Ahmer Mehmood | International Islamic University Islamabad (original) (raw)
Papers by Ahmer Mehmood
Exact solution of Navier-Stokes equations is possible only for very simple flow situations such a... more Exact solution of Navier-Stokes equations is possible only for very simple flow situations such as unidirectional flows.Due to the nonlinear nature of these equations their analytic solutions are rare and the situation gets worse in the case of unsteady and multidimensional flow problems. In this thesis we report highly accurate and purely analytic solutions to some steady/unsteady multidimensional viscous flows over flat surface. Heat transfer analysis has also been carried out where the flat surface is considered as a stretching sheet.In each case the skin friction and the rate of heat transfer has been reported.The issue of cooling of stretching sheet in the presence of viscous dissipation has been discussed in detail. We have considered multidimensional flows of viscous fluid over a flat plate in different flow situations such as flow over an impulsively started moving plate; flow over a stretching sheet, viscous flow in a channel of lower stretching wall, and the channel flow w...
Micromachines
No thermal process, even the biological systems, can escape from the long arms of the second law.... more No thermal process, even the biological systems, can escape from the long arms of the second law. All living things preserve entropy since they obtain energy from the nutrition they consume and gain order by producing disorder. The entropy generation in a biological and thermally isolated system is the main subject of current investigation. The aim is to examine the entropy generation during the convective transport of a ciliated nano-liquid in a micro-channel under the effect of a uniform magnetic field. Joint effects of electroosmosis and thermal radiation are also brought into consideration. To attain mathematical simplicity, the governing equations are transformed to wave frame where the inertial parts of the transport equations are dropped with the use of a long-wavelength approximation. This finally produces the governing equations in the form of ordinary differential equations which are solved numerically by a shooting technique. The analysis reports that the cilia motion con...
European Journal of Mechanics - B/Fluids
Abstract The existence of multiple solutions for a shrinking surface flow was first reported in t... more Abstract The existence of multiple solutions for a shrinking surface flow was first reported in the middle of the last decade. Since then, the exploration of second or even a third solution for the shrinking surface flows is a topic of great interest. Consequently, a huge volume of literature has been produced on this topic during the last one and half decade. According to such an available literature a sufficient amount of wall suction is mandatory for the existence of dual solutions. However, in the current study, it is shown that for an unsteady shrinking cylinder the existence of a second solution is not conditional to the provision of sufficient wall suction; rather it is possible in the case of no wall suction or even in the presence of sufficiently weak wall injection, also. Such a happening of the duality of solution for a shrinking surface flow in the absence of wall suction or even in the presence of wall injection is a novel finding. To the best of authors’ knowledge such kind of results have never been reported in the past. In this regard, the transverse surface curvature of the cylinder’s surface is observed to play an important role.
International Journal of Nonlinear Sciences and Numerical Simulation
The unsteady self-similar flow due to a permeable shrinking sheet is analyzed in this investigati... more The unsteady self-similar flow due to a permeable shrinking sheet is analyzed in this investigation. The current theoretical study is enacted in the light of correct self-similar formulation proposed by (Mehmood. A. Viscous flows: Stretching and shrinking of surfaces, Springer, 2017). For the existence of a meaningful solution the retarded boundary-layer developed due to retarded shrinking wall velocity \left( {{u_w}\left( x \right) = {{ \pm x} \over t}} \right) is supported by the sufficient mass suction introduced at the shrinking surface. Main theme of this paper is to utilize the correct mathematical formulation for the shrinking sheet flow in order to investigate the existence of dual solutions of the considered problem. By using suitable self-similar transformations, the nonlinear Navier–Stokes equations are converted to corresponding non-linear ordinary differential equations. A reliable numerical technique (shooting method) is applied to solve the resulting ODEs for the invo...
