Entropy generation on MHD flow of a Casson fluid over a curved stretching surface with exponential space-dependent heat source and nonlinear thermal radiation

The present model concentrates on entropy generation on a steady incompressible flow of a Casson liquid past a permeable stretching curve surface through chemical reaction and magnetic field effects. The exponential space-dependent heat source cum heat and mass convective boundary conditions are accounted for. The resulting nonlinear boundary layer model is simplified by the transformation of similarity. Chebyshev spectral technique is involved for obtaining numerical results of the converted system of the mathematical models. Behavior of the determining thermo-physical parameters on the profiles of velocity, temperature, concentration, skin friction, heat, mass transfer rate, rate of entropy generation, and finally the Bejan number are presented. The major point of the present investigation show that the curvature term weakens the mass transfer profile as the fluid temperature reduces all over the diffusion regime. A decrease in heat generation strengthens the species molecular bond, which prevents free Casson particle diffusion. Furthermore, the mass transfer field diminishes in suction and injection flow medium.     

Study of transient heat transfer in laminar flow of a non-newtonian fluid over a flat plate

Unsteady state heat transfer in laminar flow of a non-Newtonian fluid flowing over a flat plate is investigated. Effect of Prandtl number and the viscosity index on the transient is also studied. The steady state temperature profile obtained from the model agrees with the published results.     

Drag reduction and heat transfer enhancement over a heated wall of a vertical annular microchannel

An analysis for the effect of wall-surface curvature on gas microflow is performed to study the natural convection in an open-ended vertical annular microchannel with an isothermally heated inside wall. The fully developed solutions of the velocity, temperature, flow rate, shear stress, and heat flux are derived analytically and presented for air and various surfaces at the standard reference state. Results show that wall-surface curvature has a significant effect. This results in a nonlinear behavior in the temperature, which seems difficult to appear in a parallel-plate microchannel. Under certain rarefaction and fluid–wall interaction conditions, by decreasing the value of the curvature radius ratio, it is possible to obtain both reduced flow drag and enhanced heat transfer.     

Transient rotating flow over a moving surface with a magnetic field

The transient flow and heat transfer on a moving surface in a rotating fluid in the presence of a magnetic field have been investigated. The unsteadiness in the flow field has been introduced by the sudden change in the surface velocity or the fluid angular velocity. The parabolic partial differential equations governing the unsteady flow and heat transfer have been solved by using an implicit finite-difference scheme in combination with the quasilinearization technique. The computations have been carried out from the initial steady state to the final steady state. The effects of the sudden change in the surface velocity on the flow and heat transfer are found to be more significant than those of the impulsive change in the angular velocity of the fluid. When the surface velocity is suddenly reduced, the surface shear stress is found to vanish in a small time interval after the start of the impulsive motion, but it does not imply flow separation. The surface shear stress for the primary flow increases with the magnetic field and the fluid angular velocity, but the surface heat transfer decreases. The surface shear stress for the secondary flow increases with the angular velocity of the fluid, but decreases with increasing magnetic field.     

Prediction of the temperature field in flat plate heat pipes with micro-grooves – Experimental validation

A liquid and vapour flow model coupled to a thermal model is presented for a flat plate heat pipe with micro-grooves. This model allows the calculation of the liquid and vapour pressures and velocities, the meniscus curvature radius in the grooves and the temperature field in the heat pipe wall from the heat source to the heat sink. The meniscus curvature radius is introduced in the thermal model to take into account the heat transfer at the liquid–vapour interface. Experimental measurements of the meniscus curvature radius as well as temperature measurements along a grooved heat pipe are compared to the model results. Both comparisons show the good ability of the numerical model to predict the maximum heat transport capability and the temperature field in the heat pipe. The model is used to optimize the heat pipe dimensions in order to improve its thermal performances.     

Influence of conjugate heat transfer on the minimization of entropy generation for forced convective flow through parallel plate channel filled with porous material

A fluid–solid conjugate heat transfer model is developed to analyze the characteristics of entropy generation for forced convective steady hydrodynamically fully developed laminar flow of a Newtonian fluid through a parallel plate channel filled with porous material by modulating the following parameters: substrate thickness, the ratio of thermal conductivity of wall to fluid, Biot number, the axial temperature gradient in the fluid, and Peclet number. The exteriors of both the walls are subjected to the thermal boundary conditions of the third kind. The mass and Brinkman momentum conservation equations in the fluidic domain and the coupled energy conservation in both the solid and fluidic domain are solved analytically using the local thermodynamic equilibrium model, so as to derive closed-form expressions for the velocity in the fluid and the temperature both in the fluid and solid walls in terms of relevant parameters. Suitable combinations of influencing factors, namely the geometric parameters of the system, fluid, flow, and substrate properties are identified for which global entropy generation rate is minimized. The findings may be helpful in the design of thermal systems frequently used in diverse engineering applications having heat transfer in the solid wall being a crucial parameter.     

