Impact of heat generation/absorption on transient natural convective flow in an annulus filled with porous material subject to isothermal and adiabatic boundaries

  • Yusuf S. TaiwoEmail author
  • Gambo Dauda
Original Paper


This article deliberated the effects of heat generation/absorption on transient natural convective flow in infinite vertical concentric cylinder filled with a porous material. The natural convective flow is as a result of constant heating at the inner cylinder while the inner surface of the outer cylinder is thermally insulated. A combination of Laplace transform technique and Riemann-sum approximation approach has been used to transform and invert the governing equation from the Laplace domain to the time domain respectively. The numerical values obtained from the Riemann-sum approximation excellently agree with the steady state solution at large time. The obtained results are represented graphically and the effects of the governing parameters on the velocity field, temperature field, mass flow rate, heat transfer as well as the skin-friction on both surfaces of the annulus are studied in detail. In the course of numerical computations, it is found that the fluid velocity and temperature both increases with time, while the fluid velocity and skin friction on both walls are seen to be proportional to Darcy number but inversely proportional to the viscosity ratio. Furthermore, it is found that the mass flow rate can be controlled by increasing/decreasing the heat generation/absorption parameter.


Transient Isothermal Adiabatic Heat generation/absorption Darcy number 

List of symbols


Dimensional time (s)


Dimensional radial coordinate (m)


Axial velocity (m/s)


Dimensionless axial velocity


Dimensionless radial coordinate


Ambient temperature (K)


Temperature of the hot cylinder (K)


Dimensionless temperature


Radius of the inner cylinder (m)


Radius of the outer cylinder (m)


Gravitational acceleration (m/s2)


Dimensionless mass flow rate


Dimensionless nusselt number


Dimensionless heat generating/absorbing parameter


Dimensional heat generating/absorbing parameter (K)


Prandtl number (μcp/k)


Specific heat at constant pressure (kJ/kgK)


Dimensionless time


Permeability of the Porous medium (m2)


Thermal conductivity of the fluid (W/mK)


Darcy number

Greek letters


Fluid kinematic viscosity (m2/s)


Fluid kinematic effective viscosity (m2/s)


Skin friction


Density (Pa s)


Laplace parameter


Ratio of radii (r2/r1)


Viscosity ratio


Coefficient of thermal expansion

Mathematics Subject Classification

76R10 76S05 76D05 75Q30 33C10 80A20 30E25 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsAhmadu Bello UniversityZariaNigeria

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