an exponential stretching continuous sheet have been examined in this paper. Approximate analytical similarity solution of the highly non-linear momentum equation and confluent hypergeometric similarity solution of the heat transfer equation are obtained. Accuracy of the analytical solution for stream function is verified by numerical solutions obtained by employing Runge-Kutta fourth order method with shooting. These solutions involve an exponential dependent of stretching velocity, prescribed boundary temperature and prescribed boundary heat flux on the flow directional coordinate. The effects of various physical parameters like viscoelastic parameter, Prandtl number, Reynolds number, Nusselt number and Eckert number on various momentum and heat transfer characteristics are discussed in detail in this work.     

Investigations on heat and mass transfer characteristics of falling film horizontal tubular absorber

An experimental set-up is built incorporating only two principle components, viz, absorber and generator of vapor absorption refrigeration system (VARS) to investigate heat and mass transfer characteristics of absorber. The refrigerant, R134a (1,1,1,2-tetrafluroethane) is absorbed by R134a-DMAC (N,N-dimethylacetamide) solution flowing over the horizontal tubes arranged as tube bank. The effect of solution flow rate, coolant flow rate and temperature, heater load and concentration of R134a is studied. The performance parameters like solution exit temperature from tubes, state point temperatures, heat flux, mass flux, and overall heat and mass transfer coefficients are presented for different operating condition of absorber. For lower flow rate of the solution and higher flow rate of the coolant, the bulk solution temperature is found to decrease. The heat and mass transfer coefficients increase with mass flow rate of the solution. An increase in inlet temperature of coolant results into an increase in overall heat transfer coefficient and decrease in overall mass transfer coefficient.     

A general analytical solution to the equation of transient forced convection with fully developed flow

A general solution to the energy equation under zero wall temperature or zero heat flux boundary condition for the decay of an inlet and initial temperature distribution of an incompressible transient turbulent flow heat transfer between two parallel plates is given. It is shown that these solutions may then be used to obtain solutions due to unit steps in wall temperature or wall heat flux which is sufficient to sort out prescribed wall temperature and prescribed wall heat flux boundary condition. The results are confirmed experimentally by the frequency method. An experimental apparatus has been designed, built and used for this purpose.     

Inverse design involving combined radiative and turbulent convective heat transfer

This work considers an inverse boundary design problem which involves radiation and convection heat transfer. The objective is finding the heat flux distribution required on heaters located on the top and side walls of a two-dimensional enclosure that satisfies both the temperature and heat flux distributions prescribed on the design surface of the enclosure. A turbulent air flow is generated by a fan located inside the chamber. The problem is described by a system of non-linear, ill-conditioned equations, which is solved by an iterative procedure. The solution are obtained by regularizing the system of equations by means of the TSVD method.     

Note on Cortell’s non-linearly stretching permeable sheet

The effects of suction/blowing and viscous dissipation on the steady non-linear viscous flow and heat transfer over a horizontal shrinking permeable surface of variable temperature or heat flux with a power-law velocity is numerically studied. The results complete those recently reported by Cortell [10] to the case of a shrinking surface. Particular attention is given to deriving numerical results for the critical/turning points which determine the range of existence of multiple solutions. Two cases are considered, namely prescribed surface temperature (PST) and prescribed heat flux (PHF). Dual and triple solutions are found to exist for certain parameters.     

Use of CFD to Determine Effect of Wire Matrix Inserts on Crude Oil Fouling Conditions

Crude oil fouling rates are strongly affected by both local surface temperature and local surface shear stress. The use of in-tube inserts (such as hiTRAN) in heat exchangers has been shown to be effective in mitigating crude oil fouling while at the same time enhancing heat transfer. However, the introduction of inserts means that there will be axial and radial distributions of both local shear stress and local heat transfer coefficient between the repeating insert–wall contact points, which could mean that there will be local variations in fouling rate. While estimation of local shear stresses and film heat transfer coefficients is facile for bare round tubes, this is no longer the case for tubes fitted with inserts. Accordingly, this article describes a possible solution to the design challenge using computational fluid dynamics (CFD) simulation, the output of which is the temperature and velocity distributions in a three-dimensional geometry of the fluid flow in a tube fitted, for example, with a hiTRAN insert. A simple algorithm is then described for calculating the overall heat transfer coefficient based on the resulting temperature distribution along the wall of the tube. Simulated values of the overall heat transfer coefficient are then compared with those obtained by experiment, showing that there is good agreement, thereby indicating that predicted local values are accurate. Use of CFD in fouling applications now allows the prediction of local conditions when inserts are used and hence can be used to predict whether, and where, fouling might occur.     

Heat transfer in rectangular microchannels heat sink using nanofluids

The effect of using nanofluids on heat transfer and fluid flow characteristics in rectangular shaped microchannel heat sink (MCHS) is numerically investigated for Reynolds number range of 100–1000. In this study, the MCHS performance using alumina–water (Al₂O₃-H₂O) nanofluid with volume fraction ranged from 1% to 5% was used as a coolant is examined. The three-dimensional steady, laminar flow and heat transfer governing equations are solved using finite volume method. The MCHS performance is evaluated in terms of temperature profile, heat transfer coefficient, pressure drop, friction factor, wall shear stress and thermal resistance. The results reveal that when the volume fraction of nanoparticles is increased under the extreme heat flux, both the heat transfer coefficient and wall shear stress are increased while the thermal resistance of the MCHS is decreased. However, nanofluid with volume fraction of 5% could not be able to enhance the heat transfer or performing almost the same result as pure water. Therefore, the presence of nanoparticles could enhance the cooling of MCHS under the extreme heat flux conditions with the optimum value of nanoparticles. Only a slight increase in the pressure drop across the MCHS is found compared with the pure water-cooled MCHS.     

Heat transfer enhancement with the use of nanofluids in radial flow cooling systems considering temperature-dependent properties

Heat transfer enhancement capabilities of coolants with suspended metallic nanoparticles inside typical radial flow cooling systems are numerically investigated in this paper. The laminar forced convection flow of these nanofluids between two coaxial and parallel disks with central axial injection has been considered using temperature dependent nanofluid properties. Results clearly indicate that considerable heat transfer benefits are possible with the use of these fluid/solid particle mixtures. For example, a Water/Al₂O₃ nanofluid with a volume fraction of nanoparticles as low as 4% can produce a 25% increase in the average wall heat transfer coefficient when compared to the base fluid alone (i.e., water). Furthermore, results show that considerable differences are found when using constant property nanofluids (temperature independent) versus nanofluids with temperature dependent properties. The use of temperature-dependent properties make for greater heat transfer predictions with corresponding decreases in wall shear stresses when compared to predictions using constant properties. With an increase in wall heat flux, it was found that the average heat transfer coefficient increases whilst the wall shear stress decreases for cases using temperature-dependent nanofluid properties.