Robins Aikkara - Academia.edu (original) (raw)

Papers by Robins Aikkara

The interaction of combined free and forced convection heat transfer in horizontal channels with ... more The interaction of combined free and forced convection heat transfer in horizontal channels with local sources prescribed on the boundaries is investigated. The flow is assumed to be steady, constant property, laminar, and two dimensional. Both numerical and experimental results are presented. The full two dimensional equations of motion and energy transport subject to the Boussinesq approximation are solved numerically. The method of false transient is successfully applied to this problem to predict temperature profiles, local heat transfer coefficients, and flow contours. The problem of fully developed laminar channel flow with constant wall heat flux is solved numerically. In the case of both walls heated at the same rate, a separated flow is created along the upper wall. The case of flow about a high dissipation local source for a Reynold's number of 37 is presented.

Heat and Mass Transfer, 1972

An experimental study of mixed convection in an asymmetrically heated two-dimensional flow of wat... more An experimental study of mixed convection in an asymmetrically heated two-dimensional flow of water has been made. Experiments in fully developed turbulent flow (Re maximum=9000) were made initially to establish the satisfactory operation of the equipment. In the mixed convection laminar flow tests to determine local Nusselt numbers, the Reynolds number range was from about 100 to 1000 with the Rayleigh number based on heat flux varying from about 10 to 300. The data, which are presented graphically, have been compared with the results of the theoretical analyses of other workers. The effect of buoyancy in the immediate entry of the flow [(x/de)/Re Pr <.05] was found to be negligible, but at greater distances there were significant increases in the heat transfer coefficient with the larger values of Rayleigh number. Diese Arbeit behandelt Versuche über Mischkonvektion in einer zweidimensionalen Wasserströmung mit unsymmetrischer Beheizung. Zur Prüfung der Apparatur wurden auch Versuche im vollturbulenten Bereich (Remax =9000) durchgeführt. Zur Messung örtlicher Nusselt-Zahlen bei laminarer Mischkonvektion wurde die Reynolds-Zahl von 100 bis 1000 variiert bei Rayleigh-Zahlen zwischen 10 und 300 entsprechend dem jeweiligen Wärmestrom. Die graphisch wiedergegebenen Ergebnisse wurden mit theoretischen Werten anderer Autoren verglichen. Der Auftrieb hatte unmittelbar am Eintritt [(x/de)/Re Pr <0,05] keinen meßbaren Einfluß, jedoch stieg der Wärmeübergang bei größeren Abständen beträchtlich an mit höheren Rayleigh-Zahlen.

Journal of Heat Transfer-transactions of The Asme, 1987

It is the purpose of the present paper to introduce a general transformation procedure appropriat... more It is the purpose of the present paper to introduce a general transformation procedure appropriate to the problem of combined free and forced convection in a porous medium. It will be shown that particular transformations proposed in the previous papers by Cheng and Minkowycz and co-workers are simply the specific forms of the present general transformation. Pure forced convection will be treated first as a limiting case of combined free and forced convection. The analysis reveals that any two-dimensional or axisymmetric body of arbitrary shape possesses its corresponding class of wall temperature distributions which permit similarity solutions. Secondly, combined free and forced convection will be considered to seek similarity solutions. It is found that, unlike in pure forced convection, similarity solutions in mixed convection are possible only when the external free-stream velocity varies every where in proportion to the product of the streamwise component of the gravity force and the wall-ambient temperature difference.

Journal of The Franklin Institute-engineering and Applied Mathematics, 1969

The effects of natural convection on two-dimensional solidification of viscous flow over a horizo... more The effects of natural convection on two-dimensional solidification of viscous flow over a horizontal, semi-infinite flat plate is considered. The continuity, momentum, and energy equations are solved by finite-difference techniques to determine the growth of the solid phase and the velocity and temperature distributions in the liquid and solid phases. Results are presented for a range of the dimensionless parameter NGr/NRe 2·5 which illustrates the consequences of neglecting natural convection effects on the growth of the interface.

