Mathematical modelling of heat transfer in a catalytic reformer

In this work we analyse heat transfer in a system of channelsconnected by thin conducting walls. The channels are packedwith catalytic pellets that promote exothermic catalytic combustionreactions and endothermic reforming reactions in adjacent channels.A model is developed in which the thermal conductivity and thethickness of the interconnecting wall can be used as controlparameters characterizing the heat exchange between the neighbouringchannels. The model is to be used as a mathematical tool toanalyse design alternatives and develop accurate numerical techniques.Our objective is to study how the heat is transferred acrossthe conducting walls and how this influences the temperaturedistribution in the channels. We use an asymptotic techniqueto do this. The structure of the walls is then examined in detail,focusing on the case when we have layered walls.     

Mathematical modelling and optimisation of a waste water treatment plant by combined oxygen electrode and biological waste water treatment model

Structured mathematical models of oxygen electrode and biological waste water treatment were combined to optimise the position of electrode in the bioreactor. Parameters sensibility testing of mathematical model has shown that the model was most sensitive to the change of these parameters (in decreasing order of significance): oxygen consumption per unit of BOD_5, specific consumption rate of adsorbed BOD₅, volumetric coefficient of oxygen transfer rate (k_La), and waste water inflow. Two positions of electrode were tested: in the bioreactor and in the bioreactors syphon outlet shaft. Results obtained for the exchange of the oxic/anoxic phase and sludge recycling plant indicated that a reduction of electrical power for the aeration could be achieved if O₂ electrode is placed in the bioreactor tank, compared to position in outlet shaft. Better positioning of electrode has resulted in shortening of the oxic/anoxic cycle by 13% and the daily working time of aerators for 0.5 h per day, respectively. In the same time, the number of oxic/anoxic cycles per day was increased by 29%. In addition, results obtained by mathematical modelling indicated no debasement of chemical composition in out coming purified water if new position will be used.     

Mathematical modelling and dynamic response of a multi-straight-line path tracing flexible robot manipulator with rotating-prismatic joint

In this study, mathematical modelling and dynamic response of a flexible robot manipulator with rotating-prismatic joint are investigated. The tip end of the flexible robot manipulator traces a multi-straight-line path under the action of an external driving torque and an axial force. Considered robot manipulator consists of a rotating prismatic joint and a sliding flexible arm with a tip mass. Flexible arm is assumed to be an Euler–Bernoulli beam carrying an end-mass. Equations of motion of the flexible manipulator are obtained by using Lagrange’s equation of motion. Effect of rotary inertia, axial shortening and gravitation is considered in the analysis. Equations of motion are solved by using fourth order Runge–Kutta method. Numerical simulations obtained by using a developed computer program are presented and physical trend of the results are discussed.     

Numerical modelling of EHD effects on heat transfer and bubble shapes of nucleate boiling

In this article, mathematical and numerical models are developed to study pure electrohydrodynamic (EHD) effects on heat transfer and bubble shapes when an initial bubble attached to a superheated horizontal wall in nucleate boiling. In the modelling of EHD effects on heat transfer, an undeformed bubble is considered; the electric body force and Joule heat are added to the momentum and energy equations; governing equations for heat, fluid flow and electric fields are coupled numerically and solved using a non-orthogonal body-fitted mesh system with necessary interfacial treatments at the gas–liquid boundary. While, to study the pure effect of EHD on the deformation of the bubble, the evaluation of a deformable bubble without heat transfer is simulated by volume of fluid (VOF) method based on an axial symmetric Cartesian coordinate system. The simulations indicate that EHD can effectively enhance heat transfer rate of nucleate boiling by influencing the motion of the ring vortex around the bubble and that bubble can be elongated due to the pull in axial direction and push in the negative radial direction by the electric field force.     

Investigating the effect of various nanoparticle and base liquid types on the nanofluids heat and fluid flow in a microchannel

In this paper, heat transfer and pressure drop of different nanofluid types in a two-dimensional microchannel is investigated numerically. To do this, an Eulerian–Eulerian two-phase model is used for nanofluid simulation and the governing equations are solved using a finite volume method. Nine different nanoparticles and three different base liquid types (water, ethylene glycol and engine oil) are considered. Heat transfer and pressure drop of different nanofluid types are compared at Re = 100 and 1% volume concentration for different nanoparticles and at constant inlet velocity for different base liquids. Numerical results show an almost equal pressure drop for all the nanoparticles dispersed in water, while, the heat transfer coefficient is highest for water–diamond and is the lowest for water–SiO₂ nanofluids. Also, the pressure drop for water-based nanofluid is very lower than the others and the heat transfer coefficient is the highest for water-based nanofluids.     