The European Physical Journal Plus
Irreversibility phenomenon is numerically investigated for mixed convection flow along a uniforml... more Irreversibility phenomenon is numerically investigated for mixed convection flow along a uniformly heated vertical wavy surface. Surface texture of the plate does not allow for a self-similar solution due to which the nature of the problem is non-similar. The numerical solution of the governing non-similar equations has been achieved by utilizing the implicit finite difference scheme commonly known as Keller-Box method and the outputs are shown through graphical pictures. The influence of various physical parameters of interest (mixed convection parameter, wavy amplitude, Prandtl number) on entropy generation and Bejan number has been discussed in detail. It is observed that entropy production enhances with an increment in mixed convection parameter.
International Communications in Heat and Mass Transfer
Abstract This communication aims to report heat transfer characteristics from a non-isothermal wa... more Abstract This communication aims to report heat transfer characteristics from a non-isothermal wavy disk rotating in a forced flow. The primary objective of this kind of studies is to seek a suitable mechanism for the quick removal of heat energy from a rotating disk surface. The achievement of an efficient mechanism which ensures a further higher rate of heat transfer is a fundamental goal in such studies. In this regard active and passive techniques are of fundamental importance whereby the current study utilizes a combination of both. There are three key elements, namely, the non-uniform disk temperature; surface roughness, and a radial free flow, which are responsible for the augmentation of the heat transfer. The analysis has been carried out for a variety of fluids depicting the increased rate of heat transfer due to a variation of these different elements. In doing so, the local and global heat transfer rates are manipulated in order to obtain a clear picture of the heat transfer process at a corrugated disk. The considered rough non-isothermal disk (with two sinusoids) rotating in the uniform stream of air (Pr = 0.71) leads to a significant (about 263%) enhancement in the overall heat transfer rate compared to that of a flat free rotating disk having surface temperature as quatratic function of the radial coordinate. Moreover, some threshold values (which correspond to seizing the heat transfer process) of the used power-index of the disk temperature (Tw − T∞ = c0rn∗) are also identified which are observed to vary slightly due to the surface irregularities and the relative motion of fluid and disk.
Journal of Molecular Liquids
Abstract The problem of natural convective heat transfer of water-based nanofluid along wavy cone... more Abstract The problem of natural convective heat transfer of water-based nanofluid along wavy cone surface is investigated numerically. Analysis is performed to study the heat transfer augmentation due to five types of nanoparticles, namely, alumina (Al2O3), copper (Cu), silver (Ag), copper oxide (CuO) and titania (TiO2). The flow has been assumed to be steady and fluid properties have been supposed constant except for the density depending upon temperature giving rise to the buoyancy force. Famous Tiwari and Das model of nanofluid has been utilized in this study. The effects of cone half angle γ and amplitude of the waviness α on the Nusselt number (Nu) and skin friction (Cf) are studied. A comparison is made with the case of pure fluid flow past wavy cone at different values of α. It has been observed that the TiO2-nanoparticle shown to have the maximum cooling performance and Cu-nanoparticle appeared to have maximum heating performance for this study. The results shown in this research arrange for a significant source of reference for taming the natural convection heat transfer enactment along wavy cone. Present results for selected variables are matched with the already published work for pure fluid and are shown to be in good agreement.
Thermal Science
The geometric characteristics of the heat transferring surface and the outer flow conditions have... more The geometric characteristics of the heat transferring surface and the outer flow conditions have a significant impact on heat transfer augmentation. Both, the surface roughness and the pressure gradient attribute to an enhanced heat transfer. These two effects are utilized in this study to enhance the convective heat transfer rate in a non-similar boundary-layer flow induced by the rotation of a sinusoidal-shaped disk in an external forced flow. The heat transfer coefficient is calculated numerically for the laminar boundary-layer flow with the help of the Keller-box method. The numerical solution of the governing system of equations is first validated by previous published (theoretical and experimental) results for a wavy rotating disk in the absence of an external flow field and also for a flat disk rotating in a forced flow. It is observed that the effect of surface waviness along with a relative fluid motion on heat transfer rate, shear stresses, and shaft torque is quite prono...
