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1

Numerical predictions of laminar flow and free convection heat transfer from an isothermal vertical flat plate

Belhocine Ali, Stojanovic Nadica, Abdullah Oday Ibraheem

Archive of Mechanical Engineering

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2022

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LXIX, nr 4

749--773

EN

In this present work, the laminar free convection boundary layer flow of a two-dimensional fluid over the vertical flat plate with a uniform surface temperature has been numerically investigated in detail by the similarity solution method. The velocity and temperature profiles were considered similar to all values and their variations are as a function of distance from the leading edge measured along with the plate. By taking into account this thermal boundary condition, the system of governing partial differential equations is reduced to a system of non-linear ordinary differential equations. The latter was solved numerically using the Runge-Kutta method of the fourth-order, the solution of which was obtained by using the FORTRAN code on a computer. The numerical analysis resulting from this simulation allows us to derive some prescribed values of various material parameters involved in the problem to which several important results were discussed in depth such as velocity, temperature, and rate of heat transfer. The definitive comparison between the two numerical models showed us an excellent agreement concerning the order of precision of the simulation. Finally, we compared our numerical results with a certain model already treated, which is in the specialized literature.

2

Outcome of nanofluid flow containing arbitrary shape nanoparticles induced by a permeable stretching sheet

Sarkar A., Kundu P. K.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 2

142--156

EN

In this work we have discussed the impact of thermal radiation on heat transfer to nanofluid flow over an unsteady permeable stretching sheet using various types of arbitrary shape nanoparticles of Copper (Cu), Silver (Ag), Alumina [...], and Titania Oxide [...] in the base fluid. Suitable transformations have been employed to build ODEs from the partial differential equations. Numerical results are therefore obtained particularly for cylindrical shape and spherical shape nanoparticles. Our analysis substantiates that the velocity and temperature profiles increases with enhanced thermal radiation parameter. Further, Nusselt number is more advanced for the nanofluid that contains cylindrical shape nanoparticles as compared to spherical shape nanoparticles.

3

Mass transfer analysis of two-phase flow in a suspension of microorganisms

Mamatha S.U., Ramesh Babu, K., Durga Prasad Putta, Raju C.S.K., Varma S.V.K.

Archives of Thermodynamics

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2020

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Vol. 41, no 1

175--192

EN

The aim of present work is to investigate the mass transfer of steady incompressible hydromagnetic fluid near the stagnation point with deferment of dust particles over a stretching surface. Most researchers tried to improve the mass transfer by inclusion of cross-diffusion or dust particles due to their vast applications in industrial processes, extrusion process, chemical processing, manufacturing of various types of liquid drinks and in various engineering treatments. To encourage the mass transport phenomena in this study we incorporated dust with microorganisms. Conservation of mass, momentum, concentration and density of microorganisms are used in relevant flow equations. The arising system of nonlinear partial differential equations is transformed into nonlinear ordinary differential equations. The numerical solutions are obtained by the Runge-Kutta based shooting technique and the local Sherwood number is computed for various values of the physical governing parameters (Lewis number, Peclet number, Eckert number). An important finding of present work is that larger values of these parameters encourage the mass transfer rate, and the motile organisms density profiles are augmented with the larger values of fluid particle interaction parameter with reference to bioconvection, bioconvection Lewis number, and dust particle concentration parameter..

4

Electrically conducting flow through exponential power law fluid with variable thermal conductivity

Ferdows M., Bangalee M. Z. I., Liu D.

International Journal of Applied Mechanics and Engineering

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2019

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Vol. 24, no. 3

539--548

EN

The problem of exponential law of steady, incompressible fluid flow in boundary layer and heat transfer are studied in an electrically conducting fluid over a semi-infinite vertical plate assuming the variable thermal conductivity in the presence of a uniform magnetic field. The governing system of equations including the continuity equation, momentum equation and energy equation have been transformed into nonlinear coupled ordinary differential equations using appropriate similarity variables. All the numerical and graphical solutions are obtained through the use of Maple software. The solutions are found to be dependent on three dimensionless parameters including the magnetic field parameter M, thermal conductivity parameter and Prandtl number Pr. Representative velocity and temperature profiles are presented at various values of the governing parameters. The skin-friction coefficient and the rate of heat transfer are also calculated for different values of the parameters.

5

Stagnation point flow of Eyring Powell fluid in a vertical cylinder with heat transfer

Rehman A., Achakzai S., Nadeem S., Iqbal S.

