Transient Investigation of Stack-driven Air Flow Through Multiple Upper-vents in the Presence of Constant Indirect Flow Velocity in Rectangular Ventilated Building
Engineering Mathematics
Volume 4, Issue 2, December 2020, Pages: 14-30
Received: Sep. 25, 2019; Accepted: Oct. 21, 2019; Published: Sep. 3, 2020
Views 94      Downloads 39
Muhammad Auwal Lawan,, Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria
Sunusi Aminu Nata’ala, Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria
Article Tools
Follow on us
The paper investigates the time independent effect of Stack- driven airflow in cross- ventilated building with multiple opening in the presence of constant indirect flow velocity. The dimensionless model of momentum and energy equations are analyzed, using second order linear differential equation to develop the explicit expression for velocity, temperature profiles together with volumetric and mass- transfer by means of separation of variable method. Some numerical examples are presented graphically in order to illustrate the effects of physical parameters involved in the study. From the course of investigation, it was observed air temperature and velocity increase with the increase in both parameters (θ0), (Pr) and (Gr). Respectively. In addition, comparison with previously published work by A. L. Muhammad et. al (2016) was performed. In which, the study concluded that, the results for present work is more effective and efficient than the previous work in term of ventilation process. Finally, from the course of investigation, it was observed air temperature and velocity increase with the increase in both parameters (θ0), (Pr) and (Gr) respectively.
Transient Effect, Indirect Flow Velocity, Multiple Upper Vents, Ventilated Building
To cite this article
Muhammad Auwal Lawan,, Sunusi Aminu Nata’ala, Transient Investigation of Stack-driven Air Flow Through Multiple Upper-vents in the Presence of Constant Indirect Flow Velocity in Rectangular Ventilated Building, Engineering Mathematics. Vol. 4, No. 2, 2020, pp. 14-30. doi: 10.11648/j.engmath.20200402.11
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
C. Allocca, Q. Chen and L. R. Glicksman, Design analysis of single-sided natural ventilation. Building Technology, Energy and Buildings 35 (8) (2003) 785-795.
H. B. Awbi and M. M. Nemri, Scale effect in room air-flow studies, Energy and Buildings, 14 (3) (1990) 207-210.
H. B. Awbi, Air movement on naturally-ventilated buildings, Renewable Energy 8 (1) (1996) 241-247.
C. L. Chow, Air flow rate across vertical opening induced by room heat sources, International Journal on Architectural Science 8 (1) (2010) 11-16.
A. L. Muhammad and A. B. Baffa and M. Z. Ringim, Investigation of stack- driven airflow through rectangular cross- ventilated building with two openings using analytic technique, International Journal of Computer Application (IJCA) 141 (6) (2016) 5-11.
A. L. Muhammad, D. A. Gano, M. Z. Ringim, S. A. Ibrahim and A. B. Baffa, Theoretical study on steady airflow through multiple upper openings inside a rectangular building in the presence of indirect flow, Communication on applied Electronics (CAE) 7 (14) (2018) 17-25.
S. Duan and L. Yuguo, An example of solution multiplicity in a building with bi-directional flow openings, Indoor Built Environment 14 (5) (2005) 359–69.
Y. Fan, CFD modeling of the air and contaminant distribution in rooms, Energy and Building 23 (1) (1995) 33-39.
G. Gan, Evaluation of room air distribution systems using CFD, Energy and Building 23 (2) (1995) 83-93.
G. Gan, Simulation of buoyancy-driven natural ventilation of buildings-impact of computational domain, Energy and building 42 (2010) 1290-1300.
S. Murakami and S. Kato, Numerical and experimental study on room air flow- 3-D predictions using the K-ε turbulence model, Building and Environment 24 (1) (1989) 85-97.
M. W. Liddament, A review of building air flow simulation. Tech. Note AIVC 33. Air infiltration and ventilation centre, Coventry UK (1991).
