Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet

The effects of thermal radiation on the flow of micropolar fluid and heat transfer past a porous shrinking sheet is investigated. The self-similar ODEs are obtained using similarity transformations from the governing PDEs and are then solved numerically by very efficient shooting method. The analysis reveals that for the steady flow of micropolar fluid, the wall mass suction needs to be increased. Dual solutions of velocity and temperature are obtained for several values of the each parameter involved. For increasing values of the material parameter K, the velocity decreases for first solution, whereas, for second solution it increases. Due to increase of thermal radiation, the temperature and thermal boundary layer thickness reduce in both solutions and also the heat transfer from the sheet enhances with thermal radiation.     

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.     

Conjugate heat/mass transfer from a circular cylinder with an internal heat/mass source in laminar crossflow at low Reynolds numbers

This paper presents a theoretical study of conjugate heat/mass transfer from a circular cylinder with an internal heat/mass source and a surrounding fluid flow. The heat/mass source consists of a constant temperature/concentration wire imbedded in the cylinder center. A finite difference method discretizes the equations. The multigrid method solves the discrete system. Numerical investigations were carried out for cylinder Re numbers equal to 2 and 20. The values of the Pr number were selected such that the product Re × Pr is constant and equal to 100. The main aspect analysed is the influence of the conductivity ratio on the local and average Nu numbers at different values of the wire diameter.     

Thermal and water management in irrigating lands in the arid and semi-arid regions

Excess heat and scarcity of water are the two major problems, which are usually encountered in irrigating lands especially in the arid and semi-arid regions. This paper introduces a technical approach of managing agricultural lands in the arid and semi arid regions through determination of daily water requirement and amount of heat the land is being exposed at various meteorological conditions. Through setting up a mathematical model consisting of basic heat and mass transfer equations and fluid properties, daily rate of water evaporation, different modes of heat transfer such as radiation, convection and heat transfer by evaporation at a wide range relative humidities are determined. Furthermore, the analyses are performed at two different scenarios at average air velocities of 1 and 5 m/s. Our findings showed that the volume of water evaporation at relative humidity and air temperature of φ=50% and T_∞=20 °C is 22% higher than at φ=100% and T_∞=20 °C. Moreover, at a specified φ and T_∞, the total rate of heat transfer at air velocity of 5 m/s is at least 25% higher than the total rate of heat transfer at air velocity of 1 m/s.     

Stability analysis of MHD radiative mixed convective flow in vertical cylindrical annulus: Thermal nonequilibrium approach

In the present study, the influence of the induced magnetic field on the MHD mixed convective electrically conducting fluid flow inside the vertical cylindrical annulus is analyzed numerically. The heat transfer is presumed to be due to a combination of mixed convection and radiation. The stability of the flow is examined when the solid and fluid phases are not in local thermal equilibrium. The governing equations are solved numerically by both finite difference and finite element methods. To control the flow formation rate more accurately the induced magnetic field is also considered in this study. As the magnetic Prandtl number (Pm) and Hartmann number (M) get enhanced, the velocity and induced magnetic fields get retarded in the annulus due to the presence of drag-like force, namely, the Lorentz force. When there is an increase in the mixed convection parameter the induced magnetic field gets enhanced. An increase in radiation parameter tends to decline the fluid temperature and reverse the behavior of the solid temperature. Increment in Pm decreases the wall shear stress near the conducting cylinder. Increasing values of porous, magnetic, and radiation parameters lead to an unstable system with smaller heat transfer coefficient values but the system gets stabilized for larger values of heat transfer coefficient. The results could be used as first-hand information for comprehending and developing the thermal flow phenomenon in porous media. The obtained numerical results are in good accordance with the existing results. Using an artificial neural network, heat transfer characteristics are analyzed through mean square error and regression analysis.     

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.     

Mixed free and forced convection in the incompressible boundary layer along a rotating vertical cylinder with fluid injection

We examine the steady incompressible laminar boundary layer flow along a vertical cylinder with isothermal walls. The mixed free and forced convection regime is studied while injection/suction of fluid can take place through the cylinder surface. The two-dimensional boundary layer equations are solved using an efficient finite difference scheme, and velocity and temperature profiles, as well as skin friction, heat transfer and pressure coefficients, are calculated. It is proved that fluid injection can considerably reduce the skin friction and heat transfer at the wall. Also, significant differences are reported when the present results are compared with published results for the zero mass transfer case.     

Mixed convection along a rotating vertical slender cylinder in an axial flow

A general analysis has been developed to study fluid flow and heat transfer characteristics for mixed convection along a rotating vertical slender cylinder. Transformed set of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in combination with the quasilinearisation technique. The effects of rotational, buoyancy and suction/injection parameters have been investigated in the present study. The effects of various parameters on the velocity profiles in x- and θ-directions and the temperature profile are reported in the present study. The buoyancy force causes considerable velocity overshoot for low Prandtl number (Pr) fluids. The Prandtl number (Pr) strongly affects the surface heat transfer rate. Numerical results are presented for the skin friction coefficients in x- and θ-directions and for the Nusselt number.     