Numerical Heat Transfer Part A-applications, 2010

Forced convection heat transfer characteristics of a long, heated square cylinder blocking the fl... more Forced convection heat transfer characteristics of a long, heated square cylinder blocking the flow of a power-law fluid in a channel is numerically investigated in this study. In particular, the role of the power-law index n, Reynolds number Re, Prandtl number Pr, and blockage ratio β(=B/H) on the rate of heat transfer from a square cylinder in a channel has been studied over the following ranges of conditions: 0.5 ≤ n ≤ 1.8, 60 ≤ Re ≤ 160, β = 1/4, 1/2, and 0.7 ≤ Pr ≤ 50. A semi-explicit finite-volume method is used on a nonuniform collocated grid arrangement. The third-order QUICK and the second-order central difference schemes are used to discretize the convective and diffusive terms, respectively, in the momentum and energy equations. Irrespective of the type of behavior of fluid (different values of n), the average Nusselt number increases as the blockage ratio increases. Similar to the unconfined flow configuration, the average Nusselt number increases monotonically with Reynolds and Prandtl numbers for both values of the blockage ratio and for all values of power-law index considered here. Further insights into the heat transfer phenomenon are provided by presenting isotherm contours in the vicinity of the cylinder for a range of values of the Reynolds number, Prandtl number, and power-law index for the two values of β considered in this work.

An analysis of heat transfer inside a semi porous two-dimensional rectangular open cavity was num... more An analysis of heat transfer inside a semi porous two-dimensional rectangular open cavity was numerically examined. The open cavity consists of two vertical walls closed to the bottom by a uniform heat flux. One vertical wall is a porous wall and fluid inflows normal to it. The other wall transfers the same uniform heat flux to the cavity. The study shows how natural convection effects may improve the forced convection inside the open cavity. The main motivation for this research is its application for electronic equipment where the cooling devices used for the electronic equipment are frequently based on natural and forced convection and the equipment may reach dangerous limits of temperature reducing its efficiency. Governing equations are expressed in Cartesian Coordinates and numerically handled by a finite volume method. Results of the maximum temperature are presented for both Reynolds and Grashof numbers at the heated wall and in the bottom.

The Governing Principle of Dissipative Processes (GPDP) formulated by Gyarmati into non-equilibri... more The Governing Principle of Dissipative Processes (GPDP) formulated by Gyarmati into non-equilibrium thermodynamics is employed to study the effects of suction, injection in laminar, two dimensional, combined free and forced convection flow over a non-isothermal wedge. The velocity and temperature functions inside the boundary layers are approximated by simple third order polynomial and the variational principle is formulated. In addition, the Euler-Lagrange equations of the variational principle are obtained as coupled polynomial equations in terms of momentum and thermal boundary layer thicknesses. Moreover, the effect of buoyancy force on heat transfer and skin friction is analysed for different values of Reynolds, Grashof, Prandtl numbers, wedge parameter and wall temperature exponent. Finally, the obtained analytical solutions are compared with known series solutions and the comparison establishes the fact that the accuracy is remarkable.

Finite element methods are developed for free and forced convective heat transport in incompressi... more Finite element methods are developed for free and forced convective heat transport in incompressible fluids. Attention is restricted to two-dimensional problems where the flow and thermal fields are assumed to be steady. Basic equations are formulated for combined convective and conductive transfer of heat in regions containing both a moving fluid and a solid body. The discrete approximation of the equations is done through the use of the Galerkin form of the finite element method. The solution algorithm alternates between the equations for the velocity and temperature fields at each iteration. Numerical examples include forced convection in developed pipe flow, forced convection in a tube where viscosity is temperature-dependent, and free convection from a cylinder inside an enclosure. For the last-named problem, verification of the accuracy of the method was obtained by comparison with a holographically obtained visualization of the isotherms.

Combined free convection and forced convection from a flush-mounted uniform heat source on the bo... more Combined free convection and forced convection from a flush-mounted uniform heat source on the bottom of a horizontal rectangular enclosure with side openings is studied numerically. The inlet opening allows an externally induced air stream at the ambient temperature to flow through the cavity and exits from another two openings placed top of the both side walls. Two-dimensional forms of Navier-Stokes equations are solved by using control volume based finite element technique. Three typical values of the Reynolds numbers, based on the enclosure height, are chosen as Re = 50, 100 and 200, and steady, laminar results are obtained in the range of Richardson number as 0 ≤ Ri ≤ 10 and a fixed Prandtl number of 0.71. The parametric studies for a wide range of governing parameters show consistent performance of the present numerical approach to obtain as stream functions and temperature profiles. Heat transfer rates at the heated walls are presented in terms of average Nusselt numbers. The computational results indicate that the heat transfer coefficient is strongly affected by Reynolds number and Richardson number. An empirical correlation is developed by using Nusselt number, Reynolds number and Richardson number.