Convective flow and heat transfer of a viscous heat generating fluid in the presence of a moving,infinite, vertical,porous plate

The analysis of convective flow and heat transfer of a viscous heat generating fluid past a uniformly moving, infinite, vertical, porous plate has been made systematically with a view to throw adequate light on the effects of the plate-motion and the presence of heat generation/absorption on the flow and heat transfer characteristics. The equations of conservation of momentum and energy which govern the flow and heat transfer of the said problem have been solved numerically by the method of Runge-Kutta-Gill. The numerical results thus obtained for the flow and heat transfer characteristics have revealed many an interesting behaviour, of the skin friction and the rate of heat transfer coefficient at the plate.     

The influence of Hall current and heat transfer on the flow of a fourth grade fluid

In this article, a mathematical model is analyzed to investigate the effects of Hall current and heat transfer on the flow of a fourth grade fluid between two heated and rotating disks. The corresponding problem of velocity and temperature are solved analytically by homotopy analysis method. Comparison is given between the results of velocity in fourth grade, third grade, second grade, and viscous fluids. The variation of pertinent parameters are graphed and discussed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Mathematical modelling,analysis and numerical simulations for the influence of heat shock proteins on tumour invasion

Invasion is a key property of tumour cells for building metastasis. A class of functionally related proteins called heat shock proteins (HSPs), the expression of which is increased when cells are exposed to elevated temperatures or other stress, play an important role in the invasion. In this paper we develop a mathematical model focusing on the effect of HSPs on the tumour cell migration. The resulting multiscale setting accounts both for the microscopic, intracellular level on which these proteins are acting and for the macroscopic level of the cell population. We prove the local existence of a unique positive solution and perform numerical simulations in order to illustrate the behaviour of cancer cells w.r.t. the fibre density of the tissue and the matrix degrading enzymes, along with the effect of HSPs.     

Modelling and simulation of heat exchange and moisture content in a cereal storage silo

ABSTRACT

In this paper, a mathematical model is developed based on the heat transfer of stored grains aerated in a cylindrical silo. This work is a part of study that aims to model the whole process of cereal storage system including a dehumidifier. The use of dehumidifier is intended to remove excess moisture from the airflow injected by the ventilator system in the silo filled with wheat, and to keep hygroscopic properties of grain in safe level during the storage period. Temperature and humidity are the two important variables coupled to control the process and to preserve grain quality. The laboratory device permitted us to achieve several tests for different conditions of grain stored in silo without aeration. A simulation of the airflow through the thermal space of the silo and grain parameters has been carried out. The results are reasonably in agreement with experiments and other published data. The system performance is evaluated at critical conditions of storage boundaries.     

Two-phase flow modelling of spilling and plunging breaking waves

A two-phase flow model, which solves the flow in the air and water simultaneously, has been employed to investigate both spilling and plunging breakers in the surf zone with a focus during wave breaking. The model is based on the Reynolds-averaged Navier–Stokes equations with the k–?$k''–''?$ turbulence model. The governing equations are solved using the finite volume method, with the partial cell treatment being implemented in a staggered Cartesian grid to deal with complex geometries. The PISO algorithm is utilised for the pressure–velocity coupling and the air–water interface is modelled by the interface capturing method via a high-resolution volume of fluid scheme. Numerical results are compared with experimental measurements and other numerical studies in terms of water surface elevations, mean flow and turbulence intensity, in which satisfactory agreement is obtained. In addition, water surface profiles, velocity and vorticity fields during wave breaking are also presented and discussed. It is shown that the present model is capable of simulating the wave overturning, air entrainment and splash-up processes.     

Rotating disk flow and heat transfer through a porous medium of a non-Newtonian fluid with suction and injection

The steady flow of an incompressible viscous non-Newtonian fluid above an infinite rotating porous disk in a porous medium is studied with heat transfer. A uniform injection or suction is applied through the surface of the disk. Numerical solutions of the non-linear differential equations which govern the hydrodynamics and energy transfer are obtained. The effect of the porosity of the medium, the characteristics of the non-Newtonian fluid and the suction or injection velocity on the velocity and temperature distributions is considered. The inclusion of the three effects, the porosity, the non-Newtonian characteristics, and the suction or injection velocity together has shown some interesting effects.     