Effect of suction/injection on the flow of a micropolar fluid past a continuously moving plate in the presence of radiation

An analysis is carried out to study the effect of suction and injection on the flow and heat transfer characteristics for a continuous moving plate in a micropolar fluid in the presence of radiation. The boundary layer equations are transformed to non-linear ordinary differential equations. Numerical results are presented for the distribution of velocity, microrotation and temperature profiles within the boundary layer. The effects of varying the Prandtl number, Pr, the radiation parameter, N and porosity parameter, F_w, are determined.     

Transient modeling of micro-grooved heat pipe

One-dimensional transient model for fluid flow and heat transfer is presented for a micro-grooved heat pipe of any polygonal shape utilizing a macroscopic approach. The coupled non-linear governing equations for the fluid flow, heat and mass transfer are developed based on first principles and are solved simultaneously. The transient behavior for various parameters, e.g. substrate temperature, radius of curvature, liquid velocity, etc. are studied. The effects of the groove dimensions, heat input and Q-profiles on the studied parameters have been evaluated. The steady state profiles for substrate temperature, radius of curvature, liquid velocity etc. have also been generated. The model predicted steady state substrate temperature profile is successfully compared with the experimental results from the previous study. The general nature of the model and the associated parametric study ensure the wide applicability of the model.     

Waviness effect of a wavy circular cylinder on the heat transfer at a Reynolds number of 300

The present study investigates three-dimensional characteristics of fluid flow and heat transfer around a wavy cylinder which has the sinusoidal variation in the cross sectional area along the spanwise direction. The three different wavelengths of π/4, π/3 and π/2 at the fixed wavy amplitude of 0.1 have been considered to investigate the effect of waviness on especially the forced convection heat transfer around a wavy cylinder when the Reynolds and Prandtl numbers are 300 and 0.71, respectively. The numerical solution for unsteady forced convective heat transfer is obtained using the finite volume method. The immersed boundary method is used to handle the wavy cylinder in a rectangular grid system. The present computational results for a wavy cylinder are compared with those for a smooth cylinder. The fluid flow and heat transfer around the wavy cylinder depends on both the location along the spanwise direction and the wavelength. The time- and total surface-averaged Nusselt number for a wavy cylinder with λ = π/2 is larger than that for a smooth cylinder, whereas that with λ = π/4 and π/3 is smaller than that for a smooth cylinder. However, because the surface area exposed to heat transfer for a wavy cylinder is larger than that for a smooth cylinder, the total heat transfer rate for a wavy cylinder with different wavelengths of λ = π/4,π/3 and π/2 is larger than that for a smooth cylinder.     

Influence of relative motion of magnetic field on time‐dependent MHD natural convection flow

The effects of relative motion of magnetic field on unsteady magnetohydrodynamic free convection flow with ramped motion and temperature‐dependent heat source/sink have been analyzed. The motion of the inner cylinder is ramped while the motion of the outer cylinder is fixed. The momentum and energy equations are solved using the well‐known Laplace transform. The time‐domain solution is obtained using the Riemann‐sum approximation method. The influence of the governing parameters on fluid velocity, fluid temperature, volume flow rate, and rate of heat transfer are discussed with the help of line graphs. It is found that Hartmann number has a retarding effect on fluid velocity, skin friction at the outer surface of the inner cylinder, and mass flow rate when the magnetic field is fixed with the fluid and when the velocity of the magnetic field is less than the velocity of the moving cylinder. Whereas, the reverse effect is noticed when the magnetic field is fixed with the moving cylinder.     

Finite element study of mixed convection for non-Newtonian fluid between two coaxial rotating cylinders

In this work, we present a numerical simulation of the flow characteristics and the heat transfer mechanism of a non-Newtonian fluid in an annular space between two coaxial rotating cylinders. The Carreau stress–strain relation was adopted to model the rheological fluid behaviour. The problem is studied when the heated inner cylinder rotates around the common axis with constant angular velocity and the cooled outer cylinder is at the rest. The horizontal endplates are assumed adiabatic. The governing equations are solved using mixed finite elements method. The effects of the different parameters on the heat transfer and on the flow are examined. These parameters are the Reynolds (Re), the Grashof (Gr) and the Weissenberg numbers (W_e), and the flow index (n). The results of the natural, forced and mixed convections are presented and discussed.     

Entropy generation in a hollow cylinder with temperature dependent thermal conductivity and internal heat generation with convective–radiative surface cooling

This article investigates entropy generation in an asymmetrically cooled hollow cylinder with temperature dependent thermal conductivity and internal heat generation. The inside surface of the cylinder is cooled by convection on its inside surface while the outside surface experiences simultaneous convective–radiative cooling. The thermal conductivity of the cylinder as well as the internal heat generation within the cylinder are linear functions of temperature, introducing two nonlinearities in the one-dimensional steady state heat conduction equation. A third nonlinearity arises due to radiative heat loss from the outside surface of the cylinder. The nonlinear system is solved analytically using the differential transformation method (DTM) to obtain the temperature distribution which is then used to compute local and total entropy generation rates in the cylinder. The accuracy of DTM is verified by comparing its predictions with the analytical solution for the case of constant thermal conductivity and constant internal heat generation. The local and total entropy generations depend on six dimensionless parameters: heat generation parameter Q, thermal conductivity parameter β, conduction–convection parameters Nc₁ and Nc₂, conduction–radiation parameter Nr, convection sink temperature δ and radiation sink temperature η.     