The interaction of combined free and forced convection heat transfer in horizontal channels with ... more The interaction of combined free and forced convection heat transfer in horizontal channels with local sources prescribed on the boundaries is investigated. The flow is assumed to be steady, constant property, laminar, and two dimensional. Both numerical and experimental results are presented. The full two dimensional equations of motion and energy transport subject to the Boussinesq approximation are solved numerically. The method of false transient is successfully applied to this problem to predict temperature profiles, local heat transfer coefficients, and flow contours. The problem of fully developed laminar channel flow with constant wall heat flux is solved numerically. In the case of both walls heated at the same rate, a separated flow is created along the upper wall. The case of flow about a high dissipation local source for a Reynold's number of 37 is presented.

Heat and Mass Transfer, 1972

An experimental study of mixed convection in an asymmetrically heated two-dimensional flow of wat... more An experimental study of mixed convection in an asymmetrically heated two-dimensional flow of water has been made. Experiments in fully developed turbulent flow (Re maximum=9000) were made initially to establish the satisfactory operation of the equipment. In the mixed convection laminar flow tests to determine local Nusselt numbers, the Reynolds number range was from about 100 to 1000 with the Rayleigh number based on heat flux varying from about 10 to 300. The data, which are presented graphically, have been compared with the results of the theoretical analyses of other workers. The effect of buoyancy in the immediate entry of the flow [(x/de)/Re Pr <.05] was found to be negligible, but at greater distances there were significant increases in the heat transfer coefficient with the larger values of Rayleigh number. Diese Arbeit behandelt Versuche über Mischkonvektion in einer zweidimensionalen Wasserströmung mit unsymmetrischer Beheizung. Zur Prüfung der Apparatur wurden auch Versuche im vollturbulenten Bereich (Remax =9000) durchgeführt. Zur Messung örtlicher Nusselt-Zahlen bei laminarer Mischkonvektion wurde die Reynolds-Zahl von 100 bis 1000 variiert bei Rayleigh-Zahlen zwischen 10 und 300 entsprechend dem jeweiligen Wärmestrom. Die graphisch wiedergegebenen Ergebnisse wurden mit theoretischen Werten anderer Autoren verglichen. Der Auftrieb hatte unmittelbar am Eintritt [(x/de)/Re Pr <0,05] keinen meßbaren Einfluß, jedoch stieg der Wärmeübergang bei größeren Abständen beträchtlich an mit höheren Rayleigh-Zahlen.

Journal of Heat Transfer-transactions of The Asme, 1987

It is the purpose of the present paper to introduce a general transformation procedure appropriat... more It is the purpose of the present paper to introduce a general transformation procedure appropriate to the problem of combined free and forced convection in a porous medium. It will be shown that particular transformations proposed in the previous papers by Cheng and Minkowycz and co-workers are simply the specific forms of the present general transformation. Pure forced convection will be treated first as a limiting case of combined free and forced convection. The analysis reveals that any two-dimensional or axisymmetric body of arbitrary shape possesses its corresponding class of wall temperature distributions which permit similarity solutions. Secondly, combined free and forced convection will be considered to seek similarity solutions. It is found that, unlike in pure forced convection, similarity solutions in mixed convection are possible only when the external free-stream velocity varies every where in proportion to the product of the streamwise component of the gravity force and the wall-ambient temperature difference.

Journal of The Franklin Institute-engineering and Applied Mathematics, 1969

The effects of natural convection on two-dimensional solidification of viscous flow over a horizo... more The effects of natural convection on two-dimensional solidification of viscous flow over a horizontal, semi-infinite flat plate is considered. The continuity, momentum, and energy equations are solved by finite-difference techniques to determine the growth of the solid phase and the velocity and temperature distributions in the liquid and solid phases. Results are presented for a range of the dimensionless parameter NGr/NRe 2·5 which illustrates the consequences of neglecting natural convection effects on the growth of the interface.