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.     

Heat transfer from a spinning disk during semi-confined axial impingement from a rotating nozzle

Conjugate heat transfer from a uniformly heated spinning solid disk of finite thickness and radius during a semi-confined liquid jet impingement from a rotating nozzle is studied. The model covers the entire fluid region including the impinging jet on a flat circular disk and flow spreading out downstream under the spinning confinement plate and free surface flow after exposure to the ambient gaseous medium. The model examines how the heat transfer is affected by adding a secondary rotational flow under semi-confined jet impingement. The solution is made under steady state and laminar conditions. The study considered various plate materials such as aluminum, copper, silver, constantan and silicon. Ammonia, water, flouroinert FC-77 and MIL-7808 oil were used as working fluids. The range of parameters covered included Reynolds number (220–900), Ekman number (7.08 × 10^?5–∞), nozzle-to-target spacing (β = 0.25–1.0), disk thicknesses to nozzle diameter ratio (b/d_n = 0.25–1.67), Prandtl number (1.29–124.44) and solid to fluid thermal conductivity ratio (36.91–2222). It was found that a higher Reynolds number increased local heat transfer coefficient reducing the interface temperature difference over the entire disk surface. The rotational rate also increased local heat transfer coefficient under most conditions. An engineering correlation relating the Nusselt number with other dimensionless parameters was developed for the prediction of the system performance.     

Study on flow and heat transfer characteristics of heat pipe with axial “Ω”-shaped microgrooves

A theoretical model of fluid flow and heat transfer in a heat pipe with axial “Ω”-shaped grooves has been conducted to study the maximum heat transport capability of these types of heat pipes. The influence of variations in the capillary radius, liquid–vapor interfacial shear stress and the contact angle are all considered and analyzed. The effect of vapor core and wick structure on the fluid flow characteristics and the effect of the heat load on the capillary radius at the evaporator end cap, as well as the effect of the wick structure on the heat transfer performance are all analyzed numerically and discussed. The axial distribution of the capillary radius, fluid pressure and mean velocity are obtained. In addition, the calculated maximum heat transport capability of the heat pipe at different working temperatures is compared with that obtained from a traditional capillary pressure balance model, in which the interfacial shear stress is neglected. The accuracy of the present model is verified by experimental data obtained in this paper.     

Comparative analysis of a Sisko nanofluid over a stretching cylinder through a porous medium

The present article examines the Sisko nanofluid flow and heat transfer through a porous medium due to a stretching cylinder using Buongiorno's model for nanofluids. Suitable similarity transformations are used to transform the governing boundary layer equations of fluid flow into nonlinear ordinary differential equations. The finite difference method is used to solve coupled nonlinear differential equations with MATLAB software. The impact of different parameters viz., the Sisko material parameter, porosity parameter, curvature parameter, thermophoresis parameter, and Brownian diffusion parameter on the velocity and temperature distribution are presented graphically. Moreover, the effect of the involved parameters on the heat transfer rate is also studied and presented through table values. It is noticed from the numerical values that the porosity parameter reduces the velocity while enhancing the temperature. The curvature parameter enhances the velocity throughout the fluid regime and reduces the temperature near the surface while enhancing the temperature far away from the surface. The study reveals that the thermophoresis and Brownian diffusion parameters that characterize the nanofluid flow reduce the wall heat transfer rate, while the curvature parameter enhances it. This investigation of wall heating/cooling has essential applications in solar porous water absorber systems, chemical engineering, metallurgy, material processing, and so forth.     

Heat and Mass Transfer in Capillary-Pumped Liquid Films in Square Cross-Section Minichannels

This study addresses heat and mass transfer during the vaporization of a liquid in a heated square cross-section mini-channel. A theoretical model is developed in steady state using the radius of curvature as a variable. One-dimensional simulations have been performed. An analysis of this model reveals that heat and mass transfer is governed by two main groups of non-dimensional numbers (i.e., Reynolds × Boiling and Weber × Boiling² numbers). Maps of heat transfer performance are thus proposed according to these non-dimensional numbers. A reduced model is finally derived, allowing the main parameters to be expressed (such as the extended meniscus length) analytically.     

