Prof. Basant K. Jha
Ahmadu Bello University, Nigeria, Mathematics, Faculty Member
The transient flow formation in a horizontal porous channel assuming a ramped pressure gradient is presented. The equation governing the flow is modeled into a partial differential equation (PDE) which is solved by employing the Laplace... more
The transient flow formation in a horizontal porous channel assuming a ramped pressure gradient is presented. The equation governing the flow is modeled into a partial differential equation (PDE) which is solved by employing the Laplace transformation technique to transform the PDE to an ordinary differential equation (ODE). The obtained ODE is solved by employing the method of undetermined coefficients to obtain the velocity profile in the Laplace domain. The Riemann sum approximation technique is then adopted to change the obtained solution from the Laplace domain into the time domain. For accuracy checks, the numerical results of the obtained equation are reckoned with previously published work, and an excellent agreement is found. For a clearer understanding of the impact of various flow parameters entering the solutions obtained, graphical and tabular representations are offered using MATLAB software. We noticed that the velocity is slower with ramped pressure gradient compared to a constant pressure gradient. This is because the motion of the fluid occurs gradually with ramped pressure gradient.
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A numerical as well as analytical investigation is performed to study time dependent/steady state mixed convection flow in a vertical channel in presence of thermophoresis having convective boundary conditions. The main objective of this... more
A numerical as well as analytical investigation is performed to study time dependent/steady state mixed convection flow in a vertical channel in presence of thermophoresis having convective boundary conditions. The main objective of this paper is to present exact solutions for steady state mathematical model under relevant boundary conditions and numerical solutions for time dependent situation under relevant initial and boundary conditions. The impact of various controlling parameters such as dimensionless time $$t$$ t , Schmidt number $$Sc$$ Sc , Biot numbers $$Bi_{1}$$ B i 1 and $$Bi_{2}$$ B i 2 , buoyancy ratio $$b$$ b and thermophoretic coefficient $$k$$ k have on the flow patterns is discussed. Graphical results show that the effect of increasing two or more of the parameters simultaneously with high mixed convection parameter changes the flow from bi-directional to unidirectional. Also, the occurrence of a flow reversal depends on buoyancy and dimensional time. Furthermore, t...
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In this paper, we investigate steady free convective Couette flow in a vertical channel with nonlinear thermal radiation, dynamic viscosity and dynamic thermal conductivity effects. The investigation is motivated by the studies of some... more
In this paper, we investigate steady free convective Couette flow in a vertical channel with nonlinear thermal radiation, dynamic viscosity and dynamic thermal conductivity effects. The investigation is motivated by the studies of some researchers which assumed linear thermal radiation and constant fluid properties. However, this is uncalled for; as these assumptions do not reflect true behavior of the flow. For instance; increase in temperature affects fluid viscosity, thermal conductivity thereby changing the transport phenomenon. Here; the investigation considers both the fluid viscosity and thermal conductivity to be dependent on temperature with the thermal radiation adopting nonlinear form. Due to this reasons, the associated flow equations are highly nonlinear and exhibit no analytical solution and therefore require the use of Adomian decomposition method (ADM) of solution. The attained ADM solution is then coded into computer algebra package of mathematica where results unde...
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An unsteady flow formation in Couette motion of an electrically conducting fluid subject to transverse magnetic field has been analyzed in the presence of suction/injection through the porous plates when one of the porous plates is in... more
An unsteady flow formation in Couette motion of an electrically conducting fluid subject to transverse magnetic field has been analyzed in the presence of suction/injection through the porous plates when one of the porous plates is in ramped motion. It is assumed that the porous plates are uniformly permeable and the fluid is entering the flow region through one of the porous plates at same rate as it is leaving through the other porous plate. The resulting boundary value problem has been solved exactly under the assumption of a negligible induced magnetic field, external electric field and pressure gradient. Unified closed form expressions for the velocity field and skin-friction corresponding to the case of a magnetic field fixed relative to the fluid or to the moving porous plate have been presented. In order to highlight the impact of the ramp motion of the porous plate on the fluid flow, it has also been compared with Couette flow between porous plates when one of the porous pl...