Mathematical modeling and comparison of air standard Dual and Dual-Atkinson cycles with friction,heat transfer and variable specific-heats of the working fluid

Based on finite-time thermodynamics, a comparative performance analysis of air standard Dual and Dual-Atkinson cycles with heat-transfer loss, friction like term losses and variable specific-heats of the working fluid have been performed. Also the effects of heat loss, as characterized by a percentage of the fuel’s energy, friction and variable specific-heats of the working fluid, on performance of the mentioned irreversible cycles are analyzed. Moreover, detailed numerical examples show the relations between the power output and the compression ratio, between the thermal efficiency and the compression ratio, as well as the optimal relation between the power output and the thermal efficiency of cycles. Results show the importance of consideration of heat loss effects on the both cycles’ performance. Also performance comparison of two cycles show that heat efficiency and power output of a Dual-Atkinson cycle are higher than a Dual cycle’s ones. The results obtained from this paper will provide guidance for the design of Dual-Atkinson engines.     

Hall effect on unsteady MHD Couette flow and heat transfer of a Bingham fluid with suction and injection

The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid bounded by two parallel non-conducting porous plates is studied with heat transfer considering the Hall effect. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a uniform suction and injection. The lower plate is stationary and the upper plate moves with a constant velocity and the two plates are kept at different but constant temperatures. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions are studied.     

Effects of heat transfer and space porosity on peristaltic flow in a vertical asymmetric channel

This article discusses the effect of heat transfer on the peristaltic flow of a Newtonian fluid through a porous space in a vertical asymmetric channel. Long wavelength approximation is used to linearize the governing equations. The system of the governing nonlinear PDE is solved by using the perturbation method. The solutions are obtained for the velocity and the temperature fields. The flow is investigated in a wave frame of reference moving with velocity of the wave. Numerical calculations are carried out for the pressure rise, frictional forces, and the features of the flow and temperature characteristics are analyzed by plotting graphs and discussed in detail. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Effects of hall current and heat transfer on MHD flow of a Burgers’ fluid due to a pull of eccentric rotating disks

The effect of Hall current and heat transfer on the magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible Burgers’ fluid between two infinite disks rotating about non-coaxial axes perpendicular to the disks is studied. The flow is due to a pull with constant velocities of eccentric rotating infinite disks and an external uniform magnetic field normal to the disks is applied. Exact solutions are obtained for the governing momentum and energy equations. The effects of Hartmann number M, Prandtl number Pr, Eckert number Ec and Hall parameter η are studied.     

Combined effect of magnetic field and heat absorption on unsteady free convection and heat transfer flow in a micropolar fluid past a semi-infinite moving plate with viscous dissipation using element free Galerkin method

The fully developed electrically conducting micropolar fluid flow and heat transfer along a semi-infinite vertical porous moving plate is studied including the effect of viscous heating and in the presence of a magnetic field applied transversely to the direction of the flow. The Darcy-Brinkman-Forchheimer model which includes the effects of boundary and inertia forces is employed. The differential equations governing the problem have been transformed by a similarity transformation into a system of non-dimensional differential equations which are solved numerically by element free Galerkin method. Profiles for velocity, microrotation and temperature are presented for a wide range of plate velocity, viscosity ratio, Darcy number, Forchhimer number, magnetic field parameter, heat absorption parameter and the micropolar parameter. The skin friction and Nusselt numbers at the plates are also shown graphically. The present problem has significant applications in chemical engineering, materials processing, solar porous wafer absorber systems and metallurgy.     

A numerical study of boundary layer flow of viscous incompressible fluid past an inclined stretching sheet and heat transfer using nonpolynomial spline method

In the present paper, we study the boundary layer flow of viscous incompressible fluid over an inclined stretching sheet with body force and heat transfer. Considering the stream function, we convert the boundary layer equation into nonlinear third-order ordinary differential equation together with appropriate boundary conditions in an infinite domain. The nonlinear boundary value problem has been linearized by using the quasilinearization technique. Then, we develop a nonpolynomial spline method, which is used to solve the flow problem. The convergence analysis of the method is also discussed. We study the velocity function for different angles of inclination and Froude number with the help of various graphs and tables. Then using these in heat convection flow, we obtain the expression for temperature field. Skin friction is also calculated. The various results have been given in tables. At last, we calculated the Nusselt number.