Numerical Heat Transfer Part A-applications, 2010

Forced convection heat transfer characteristics of a long, heated square cylinder blocking the fl... more Forced convection heat transfer characteristics of a long, heated square cylinder blocking the flow of a power-law fluid in a channel is numerically investigated in this study. In particular, the role of the power-law index n, Reynolds number Re, Prandtl number Pr, and blockage ratio β(=B/H) on the rate of heat transfer from a square cylinder in a channel has been studied over the following ranges of conditions: 0.5 ≤ n ≤ 1.8, 60 ≤ Re ≤ 160, β = 1/4, 1/2, and 0.7 ≤ Pr ≤ 50. A semi-explicit finite-volume method is used on a nonuniform collocated grid arrangement. The third-order QUICK and the second-order central difference schemes are used to discretize the convective and diffusive terms, respectively, in the momentum and energy equations. Irrespective of the type of behavior of fluid (different values of n), the average Nusselt number increases as the blockage ratio increases. Similar to the unconfined flow configuration, the average Nusselt number increases monotonically with Reynolds and Prandtl numbers for both values of the blockage ratio and for all values of power-law index considered here. Further insights into the heat transfer phenomenon are provided by presenting isotherm contours in the vicinity of the cylinder for a range of values of the Reynolds number, Prandtl number, and power-law index for the two values of β considered in this work.

An analysis of heat transfer inside a semi porous two-dimensional rectangular open cavity was num... more An analysis of heat transfer inside a semi porous two-dimensional rectangular open cavity was numerically examined. The open cavity consists of two vertical walls closed to the bottom by a uniform heat flux. One vertical wall is a porous wall and fluid inflows normal to it. The other wall transfers the same uniform heat flux to the cavity. The study shows how natural convection effects may improve the forced convection inside the open cavity. The main motivation for this research is its application for electronic equipment where the cooling devices used for the electronic equipment are frequently based on natural and forced convection and the equipment may reach dangerous limits of temperature reducing its efficiency. Governing equations are expressed in Cartesian Coordinates and numerically handled by a finite volume method. Results of the maximum temperature are presented for both Reynolds and Grashof numbers at the heated wall and in the bottom.

The Governing Principle of Dissipative Processes (GPDP) formulated by Gyarmati into non-equilibri... more The Governing Principle of Dissipative Processes (GPDP) formulated by Gyarmati into non-equilibrium thermodynamics is employed to study the effects of suction, injection in laminar, two dimensional, combined free and forced convection flow over a non-isothermal wedge. The velocity and temperature functions inside the boundary layers are approximated by simple third order polynomial and the variational principle is formulated. In addition, the Euler-Lagrange equations of the variational principle are obtained as coupled polynomial equations in terms of momentum and thermal boundary layer thicknesses. Moreover, the effect of buoyancy force on heat transfer and skin friction is analysed for different values of Reynolds, Grashof, Prandtl numbers, wedge parameter and wall temperature exponent. Finally, the obtained analytical solutions are compared with known series solutions and the comparison establishes the fact that the accuracy is remarkable.

Finite element methods are developed for free and forced convective heat transport in incompressi... more Finite element methods are developed for free and forced convective heat transport in incompressible fluids. Attention is restricted to two-dimensional problems where the flow and thermal fields are assumed to be steady. Basic equations are formulated for combined convective and conductive transfer of heat in regions containing both a moving fluid and a solid body. The discrete approximation of the equations is done through the use of the Galerkin form of the finite element method. The solution algorithm alternates between the equations for the velocity and temperature fields at each iteration. Numerical examples include forced convection in developed pipe flow, forced convection in a tube where viscosity is temperature-dependent, and free convection from a cylinder inside an enclosure. For the last-named problem, verification of the accuracy of the method was obtained by comparison with a holographically obtained visualization of the isotherms.

Combined free convection and forced convection from a flush-mounted uniform heat source on the bo... more Combined free convection and forced convection from a flush-mounted uniform heat source on the bottom of a horizontal rectangular enclosure with side openings is studied numerically. The inlet opening allows an externally induced air stream at the ambient temperature to flow through the cavity and exits from another two openings placed top of the both side walls. Two-dimensional forms of Navier-Stokes equations are solved by using control volume based finite element technique. Three typical values of the Reynolds numbers, based on the enclosure height, are chosen as Re = 50, 100 and 200, and steady, laminar results are obtained in the range of Richardson number as 0 ≤ Ri ≤ 10 and a fixed Prandtl number of 0.71. The parametric studies for a wide range of governing parameters show consistent performance of the present numerical approach to obtain as stream functions and temperature profiles. Heat transfer rates at the heated walls are presented in terms of average Nusselt numbers. The computational results indicate that the heat transfer coefficient is strongly affected by Reynolds number and Richardson number. An empirical correlation is developed by using Nusselt number, Reynolds number and Richardson number.