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This study presents similarity solution for boundary layer flow near a vertical porous plate with combined effects of nonlinear density variation with temperature and nonlinear thermal radiation. To accurately predict the flow phenomenon... more
This study presents similarity solution for boundary layer flow near a vertical porous plate with combined effects of nonlinear density variation with temperature and nonlinear thermal radiation. To accurately predict the flow phenomenon near the porous plate, the convective boundary condition is considered at the plate surface. The two-dimensional partial differential equations are transformed to ordinary differential equations through the similarity transformation. The resulting ordinary differential equations are solved numerically in Maple software using the Runge–Kutta–Ferhlberg fourth-fifth order (RKF45) algorithm. The influence of the inherit parameters like the nonlinear thermal radiation parameter, suction/injection parameter, nonlinear Boussinesq approximation parameters, local convective heat transfer parameter, local Grashof number, and Prandtl number governing the fluid behaviour is discussed. We found that the rate of heat transfer improves with the injection and nonli...
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The sole aim of this article is to examine the relative contribution of suction/injection parameter on Taylor–Dean flow in a composite annular gap partially filled with porous material. In the present setup, the Newtonian fluid flow is... more
The sole aim of this article is to examine the relative contribution of suction/injection parameter on Taylor–Dean flow in a composite annular gap partially filled with porous material. In the present setup, the Newtonian fluid flow is induced by the circumferential motion of both cylinders and pressure gradient imposed in the Azimuthal direction. The mathematical model governing the flow is rendered dimensionless using appropriate dimensionless quantities transformed using the Laplace transform technique. Using suitable Ansatz, the equation is reduced to the Bessel differential equations and solved. The solution of converted to the time domain using a well-known numerical scheme known as the Riemann-sum approximation. The variation of the Newtonian fluid for different flow parameters is presented graphically. The solution method is validated by obtaining the steady-state solution and also using the implicit finite different approach (IFD); comparison of the methods is depicted in t...
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An analysis into the transient natural convective flow of a nanofluid in a vertical tube is made. The governing equations of momentum, heat transfer and nanoparticle volume fraction are deduced, and the influence of the thermophoresis... more
An analysis into the transient natural convective flow of a nanofluid in a vertical tube is made. The governing equations of momentum, heat transfer and nanoparticle volume fraction are deduced, and the influence of the thermophoresis parameter and Brownian motion is incorporated. By direct integration and variation of the parameter, analytical solutions are obtained for flow formation and heat/mass transfer at steady-state. On the other hand, due to the complexity of same problem at transient state, a numerical solution is used to solve the discretized equations of motion using the implicit finite difference technique. The influence of the thermophoresis parameter and Brownian motion is noted and well discussed. For accuracy check, a numerical comparison is made between the steady state and transient state solution at large time; this comparison gives an excellent agreement. The role of various principal parameters on velocity profile, temperature, concentration of nanoparticles, S...
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This paper examines the role of magnetic field on fully developed natural convection flow in an annulus due to symmetric of surfaces. The transport equations concerned with the model under consideration are rendered non-dimensional and... more
This paper examines the role of magnetic field on fully developed natural convection flow in an annulus due to symmetric of surfaces. The transport equations concerned with the model under consideration are rendered non-dimensional and transformed into the ordinary differential equation using Laplace transform technique. The solution obtained is then transformed to time domain using the Riemann-sum approximation approach. The governing equations are also solved using implicit finite difference method so as to establish the accuracy of the Riemann-sum approximation approach at transient as well as at steady state solution. The solutions obtained are graphically represented and the effects of pertinent parameters on the flow formation are investigated in detail. The Hartmann number (M), is seen to have a retarding effect on the velocity, skin-frictions and the mass flow rate. Also, skin-friction at both surfaces and the mass flow rate within the annulus are found to be directly propor...
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Purpose The purpose of this paper is to present a semi-analytical solution for time-dependent natural convection flow with heat generation/absorption in an annulus partially filled with porous material. Design/methodology/approach The... more
Purpose The purpose of this paper is to present a semi-analytical solution for time-dependent natural convection flow with heat generation/absorption in an annulus partially filled with porous material. Design/methodology/approach The governing partial differential equations are transformed into the ordinary differential equations using the Laplace transform technique. The exact solution obtained is inverted from the Laplace domain to time domain using the Riemann-sum approximation approach. Justification of the Riemann-sum approximation approach is achieved by comparing the values obtained with those of the implicit finite difference method at both the transient state and the steady state at large time. Findings If is found that the peak axial velocity always occur in the clear fluid region. In addition, there is an indication that heat generating fluid is desirable for optimum mass flux in the annular gap most importantly when the convection current is enhanced by constant heat fl...