Journal of Power Technologies

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2016

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Vol. 96, nr 1

57--62

EN

In this paper an analysis is carried out to examine the effects of natural convection heat transfer for steady boundary layer flow of an Eyring Powell fluid flowing through a vertical circular cylinder. The governing partial differential equations along with the boundary conditions are reduced to dimensionless form by using the boundary layer approximation and applying suitable similarity transformations. The resulting nonlinear coupled system of ordinary differential equations subject to the appropriate boundary conditions is solved using the analytic technique homotopy analysis method (HAM). The effects of the physical parameters on the flow and heat transfer characteristics are presented. The behavior of skinfriction coefficient and Nusselt numbers are also studied for different parameters.

6

Unsteady laminar mixed convection boundary layer flow near a vertical wedge due to oscillations in the free-stream and surface temperature

Roy N. C., Hossain A., Hussain S.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 1

169--186

EN

The unsteady laminar boundary layer characteristics of mixed convection flow past a vertical wedge have been investigated numerically. The free-stream velocity and surface temperature are assumed to be oscillating in the magnitude but not in the direction of the oncoming flow velocity. The governing equations have been solved by two distinct methods, namely, the straightforward finite difference method for the entire frequency range, and the extended series solution for low frequency range and the asymptotic series expansion method for high frequency range. The results demonstrate the effects of the Richardson number, Ri, introduced to quantify the influence of mixed convection and the Prandtl number, Pr, on the amplitudes and phase angles of the skin friction and heat transfer. In addition, the effects of these parameters are examined in terms of the transient skin friction and heat transfer.

7

Mixed convection in the stagnation-point flow over a vertical stretching sheet in the presence of thermal radiation

Manjunatha S., Gireesha B. J., Bagewadi C. S.

International Journal of Applied Mechanics and Engineering

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2015

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Vol. 20, no. 4

871--888

EN

An unsteady two-dimensional stagnation-point mixed convection flow of a viscous, incompressible dusty fluid towards a vertical stretching sheet has been examined. The stretching velocity and the free stream velocity are assumed to vary linearly with the distance from the stagnation point. The problem is analyzed using similarity solutions. The similarity ordinary differential equations were then solved numerical by using the RKF-45 method. The effects of various physical parameters on the velocity profile and skin-friction coefficient are also discussed in this paper. Some important findings reported in this work reveal that the effect of radiation has a significant impact on controlling the rate of heat transfer in the boundary layer region.

8

Stagnation flow of couple stress nanofluid over an exponentially stretching sheet through a porous medium

Rehman A., Nadeem S., Malik M. Y.

Journal of Power Technologies

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2013

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Vol. 93, nr 2

122--132

EN

The present investigation is carried for the problem of boundary layer stagnation point flow and heat transfer of couple stress fluid containing nanoparticles and flowing over an exponentially stretching surface in a porous medium. The governing equations of couple stress fluid model for velocity, temperature and nanoparticle profiles are given under boundary layer approach. The nonlinear partial differential equations are simplified by using similar transformations. The analytical solutions of simplified equations are found with the help of homotopy analysis method. The convergence of the HAM solutions has been discussed by plotting - curves and also through homotopy pade approximation. The physical features of pertinent parameters have been discussed through graphs.

9

Heat transfer of viscoelastic fluid flow due to nonlinear stretching sheet with internal heat source

Nandeppanavar M. M., Siddalingappa M. N., Jyoti H.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 3

739--760

EN

In the present paper, a viscoelastic boundary layer flow and heat transfer over an exponentially stretching continuous sheet in the presence of a heat source/sink has been examined. Loss of energy due to viscous dissipation of the non-Newtonian fluid has been taken into account in this study. Approximate analytical local similar solutions of the highly non-linear momentum equation are obtained for velocity distribution by transforming the equation into Riccati-type and then solving this sequentially. Accuracy of the zero-order analytical solutions for the stream function and velocity are verified by numerical solutions obtained by employing the Runge-Kutta fourth order method involving shooting. Similarity solutions of the temperature equation for non-isothermal boundary conditions are obtained in the form of confluent hypergeometric functions. The effect of various physical parameters on the local skin-friction coefficient and heat transfer characteristics are discussed in detail. It is seen that the rate of heat transfer from the stretching sheet to the fluid can be controlled by suitably choosing the values of the Prandtl number Pr and local Eckert number E, local viscioelastic parameter k1 and local heat source/ sink parameter β.