Alexandria Engineering Journal
Abstract The effects of non-uniform nanoparticle concentration within the boundary layer flow due... more Abstract The effects of non-uniform nanoparticle concentration within the boundary layer flow due to stretching surface are analyzed by employing a non-homogeneous model of nanofluid which passively controls the concentration of nanoparticles at the surface. All fluid properties are simulated as function of nanoparticle concentration. For such a consideration a self-similar solution exists and its worth mentioning influence is to control the boundary layer separation which is subsequently found to depend upon diffusion parameter and nanoparticle concentration. Furthermore the results show that the behavior of nanoparticles distribution across the boundary layer is highly dependent upon variation of different parameters. For instance, Shmidt number leads to decrease the concentration layer thickness and nanoparticle concentration at the sheet but hydrodynamic and thermal boundary layers remained unaffected. The heat transfer and drag coefficient enhancement are also directly affected by the non-uniform behavior of nanoparticle is also an important observation towards the understanding of role of nanoparticle in momentum and thermal transport.
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences
In this article, we examine the hydromagnetic stagnation point flow of a dusty fluid towards a ra... more In this article, we examine the hydromagnetic stagnation point flow of a dusty fluid towards a radially stretching surface in the presence of internal heat generation. By suitable similarity transformation, the governing coupled nonlinear partial differential equations with their corresponding boundary conditions are converted into a set of nonlinear coupled ordinary differential equations. The resulting equations are then solved numerically and the numerical solutions are then compared with existing literature. The effects of the parameters involving in the problem on flow and heat transfer characteristics are presented and discussed with the aid of graphs and tables.
Journal of Molecular Liquids
Abstract Effects of heat absorption and nanoparticle on natural convection heat transfer along ve... more Abstract Effects of heat absorption and nanoparticle on natural convection heat transfer along vertical wavy surface have been investigated. Transport equations have been solved numerically by accurate implicit finite difference scheme. The skin friction and Nusselt number are plotted against variation of several parameters for two types of nanoparticles namely, alumina (Al 2 O 3 ) and magnetite (Fe 3 O 4 ). The impact of nanoparticle concentration on flow and heat transfer process in the problem under investigation has been studied in detail. The results indicate that Al 2 O 3 -water nanofluid exhibits higher skin friction and heat transfer rate in comparison to Fe 3 O 4 water based nanofluid. The influence of heat absorption parameter is to increase the heat transfer rate and decrease the skin friction coefficient. For heat absorption case percent change in the skin friction and Nusselt number for two nanoparticles is shown in tabular form where comparison to the flat plate (pure fluid) and wavy surface (pure fluid) cases have also been made. The present results have been validated by producing the results available in literature and a very good agreement is observed.
Mathematical Engineering, 2017
Boundary layer flows due to different stretching surfaces have been considered in this chapter. T... more Boundary layer flows due to different stretching surfaces have been considered in this chapter. The designation of the wall velocities as accelerated or decelerated has also been highlighted as it plays an important role in the understanding of shrinking sheet flows, in particular. Equivalence of the two-dimensional and the disk cases has been proved and it is shown that the disk case can easily be recovered from the two-dimensional case.
Mathematical Engineering, 2017
Mathematical Engineering, 2017
In the previous part, it has already been seen that the concept of similarity is not particular t... more In the previous part, it has already been seen that the concept of similarity is not particular to the space variables only but is also equally applicable to the time variable. Ultimately, the happening of nonsimilar flows due to the time variable can never be ignored. In this chapter, the temporal nonsimilarity has been modeled and some particular time-dependent nonsimilar flows have also been investigated.