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This study examines the impact of induced magnetic field and Hall current on steady fully developed hydromagnetic natural convection flow in a micro-channel under the action of an inclined magnetic field. The mathematical model... more
This study examines the impact of induced magnetic field and Hall current on steady fully developed hydromagnetic natural convection flow in a micro-channel under the action of an inclined magnetic field. The mathematical model responsible for the present physical situation is presented in a dimensionless form under relevant boundary conditions. The governing coupled equations are solved exactly. A parametric study of some physical parameters is conducted and a representative set of numerical results for the velocity field, the induced magnetic field, induced current density, volume flow rate, and skin friction on the micro-channel surfaces are illustrated graphically. It is observed that magnetic field inclination plays an important role in flow formation inside the micro-channel. Numerical computation reveals that the increase in inclination angle reduces the hydromagnetic drag leading to enhancement in primary fluid velocity, while the impact is just converse on the secondary flu...
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In this paper, we have obtained an analytical solution to the problem of unsteady free convection and mass transfer flow of an incompressible fluid through a vertical channel in the presence of Dufour effect (or diffusion thermo). The... more
In this paper, we have obtained an analytical solution to the problem of unsteady free convection and mass transfer flow of an incompressible fluid through a vertical channel in the presence of Dufour effect (or diffusion thermo). The bounding plates are assumed to have ramped wall temperature as well as specie concentration. The mathematical model responsible for the physical situation is presented in dimensionless form and solved analytically using the powerful Laplace Transform Technique (LTT) under relevant initial and boundary conditions. In order to cross check the accuracy of the analytical results, numerical solutions are obtained using PDEPE solver in MATLAB. The expressions for temperature, concentration, and velocity are obtained. The effects of Dufour parameter, Prandtl number (Pr), Schmidt number (Sc), and dimensionless time are described during the course of these discussions. The temperature, concentration, and velocity profiles are graphically presented for some real...
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Purpose The purpose of this paper is to further extend the work of Weng and Chen (2009) by considering heat generation/absorption nature of fluid. Design/methodology/approach Exact solution of momentum equation is derived separately in... more
Purpose The purpose of this paper is to further extend the work of Weng and Chen (2009) by considering heat generation/absorption nature of fluid. Design/methodology/approach Exact solution of momentum equation is derived separately in terms of Bessel’s function of first and second kind for heat-generating fluid and modified Bessel’s function of first and second kind for heat absorbing fluid. Findings During the course of numerical computations, it is found that skin friction and rate of heat transfer at outer surface of inner cylinder and inner surface of outer cylinder increases with the increase in heat generation parameter while the reverse trend is found in the case of heat absorption parameter. Originality/value In view of the amount of works done on natural convection with internal heat generation/absorption, it becomes interesting to investigate the effect of this important activity on natural convection flow in a vertical annular micro-channel. The purpose of this paper is to further extend the work of Weng and Chen (2009) by considering heat generation/absorption nature of fluid.
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In this research paper, fully developed natural convection flow in a vertical parallel plate's micro-channel in the presence of viscous dissipation is theoretically examined by using a perturbation series method. The effects of... more
In this research paper, fully developed natural convection flow in a vertical parallel plate's micro-channel in the presence of viscous dissipation is theoretically examined by using a perturbation series method. The effects of velocity slip and temperature jump are taken to consideration. Due to the presence of viscous dissipation, the momentum and energy equations are coupled system of ordinary differential equations. The influences of Knudsen number, fluid wall interaction parameter, and viscous dissipation on the flow formation and heat transfer aspects are demonstrated through graphs and tables. This result indicates that increasing the value of rarefaction parameter decreases the effect of viscous dissipation on the Nusselt number. Furthermore, it is found that the effects of rarefaction parameter as well as buoyancy parameter on temperature and velocity are significantly pronounced in the case of symmetric heating
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The problem of fully-developed transient mixed convection flow of viscous reactive fluid in a vertical tube is analysed both analytically and numerically. The study reports the effect of several operating parameters on the flow... more
The problem of fully-developed transient mixed convection flow of viscous reactive fluid in a vertical tube is analysed both analytically and numerically. The study reports the effect of several operating parameters on the flow hydrodynamics and thermal characteristics. The solutions for transient velocity and temperature fields are obtained by implicit finite difference method. To check the accuracy of the numerical solution steady-state solutions for temperature and velocity field are obtained by using perturbation series method. Skin-friction and Nusselt number at the surface of tube are determined. A selected set of graphical results illustrating the effects of the various parameters involved in the problem including mixed convection parameter, pressure gradient, reactant consumption parameter on the velocity and temperature profiles as well as flow reversal situations and Nusselt numbers are presented and discussed.