10

Flow and heat transfer at a nonlinearly shrinking porous sheet: the case of asymptotically large powerlaw shrinking rates

Prasad K. V., Vajravelu K., Pop I.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 3

779--791

EN

The boundary layer flow and heat transfer of a viscous fluid over a nonlinear permeable shrinking sheet in a thermally stratified environment is considered. The sheet is assumed to shrink in its own plane with an arbitrary power-law velocity proportional to the distance from the stagnation point. The governing differential equations are first transformed into ordinary differential equations by introducing a new similarity transformation. This is different from the transform commonly used in the literature in that it permits numerical solutions even for asymptotically large values of the power-law index, m. The coupled non-linear boundary value problem is solved numerically by an implicit finite difference scheme known as the Keller- Box method. Numerical computations are performed for a wide variety of power-law parameters (1 < m < 100,000) so as to capture the effects of the thermally stratified environment on the velocity and temperature fields. The numerical solutions are presented through a number of graphs and tables. Numerical results for the skin-friction coefficient and the Nusselt number are tabulated for various values of the pertinent parameters.

11

Effect of magnetic field and heat generation/absorption on free convection along semi-infinite vertical porous plate

Tak S. S., Gehlot R. K., Mathur R.

International Journal of Applied Mechanics and Engineering

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2010

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Vol. 15, no 1

237-248

EN

Heat and momentum transfer in the case of a steady free convection flow along a semi-infinite vertical porous/non-porous plate in the presence of a uniform transverse magnetic field and uniform heat generation/absorption have been investigated. Non-similar solutions of the governing equations have been obtained by taking series expansions of stream function and temperature function. The resulting set of non-linear coupled ordinary differential equations with the appropriate boundary conditions has been solved numerically, using Newton's shooting technique. Numerical values of functions that correspond to the local wall shear stress and the rate of surface heat transfer are tabulated. The velocity function, temperature function, local skin-friction and local Nusselt number are shown graphically for various values of parameters involved and discussed in detail.

12

Effect of radiation on unsteady free convection flow bounded by an oscillating plate with variable wall temperature

Pathak G., Maheshwari C., Gupta S. P.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 2

371-382

EN

The object of the paper is to study the radiation effects on an unsteady free convective flow through a porous medium bounded by an oscillating plate with a variable wall temperature. The momentum and energy boundary layer equations have been solved by taking series expansions of velocity and temperature function in powers of product of magnetic field and time. The analytical solution of resulting ordinary differential equations has been obtained in terms of repeated integrals of complementary error functions. Also, the velocity and temperature profiles, for different values of the parameters, have been drawn and discussed.

13

Boundary layer viscoelastic fluid flow over an exponentially stretching sheet

Khan S. K.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 2

321-335

EN

In the present paper, a viscoelastic boundary layer fluid flow over an exponentially stretching continuous sheet has been examined. The flow is assumed to be generated solely by the application of two equal and opposite forces along the x-axis such that stretching of the boundary surface is of exponential order in x. Approximate analytical similarity solutions (zero and first order) of the highly non-linear boundary layer equation are obtained for the dimensionless stream function and velocity distribution function after transforming the boundary layer equation into Riccati type and solving that sequentially. The first-order solution is derived in the form of confluent hypergeometric Whittaker functions. The solutions are verified at the boundary sheet. These solutions (zero and first order) involve an exponential dependence of the similarity variable, the stretching velocity and the stream function on the axial coordinate. The accuracy of the analytical solutions is also verified by the numerical solutions obtained by employing the Runge-Kutta fourth order method with shooting. The effects of various physical parameters on the velocity profile and skin-friction coefficient are also discussed in this paper.

14

Compressible boundary layer flow in the stagnation region of a rotating sphere with large injection rates and a magnetic field.

Kumari Mahesh, Nath G.