Mathematical Engineering, 2017
Mathematical Engineering, 2017
Zeitschrift für Naturforschung A, 2016
Heat transfer analysis has been carried out in the Magnetohydrodynamic (MHD) boundary layer forme... more Heat transfer analysis has been carried out in the Magnetohydrodynamic (MHD) boundary layer formed near the wavy rough plate moving in
Exact solution of Navier-Stokes equations is possible only for very simple flow situations such a... more Exact solution of Navier-Stokes equations is possible only for very simple flow situations such as unidirectional flows.Due to the nonlinear nature of these equations their analytic solutions are rare and the situation gets worse in the case of unsteady and multidimensional flow problems. In this thesis we report highly accurate and purely analytic solutions to some steady/unsteady multidimensional viscous flows over flat surface. Heat transfer analysis has also been carried out where the flat surface is considered as a stretching sheet.In each case the skin friction and the rate of heat transfer has been reported.The issue of cooling of stretching sheet in the presence of viscous dissipation has been discussed in detail. We have considered multidimensional flows of viscous fluid over a flat plate in different flow situations such as flow over an impulsively started moving plate; flow over a stretching sheet, viscous flow in a channel of lower stretching wall, and the channel flow w...
Micromachines
No thermal process, even the biological systems, can escape from the long arms of the second law.... more No thermal process, even the biological systems, can escape from the long arms of the second law. All living things preserve entropy since they obtain energy from the nutrition they consume and gain order by producing disorder. The entropy generation in a biological and thermally isolated system is the main subject of current investigation. The aim is to examine the entropy generation during the convective transport of a ciliated nano-liquid in a micro-channel under the effect of a uniform magnetic field. Joint effects of electroosmosis and thermal radiation are also brought into consideration. To attain mathematical simplicity, the governing equations are transformed to wave frame where the inertial parts of the transport equations are dropped with the use of a long-wavelength approximation. This finally produces the governing equations in the form of ordinary differential equations which are solved numerically by a shooting technique. The analysis reports that the cilia motion con...
European Journal of Mechanics - B/Fluids
Abstract The existence of multiple solutions for a shrinking surface flow was first reported in t... more Abstract The existence of multiple solutions for a shrinking surface flow was first reported in the middle of the last decade. Since then, the exploration of second or even a third solution for the shrinking surface flows is a topic of great interest. Consequently, a huge volume of literature has been produced on this topic during the last one and half decade. According to such an available literature a sufficient amount of wall suction is mandatory for the existence of dual solutions. However, in the current study, it is shown that for an unsteady shrinking cylinder the existence of a second solution is not conditional to the provision of sufficient wall suction; rather it is possible in the case of no wall suction or even in the presence of sufficiently weak wall injection, also. Such a happening of the duality of solution for a shrinking surface flow in the absence of wall suction or even in the presence of wall injection is a novel finding. To the best of authors’ knowledge such kind of results have never been reported in the past. In this regard, the transverse surface curvature of the cylinder’s surface is observed to play an important role.
International Journal of Nonlinear Sciences and Numerical Simulation
The unsteady self-similar flow due to a permeable shrinking sheet is analyzed in this investigati... more The unsteady self-similar flow due to a permeable shrinking sheet is analyzed in this investigation. The current theoretical study is enacted in the light of correct self-similar formulation proposed by (Mehmood. A. Viscous flows: Stretching and shrinking of surfaces, Springer, 2017). For the existence of a meaningful solution the retarded boundary-layer developed due to retarded shrinking wall velocity \left( {{u_w}\left( x \right) = {{ \pm x} \over t}} \right) is supported by the sufficient mass suction introduced at the shrinking surface. Main theme of this paper is to utilize the correct mathematical formulation for the shrinking sheet flow in order to investigate the existence of dual solutions of the considered problem. By using suitable self-similar transformations, the nonlinear Navier–Stokes equations are converted to corresponding non-linear ordinary differential equations. A reliable numerical technique (shooting method) is applied to solve the resulting ODEs for the invo...