Free convective flow of heat generating/absorbing fluid between vertical porous plates with periodic heat input

This study investigates the free convective flow of heat generating/absorbing fluid between vertical parallel porous plates due to periodic heating of the porous plates. The analysis is performed by considering fully developed flow and steady-periodic regime. The momentum and energy equations, which arise from the definition of velocity and temperature, are written in dimensionless form. Separating the temperature and velocity fields into steady and periodic parts, the resulting second order differential equations are solved to obtain the expressions for velocity, temperature, skin friction and the rate of heat transfer. The effects of various flow parameters such as the suction/injection (s), heat source/sink (δ), Strouhal (St) and Prandtl (Pr) numbers on the skin friction coefficient, rate of heat transfer, velocity and temperature profiles are discussed with the aid of line graphs and contour maps.     

Effects of mass transfer on the transient free convection flow of a dissipative fluid along a semi-infinite vertical plate with constant heat flux

Effect of mass transfer on the transient free convection flow of a dissipative fluid along a semi-infinite vertical plate in presence of constant heat flux, is studied by solving coupled non-linear system of partial differential equations, using Crank-Nicolson technique which is stable and convergent. Transient temperature, concentration and velocity profiles, local and average skin-friction, Nusselt number and Sherwood number are shown graphically for air. The effects of ε, viscous dissipative parameter, Schmidt number, buoyancy ratio parameter on the transient state are discussed.     

Heat and mass transfer of an unsteady MHD natural convection flow of a rotating fluid past a vertical porous flat plate in the presence of radiative heat transfer

Analytical closed-form solution of the unsteady hydro-magnetic natural convection heat and mass transfer flow of a rotating, incompressible, viscous Boussinesq fluid is presented in this study in the presence of radiative heat transfer and a first order chemical reaction between the fluid and the diffusing species. The Rosseland approximation for an optically thick fluid is invoked to describe the radiative flux. Results obtained show that a decrease in the temperature boundary layer occurs when the Prandtl number and the radiation parameter are increased and the flow velocity approaches steady state as the time parameter t, is increased. These findings are in quantitative agreement with earlier reported studies.     

Forced convection heat transfer of a Robertson-Stiff fluid between two coaxial rotating cylinders

Laminar flow and forced convection heat transfer of the time independent non-Newtonian fluid obeying Robertson-Stiff stress-strain relation have been investigated numerically in the annular space between two coaxial rotating cylinders. The problem is considered when the inner cylinder rotates about the common axis with constant angular velocity and the outer cylinder at the rest, and two cases of the third kind of the thermal boundary conditions. The tangential and axial momentum equations have been solved iteratively by using a finite difference method. Then the energy equation has been solved for the two cases. For the steady fully developed flow, the velocity distributions, temperature profiles, the average volumetric flow rate, torque and the average Nusselt numbers have been obtained for different values of the radius ratio and model parameters.     

Forced convection heat transfer in microchannel heat sinks

This paper presents an analysis of forced convection heat transfer in microchannel heat sinks for electronic system cooling. In view of the small dimensions of the microstructures, the microchannel is modeled as a fluid-saturated porous medium. Numerical solutions are obtained based on the Forchheimer–Brinkman-extended Darcy equation for the fluid flow and the two-equation model for heat transfer between the solid and fluid phases. The velocity field in the microchannel is first solved by a finite-difference scheme, and then the energy equations governing the solid and fluid phases are solved simultaneously for the temperature distributions. Also, analytical expressions for the velocity and temperature profiles are presented for a simpler flow model, i.e., the Brinkman-extended Darcy model. This work attempts to perform a systematic study on the effects of major parameters on the flow and heat transfer characteristics of forced convection in the microchannel heat sink. The governing parameters of engineering importance include the channel aspect ratio (α_s), inertial force parameter (Γ), porosity (ε), and the effective thermal conductivity ratio (k_r). The velocity profiles of the fluid in the microchannel, the temperature distributions of the solid and fluid phases, and the overall Nusselt number are illustrated for various values of the problem parameters. It is found that the fluid inertia force alters noticeably the dimensionless velocity distribution and the fluid temperature distribution, while the solid temperature distribution is almost insensitive to the fluid inertia. Moreover, the overall Nusselt number increases with increasing the values of α_s and ε, while it decreases with increasing k_r.     

