Temperature profiles due to continuous hot water injection into homogeneous fluid-saturated porous media through a line source


  • Abraham Medina ESIME Azcapotzalco, IPN
  • Francisco J. Higuera ETSI Aeronáutica y del Espacio, UPM.
  • Máximo Pliego Instituto Tecnológico de Querétaro
  • Gustavo Gomez ESIME Zacatenco, IPN.




Heat flow in porous media, Flows through porous media, Analytical and numerical techniques of heat transfer


We report a theoretical study to determine the temperature profiles due to the continuous and
constant injection of hot water through a line source, into a homogeneous fluid-saturated porous medium which has had initially a constant temperature T∞. In our treatment we have taken in to account the simultaneous injection of constant fluxes of volume fluid, q, and of heat, φ. By using a far-field description, we found similarity solutions for the dimensionless temperature depending on the Peclet number, P e, as the single parameter of the problem.


H. A. Lauwerier, Appl. Sci. Res. 5 (1955) 145.

A. G. Spillette, Jour. Can. Petr. Tech. 4 (1965) 213.

K. Yu, G. Zhao, Modeling of heat transfer coupled

with fluid flow for temperature transient analysis during

SAGD process, SPE Latin America and Caribbean Heavy

and Extra Heavy Oil Conference, SPE-181208-MS 2016.

M. I. Miah, M. A. Elhaj, S. Ahmed, M. E. Hossain, Fuel

(2018) 423. And references therein.

N. Chevarunotai, A. R. Hasan, C. S. Kabir, R. Islam,

Jour. Petrol. Explor. Prod. Techol. 8 (2018) 799.

Z. Wu, H. Liu, Jour. Petrol. Explor. Prod. Techol. 9

(2019) 1547.

G. Bodvarsson, Geothermics 1 (1972) 63.

A. W. Woods, S. D. Fitzgerald, Jour. Fluid Mech. 343

(1997) 303.

A. W.Woods, Annu. Rev. Fluid Mech. 31 (1999) 171.

A. W. Woods, Flow in Porous Rocks: Energy

and Environmental Applications (Cambridge University

Press, Cambrige 2015).

S. Ganguly, M. S. Mohan Kumar, Hydrogeol. Jour. 22

(2014) 351.

P. Dudfield, A. W. Woods, Jour. Fluid Mech. 707 (2012)

V. N. Kurdyumov, A. Linan, Jour. Fluid Mech. 427 (2001) 389.

S. S. Gopalakrishnan, Jour. Fluid Mech. 892 (2020) A13.

T. Menand, A. Raw, A. W. Woods, Geophys. Res. Lett.

(2003) 1291.

D. A. Nield, A. Bejan, Convection in porous media

(Springer, New York 2013).

R. A. Wooding, Jour. Fluid Mech. 15 (1963) 527.

O. M. Phillips, Geological fluid dynamics: Sub-surface

flow and reactions (Cambridge: Cambridge University

Press, Cambridge 2009).

X. Liu, Z. Xie, S. Dong, Int. Jour. Heat Mass Transf.

(2020) 119355.

Z. Abdulagatova, I.M. Abdulagatov, V.N. Emirov, Int.

Jour. Rock Mech. Min. Sci. 46 (2009) 1055.

M. Labus, K. Labus, Jour. Therm. Anal. Calorim. 132

(2018) 1669.

S. Gehlin, Borehole thermal energy storage, in Advances

in Ground-Source Heat Pump Systems, S. Rees (Ed.)

–327 (Woodhead Publishing, Duxford, UK, 2016).





How to Cite

A. Medina, F. J. Higuera, M. Pliego, and G. Gomez, “Temperature profiles due to continuous hot water injection into homogeneous fluid-saturated porous media through a line source”, Rev. Mex. Fís., vol. 67, no. 3 May-Jun, pp. 365–368, May 2021.