The European Physical Journal Plus
Irreversibility phenomenon is numerically investigated for mixed convection flow along a uniforml... more Irreversibility phenomenon is numerically investigated for mixed convection flow along a uniformly heated vertical wavy surface. Surface texture of the plate does not allow for a self-similar solution due to which the nature of the problem is non-similar. The numerical solution of the governing non-similar equations has been achieved by utilizing the implicit finite difference scheme commonly known as Keller-Box method and the outputs are shown through graphical pictures. The influence of various physical parameters of interest (mixed convection parameter, wavy amplitude, Prandtl number) on entropy generation and Bejan number has been discussed in detail. It is observed that entropy production enhances with an increment in mixed convection parameter.
International Communications in Heat and Mass Transfer
Abstract This communication aims to report heat transfer characteristics from a non-isothermal wa... more Abstract This communication aims to report heat transfer characteristics from a non-isothermal wavy disk rotating in a forced flow. The primary objective of this kind of studies is to seek a suitable mechanism for the quick removal of heat energy from a rotating disk surface. The achievement of an efficient mechanism which ensures a further higher rate of heat transfer is a fundamental goal in such studies. In this regard active and passive techniques are of fundamental importance whereby the current study utilizes a combination of both. There are three key elements, namely, the non-uniform disk temperature; surface roughness, and a radial free flow, which are responsible for the augmentation of the heat transfer. The analysis has been carried out for a variety of fluids depicting the increased rate of heat transfer due to a variation of these different elements. In doing so, the local and global heat transfer rates are manipulated in order to obtain a clear picture of the heat transfer process at a corrugated disk. The considered rough non-isothermal disk (with two sinusoids) rotating in the uniform stream of air (Pr = 0.71) leads to a significant (about 263%) enhancement in the overall heat transfer rate compared to that of a flat free rotating disk having surface temperature as quatratic function of the radial coordinate. Moreover, some threshold values (which correspond to seizing the heat transfer process) of the used power-index of the disk temperature (Tw − T∞ = c0rn∗) are also identified which are observed to vary slightly due to the surface irregularities and the relative motion of fluid and disk.
Journal of Molecular Liquids
Abstract The problem of natural convective heat transfer of water-based nanofluid along wavy cone... more Abstract The problem of natural convective heat transfer of water-based nanofluid along wavy cone surface is investigated numerically. Analysis is performed to study the heat transfer augmentation due to five types of nanoparticles, namely, alumina (Al2O3), copper (Cu), silver (Ag), copper oxide (CuO) and titania (TiO2). The flow has been assumed to be steady and fluid properties have been supposed constant except for the density depending upon temperature giving rise to the buoyancy force. Famous Tiwari and Das model of nanofluid has been utilized in this study. The effects of cone half angle γ and amplitude of the waviness α on the Nusselt number (Nu) and skin friction (Cf) are studied. A comparison is made with the case of pure fluid flow past wavy cone at different values of α. It has been observed that the TiO2-nanoparticle shown to have the maximum cooling performance and Cu-nanoparticle appeared to have maximum heating performance for this study. The results shown in this research arrange for a significant source of reference for taming the natural convection heat transfer enactment along wavy cone. Present results for selected variables are matched with the already published work for pure fluid and are shown to be in good agreement.
Thermal Science
The geometric characteristics of the heat transferring surface and the outer flow conditions have... more The geometric characteristics of the heat transferring surface and the outer flow conditions have a significant impact on heat transfer augmentation. Both, the surface roughness and the pressure gradient attribute to an enhanced heat transfer. These two effects are utilized in this study to enhance the convective heat transfer rate in a non-similar boundary-layer flow induced by the rotation of a sinusoidal-shaped disk in an external forced flow. The heat transfer coefficient is calculated numerically for the laminar boundary-layer flow with the help of the Keller-box method. The numerical solution of the governing system of equations is first validated by previous published (theoretical and experimental) results for a wavy rotating disk in the absence of an external flow field and also for a flat disk rotating in a forced flow. It is observed that the effect of surface waviness along with a relative fluid motion on heat transfer rate, shear stresses, and shaft torque is quite prono...