Transient natural convection of micropolar fluids between concentric and vertically eccentric spheres

Micropolar fluids in transient analysis have been investigated numerically to determine heat transfer by natural convection between concentric and vertically eccentric spheres with specified isothermal boundary conditions. Calculations were carried out systematically for several different eccentricities and a range of Rayleigh numbers to determine the average Nusselt numbers which are affected by the micropolar parameters (F) on the flow and temperature fields. The skin friction stress on the walls has also been studied and discussed. The governing equations, in terms of vorticity, stream function, temperature and angular momentum are expressed in a spherical polar coordinate system. Results were obtained for steady and transient heat-transfer in vertically eccentric spheres at a Prandtl number of 0.7, with the Rayleigh number ranging from 10³ to 5 × 10⁵, for a radius ratio of 2.0 and eccentricities varying from −0.625 to +0.625, and for the value of micropolar parameters are 0, 1 and 5 respectively. Comparisons are attempted between the Newtonian fluid and micropolar fluid.     

Direct numerical simulation of fluid flow and heat transfer in periodic wavy channels with rectangular cross-sections

Fully-developed flow and heat transfer in periodic wavy channels with rectangular cross sections are studied using direct numerical simulation, for increasing Reynolds numbers spanning from the steady laminar to transitional flow regimes. The results show that steady flow is characterized by the formation of symmetric secondary flow or Dean vortices when liquid flows past the bends. It is found that the patterns of Dean vortices may evolve along the flow direction, thus leading to chaotic advection, which can greatly enhance the convective fluid mixing and heat transfer. With increasing Reynolds numbers, the flow undergoes transition from a steady state to a periodic one with a single frequency, and subsequently to a quasiperiodic flow with two incommensurate fundamental frequencies. Within these unsteady regimes, the flow is characterized by very complex Dean vortices patterns which evolve temporally and spatially along the flow direction, and the flow symmetry may even be lost. Further increase in Reynolds number leads to chaotic flow, where the Fourier spectrum of the velocity evolution becomes broadband. The bifurcation scenario in wavy channels may thus share some common features with the well-known Ruelle–Takens–Newhouse scenario. Heat transfer simulation in all flow regimes is carried out with constant wall temperature condition and liquid water as the coolant. It is found that due to the efficient mixing in wavy channels, the heat transfer performance is always significantly more superior to that of straight channels with the same cross sections; at the same time the pressure drop penalty of wavy channels can be much smaller than the heat transfer enhancement. The present study shows that these wavy channels may have advantages over straight channels and thus serve as promising candidates for incorporation into efficient heat transfer devices.     

Electro-osmotic flow of fractional second-grade fluid with fractional Cattaneo heat flux through a vertical microchannel

This study investigates the unsteady electro-osmotic flow (EOF) of a fractional second-grade fluid through a vertical microchannel with convection heat transfer. The fractional Cattaneo heat flux model will be used to modify the heat equation. The solutions for the velocity and the temperature have been derived by employing the Laplace and finite Fourier sine transforms and their numerical inverses. The results show that at the beginning of the time period, the fractional parameter postpones the movement of the fluid. Furthermore, the results show that at the high values of retardation time (non-Newtonian case), the required time for the velocity and the flow rate to reach the steady state increases. Moreover, the heat relaxation time reduces the heat transfer until a critical time, and then the effect reverses.     

Transient natural convection heat transfer of liquid D-mannitol on a horizontal cylinder

Transient and steady state natural convection heat transfer for D-mannitol on a horizontal cylinder was investigated experimentally at various liquid temperatures and heat input conditions. To clarify the natural convection phenomena of D-mannitol, transient and steady heat transfer coefficients were measured under various liquid temperatures of D-mannitol and periods of heat generation rates from a horizontal platinum cylinder. The platinum cylinder with a diameter of 1 mm and a length of 43.5 mm was used as the test heater in this experiment. Experimental results indicated that the steady heat transfer coefficient of D-mannitol was affected by the liquid temperature. As the liquid temperature increased, it was understood that the effect of liquid temperature weakened. When the period of the heat generation rate was changed, the heat transfer process was divided into natural convection heat transfer and conductive heat transfer. It was considered that the conductive heat transfer was more dominant as the period of the heat generation rate decreased. The empirical correlations of steady and transient heat transfer coefficients for D-mannitol were obtained.