Convective heat transfer in cross-corrugated triangular ducts under uniform heat flux boundary conditions

Cross-corrugated triangular ducts provide high heat mass transfer capabilities in membrane based air-to-air heat mass exchangers. The mixing effect would intensify the convective heat mass transfer coefficients on membrane surfaces. In this study, the fluid flow and convective heat transfer in a cross-corrugated triangular duct under uniform heat flux boundary condition is modeled and experimentally studied. A low Reynolds number k–ω (LKW) turbulence model is employed to account for the turbulence in the flow. Heat transfer experiments and high speed hot wire anemometry technology are used to validate the model. The transitional behavior of fluid flow in the duct is disclosed by velocity measurements and Fourier transforms. Correlations are provided for estimation of the pressure drop and the mean Nusselt numbers under uniform heat flux boundary conditions. The established correlations can be extended to estimate the convective mass transfer coefficients through heat mass analogy.     

Effect of rotating cylinder on heat transfer in a square enclosure filled with nanofluids

Convective heat transfer in a differentially heated square enclosure with an inner rotating cylinder is studied theoretically. The free space between the cylinder and the enclosure walls is filled with water–Ag, water–Cu, water–Al₂O₃ or water–TiO₂ nanofluids. The governing equations are formulated for velocity, pressure and temperature formulation and are modeled in COMSOL, a partial differential equation (PDE) solver based on the Galerkin finite element method (GFEM). The governing parameters considered are the solid volume fraction, 0.0 ? ? ? 0.05, the cylinder radius, 0 ? R ? 0.3 and the angular rotational velocity, ?1000 ? Ω ? 1000. The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. It is found that the strength of the flow circulation is much stronger for a higher nanoparticle concentration, a better thermal conductivity value and a smaller cylinder with a faster, negative rotation. The maximum heat transfer are obtained at a high nanoparticle concentration with a good conductivity value, a slow positive rotation and a moderate cylinder size located in the center of the enclosure.     

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.     

Turbulent natural convection in a vertical parallel-plate channel with asymmetric heating

Turbulent natural convection in a vertical parallel plate channel has been investigated both experimentally and numerically. The experimental channel is formed of a uniform temperature heater wall and an opposing glass wall. A fibre flow laser doppler anemometer (LDA) is used to measure velocity profiles along the channel. Simultaneous velocity and temperature profile measurements are made at the channel outlet. A commercial computational fluid dynamics (CFD) code is used to simulate heat transfer and fluid flow in the channel numerically. The code is customised building in some low Reynolds number (LRN) k–ε turbulence models. The numerical method used in this study is found to predict heat transfer and flow rate fairly accurately. It is also capable of capturing velocity and temperature profiles with some accuracy. Experimental and numerical data are presented comparatively in the form of velocity, temperature, and turbulent kinetic energy profiles along the channel for a case. Correlating equations are obtained from the numerical results for heat transfer and induced flow rate and, are presented graphically comparing with other studies available in the literature.     

Numerical Investigation of Conjugate Heat Transfer to Supercritical CO2 in a Vertical Tube-in-Tube Heat Exchanger

Conjugate heat transfer to supercritical CO₂ in a vertical tube-in-tube heat exchanger was numerically investigated. The results demonstrate that most models considered are able to reproduce the heat transfer processes qualitatively, and the Abe, Kondoh, and Nagano model shows optimal agreement with the experimental data. The influences of hot fluid mass flux and temperature of the shell side, supercritical fluid mass flux of the tube side, flow direction, and pipe diameter on conjugate heat transfer were investigated based on velocity and turbulence fields. It is concluded that hot fluid mass flux and temperature of the shell side significantly affect heat transfer of the tube side. Mixed convection is the main heat transfer mechanism for the supercritical CO₂ conjugate heat transfer process when the inner diameter of the tube is greater than 1 mm. In addition, density variation is highly significant for heat transfer of supercritical CO₂ while high viscosity hinders the distortion of the flow field and reduces deterioration in heat transfer.     

Energy separation in the wake of a cylinder: Effect of Reynolds number and acoustic resonance

Energy separation is a spontaneous redistribution of total energy in a flowing fluid without external work or heat transfer. The energy separation mechanism in the vortex field behind an adiabatic circular cylinder in a cross flow of air is investigated. Time-averaged velocity and temperature measurements taken one diameter downstream of the cylinder (Re ～ 10⁵, M_∞ ～ 0.25) indicate flow reversal. The measured recovery temperature, expressed as distribution of energy separation factor indicates that energy separation is caused by the vortex flow in the wake, enhanced by acoustic excitation, and is insensitive to Reynolds number in the sub critical range studied.