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A transient flow formation of an incompressible fluid through a horizontal porous channel assuming a ramped pressure gradient is considered with the velocity slip boundary conditions. The flow is a laminar flow caused by ramped pressure... more
A transient flow formation of an incompressible fluid through a horizontal porous channel assuming a ramped pressure gradient is considered with the velocity slip boundary conditions. The flow is a laminar flow caused by ramped pressure gradient along the flow direction. The equation governing the flow is modeled, and solved by the Laplace transformation technique to obtain a semi-analytical solution under slip boundary conditions. It was noted that the flow velocity increases as the slip parameter is increased.
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This article investigates the impact of electric body force on transient natural convection flow in a vertical microannulus with velocity slip and temperature jump. The governing momentum, energy, and Poisson-Boltzmann equations are... more
This article investigates the impact of electric body force on transient natural convection flow in a vertical microannulus with velocity slip and temperature jump. The governing momentum, energy, and Poisson-Boltzmann equations are presented for the current physical situation. The Laplace transform technique is employed to transform the governing partial differential equations into ordinary differential equations and then solved exactly in the Laplace domain using the method of undetermined coefficients. Line graphs and tables are simulated to properly explain the effect of various pertinent parameters entering flow formation and temperature distribution. It is found that the time taken to attain a steady-state solution significantly depends on slip-length and Electric Double Layer (EDL) length. In addition, the role of increasing the annular gap is to minimize the skin friction, electric field strength, and volumetric flow rate.
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Abstract Our study probes the impact of an exponentially decaying/growing time-dependent pressure gradient on unsteady Dean flow in a curved concentric cylinder. A two-step method of solution has been employed in the treatment of the... more
Abstract Our study probes the impact of an exponentially decaying/growing time-dependent pressure gradient on unsteady Dean flow in a curved concentric cylinder. A two-step method of solution has been employed in the treatment of the governing momentum equation. Accordingly, the exact solution of the time-dependent partial differential equation is derived in terms of the Laplace variable. The Laplace domain solution is then transformed to the time domain using a numerical inversing scheme known as Riemann-sum approximation. The effect of the various dimensionless parameters involved in the problem on the Dean velocity, skin drags and Dean vortex are illustrated graphically. It was established that maximum Dean velocity is due to an exponentially growing time-dependent pressure gradient. However, the instability of the Dean vortex is rendered less effective by reducing time and applying an exponentially decaying time-dependent pressure gradient.
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This research work inspects mass transport phenomenon of Saffman’s dusty fluid model for transient magnetohydrodynamics fluid flow of a binary mixture passing through an annular duct. Particularly, effort has been devoted to theoretically... more
This research work inspects mass transport phenomenon of Saffman’s dusty fluid model for transient magnetohydrodynamics fluid flow of a binary mixture passing through an annular duct. Particularly, effort has been devoted to theoretically explore the role of velocity of applied magnetic field. Here, our treatment of the governing momentum equations accountable for the flow is done using the classical Laplace transform technique and Riemann-Sum Approximation. The effects of the physical parameters such as time, relaxation time parameter, radii ratio, Hartmann number, variable mass parameter and velocity of applied magnetic field on the fluid phase velocity, dust phase velocity and skin friction have been illustrated pictorially. It is concluded that contrary to the known classical effect of boosting Hartmann number on velocity, both components of flow (fluid and dust phase) and skin friction are seen to be heightened with an overwhelming presence of velocity of applied magnetic field...
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An incompressible and viscous fluid flow past a constant moving plate with convective boundary condition considering the variable viscosity effect is fully presented. The solution to the governing equation is obtained by Runge Kutta... more
An incompressible and viscous fluid flow past a constant moving plate with convective boundary condition considering the variable viscosity effect is fully presented. The solution to the governing equation is obtained by Runge Kutta Ferberg four-fifth order (RKF45) method in Maple software. Four fluids namely; mercury, air, sulphur oxide and water whose respective Prandtl numbers are 0.044, 0.72, 2 and 7 are considered during the computation. The effect of the controlling parameters such Biot number ( $$Bi$$ ), Prandtl number (Pr), reference temperature ( $$\theta_{r}$$ ) and exponential constant (N) on the temperature distribution, velocity profile, Nusselt number and the Skin friction is presented using tables and line graphs. It is found that the temperature distribution is inversely proportional to Biot number ( $$Bi$$ ) augment whereas the velocity profile decreases as the reference temperature ( $$\theta_{r}$$ ) propagates. The results also revealed that the thickness of the thermal boundary layer decrease as Prandtl number (Pr) increases. For liquids fluid, the skin friction increases with the exponential constant (N) propagation whereas decreases for gases fluid. The effect of the Biot number on the skin friction exhibits opposite behaviour with that of the exponential constant. Regarding the Nusselt number, the exponential constant augment increases the Nusselt number for both gases and liquids fluid.