Archive of Mechanical Engineering

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2000

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Vol. XLVII, nr 4

289-309

EN

The effect of large injection rates on the steady laminar compressible boundary layer in the front stagnation-point region of a rotating sphere with a magnetic field has been studied. The effect of variable gas properties, non-unity Prandtl number and viscous dissipation are included in the anlysis. The nonlinear coupled ordinary differential equations govering the flow are first linearized using quasilinearization technique, and the resulting system of linear equations are then solved using an implicit finite-difference scheme with non-uniform step-size. For large injection rates, analytical expressions for the surface shear stresses in the longitudinal and rotating directions and the surface heat transfer are also obtained using an aproximate method. For large injection rates, the surface heat transfer tends to zero, but the surface shear stresses in the longitudinal and rotating directions remain finite but small. The surface shear stresses and the surface heat transfer decrease with increasing rate of inspection, but they increase with the magnetic field and the rotation parameter. The magnetic field or the rotation parameter induces an overshoot increases significantly with the rotation parameters and the injection parameter. The location of the dividing streamline moves away from the boundary with increasing injection rate, but it moves towards the boundary with increasing magnetic and rotation parameters.

PL

W pracy zbadano efekt dużych szybkości wtryskiwania płynu na stabilną, laminarną, ściśliwą warstwę graniczną w regionie czołowego punktu zastoju dla wirującej kuli w obecności pola mgnetycznego. W analizie uwzględniono efekt zmienności właściwości gazu, efekt rozpraszania lepkiego oraz wpływ różnej od jedności liczby Prandtla. Nieliniowe sprzężone zwyczajnie równania różniczowe, które opisują przepływ, zostały najpierw zlinearyzowane przy zastosowaniu techniki quasi-linearyzacji, a uzyskany stąd układ równań liniowych został rozwiązany bezpośrednią metodą różnic skończonych przy zmiennej długości kroku. Wyrażenia analityczne powierzchniowych naprężeń ścinających w kierunku wzdłużnym i kierunku rotacji, jak i wyrażenia powierzchniowego transferu ciepła, uzyskano dla dużych szybkości wtryskiwania, także przy użyciu metody przybliżonej. Dla dużych szybkości wtryskiwania transfer ciepła dąży do zera, lecz powierzchniowe naprężenie ścinające w kierunku wzdłużnym i kierunku rotacji pozostają skończone, choć małe. Powierzchniowe napężenie ścinające i powierzchniowy transfer ciepła maleją ze wzrostem szybkości wtryskiwania, ale wzrastają z polem magnetycznym i parametrem rotacji. Pole magnetyczne, podobnie jak parametr rotacji, powodują powstanie efektu przerzutu w profilu szybkości wzdłużnej, a wartość tego przerzutu wzrasta znacząco przy zwiększaniu paramatrów rotacji i parametrów wtryskiwania. Położenie linii podziału strumienia oddala się od granicy przy wzrastającej szybkości wtryskiwania, lecz zbliża się do niej przy wzroście parametrów rotacji i pola magnetycznego.

15

The axisymmetric compressible boundary layer flow along a circular cylinder

Elliott J. W.

Applied Mechanics and Engineering

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2000

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Vol. 5, no 3

715-751

EN

A numerical and analytical investigation of the compressible axisymmetric boundary-lager flow over a circular cylinder is presented for both adiabatic flow and the case of heated or cooled walk. First, a numerical solution to the governing equations is presented for a variety of wall conditions. The remainder and majority of the paper is then concerned with an analysis of the far-downstream flow where curvature becomes a dominant feature. Here the flow takes on a double structure, with an Oseen type of outer flow. The problem reduces to matching to an inner solution which, in contrast to the incompressible case, is found to be non-trivial. Three forms of the inner solution are constructed, firstly to justify obtaining a new result and secondly to rebut the assertion that matching is only possible for a single approach. Further the use of a general power law form for the viscosity law is considered. The resulting asymptotic forms are then compared with the numerical results of the far downstream flow.

16

Effect of radiation on mixed convection boundary layer flow along a vertical cylinder

Hossain M. A., Alim M. A., Takhar H. S.

Applied Mechanics and Engineering

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1998

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Vol. 3, no 3

393-404

EN

Mixed convection flow of an optically dense viscous incompressible fluid along a vertical cylinder including the effects of radiation has been studied when the surface temperature is kept uniform. With appropriate transformations, the boundary layer equations governing the flow are reduced to local non-similarity equations. Solutions to the governing equations are obtained by employing an implicit finite difference method together with the Keller box scheme, as well the local non-similar method with a second order trunction, for values of the transverse curvature parameter, x, in the range [0,10]. Effects of the pertinant parameters, such as the radiation parameter, Rd, the surface temperature parameter, qw, and the buoyancy parameter W , taking Prandtl number, Pr, equal to 0.7, on the local skin-friction and the local Nusselt are explored in this stidy.