Alexandria Engineering Journal
Abstract The effects of non-uniform nanoparticle concentration within the boundary layer flow due... more Abstract The effects of non-uniform nanoparticle concentration within the boundary layer flow due to stretching surface are analyzed by employing a non-homogeneous model of nanofluid which passively controls the concentration of nanoparticles at the surface. All fluid properties are simulated as function of nanoparticle concentration. For such a consideration a self-similar solution exists and its worth mentioning influence is to control the boundary layer separation which is subsequently found to depend upon diffusion parameter and nanoparticle concentration. Furthermore the results show that the behavior of nanoparticles distribution across the boundary layer is highly dependent upon variation of different parameters. For instance, Shmidt number leads to decrease the concentration layer thickness and nanoparticle concentration at the sheet but hydrodynamic and thermal boundary layers remained unaffected. The heat transfer and drag coefficient enhancement are also directly affected by the non-uniform behavior of nanoparticle is also an important observation towards the understanding of role of nanoparticle in momentum and thermal transport.
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences
In this article, we examine the hydromagnetic stagnation point flow of a dusty fluid towards a ra... more In this article, we examine the hydromagnetic stagnation point flow of a dusty fluid towards a radially stretching surface in the presence of internal heat generation. By suitable similarity transformation, the governing coupled nonlinear partial differential equations with their corresponding boundary conditions are converted into a set of nonlinear coupled ordinary differential equations. The resulting equations are then solved numerically and the numerical solutions are then compared with existing literature. The effects of the parameters involving in the problem on flow and heat transfer characteristics are presented and discussed with the aid of graphs and tables.
Journal of Molecular Liquids
Abstract Effects of heat absorption and nanoparticle on natural convection heat transfer along ve... more Abstract Effects of heat absorption and nanoparticle on natural convection heat transfer along vertical wavy surface have been investigated. Transport equations have been solved numerically by accurate implicit finite difference scheme. The skin friction and Nusselt number are plotted against variation of several parameters for two types of nanoparticles namely, alumina (Al 2 O 3 ) and magnetite (Fe 3 O 4 ). The impact of nanoparticle concentration on flow and heat transfer process in the problem under investigation has been studied in detail. The results indicate that Al 2 O 3 -water nanofluid exhibits higher skin friction and heat transfer rate in comparison to Fe 3 O 4 water based nanofluid. The influence of heat absorption parameter is to increase the heat transfer rate and decrease the skin friction coefficient. For heat absorption case percent change in the skin friction and Nusselt number for two nanoparticles is shown in tabular form where comparison to the flat plate (pure fluid) and wavy surface (pure fluid) cases have also been made. The present results have been validated by producing the results available in literature and a very good agreement is observed.
Mathematical Engineering, 2017
Boundary layer flows due to different stretching surfaces have been considered in this chapter. T... more Boundary layer flows due to different stretching surfaces have been considered in this chapter. The designation of the wall velocities as accelerated or decelerated has also been highlighted as it plays an important role in the understanding of shrinking sheet flows, in particular. Equivalence of the two-dimensional and the disk cases has been proved and it is shown that the disk case can easily be recovered from the two-dimensional case.
Mathematical Engineering, 2017
Mathematical Engineering, 2017
In the previous part, it has already been seen that the concept of similarity is not particular t... more In the previous part, it has already been seen that the concept of similarity is not particular to the space variables only but is also equally applicable to the time variable. Ultimately, the happening of nonsimilar flows due to the time variable can never be ignored. In this chapter, the temporal nonsimilarity has been modeled and some particular time-dependent nonsimilar flows have also been investigated.
Mathematical Engineering, 2017
Mathematical Engineering, 2017
Zeitschrift für Naturforschung A, 2016
Heat transfer analysis has been carried out in the Magnetohydrodynamic (MHD) boundary layer forme... more Heat transfer analysis has been carried out in the Magnetohydrodynamic (MHD) boundary layer formed near the wavy rough plate moving in