C. Gladstone, A. Woods, J. Philips and C. Caulfied, Experimental study of mixing in a closed room by doorway exchange flow, Proc, ROOMVENT’98. Stockholm, Sweden (1998).
P. F. Linden, G. F. Lane- Serff and D. A. Smeed, Emptying filling spaces: the fluid mechanics of natural ventilation, Journal of Fluid Mechanics 212 (1990) 309-335.
A. L. Muhammad, A. B. Baffa and U. M. Dauda, Transient airflow process across three vertical vents induced by Stack- driven effect inside Un- Stratified cross- ventilated rectangular building with an opposing flow in one of the upper Opening, International Journal of Computer Application (IJCA) 148 (1) (2016) 4-11.
D. N. Riahi, Mathematical modeling of wind forces. Department of theoretical and applied mechanics, University of Illinois at Urbana- Champaign USA (2005) 1-14.
S. C. Henry and N. K. Leslie, naturally ventilated and mixed-mode buildings Part I: Thermal modeling, Building and Environment 44 (2009) 736–749.
G. R. Hunt and P. F. Linden, Steady-state flows in an enclosure ventilated by buoyancy forces assisted by wind, J. Fluid Mech. 426 (2001) 355-386.
Z. Luo, J. Zhao, J. Gao and L. He, Estimating natural ventilation potential considering both thermal comfort and IQA issues, Build. Environ., 42 (2007) 2289-2298.
F. Roberto, Experimental and Numerical analysis of heat transfer and airflow on an interactive building façade, Energy and Buildings 42 (1) (2010) 23-28.
M. Santamouris, A. Argiriou, D. Asimakopoulos, N. Klitsikas and A. Dounis, Heat and Mass- transfer through large openings by natural convection, Energy and Buildings 23 (1995) 1-8.
T. Van Hooff, and B. Blocken, CFD evaluation of natural ventilation of indoor environments by the concentration decay method: CO2 gas dispersion from a semi-enclosed stadium, Building and Environment 61 (2013) 1-17.
Y. Wei, Z. Guoqiang, Y. Wei and W. Xiao, Natural ventilation potential model considering solution multiplicity, window opening percentage, air velocity and humidity in china, Building and Environment 45 (2010) 338-344.
D. J. Wilson and D. E. Keil, Gravity-driven coun-terflow through an open door in a sealed room, Building and Environment 25 (1990) 379–388.
W. Xin, H. Chen and C. Weiwu, Mathematical modeling and experimental study on vertical temperature distribution of hybrid ventilation in an atrium building, Energy and Buildings 41 (2009) 907–914.
J. Yi and C. Qingyan, Buoyancy-driven single-sided natural ventilation in buildings with large openings, International Journal of Heat and Mass transfer 46 (2003) 973-988.
A. Zollner, E. R. F. Winter and R. Viskanta, Experimental studies of combined heat transfer in turbulent mixed convection fluid flow in double- skin façades, Int. J. of Heat and mass transfer 45 (2002) 4401-4408.
L. Yuguo, A. Delsante and J. Symons, Prediction of natural ventilation in buildings with large openings, Builing and Environment 35 (2000) 191-206.
L. Yugou and A. Delsante, Natural ventilation induced by combined wind and thermal forces, Building and Environment 36 (1) (2001) 59-71.
R. E. Britter, J. C. R. Hunt and J. C. Mumford, The distortion of turbulence by a circular cylinder, J. Fluid Mech. 92 (1979) 269-301.
L. C. James Lo, Predicting wind driven cross ventilation in buildings with small openings. Doctoral thesis. University of Texas, USA (2012).
A. Acred, G. R. Hunt, A simplified mathematical approach for modelling stack ventilation in multi-compartment buildings, Builing and Environment 71 (2014) 121-130.
M. Colombari and C. Balocco, Thermal behavior of interactive mechanically ventilated double glazed façade: Non- dimensional analysis, Energy and Building 38 (2005) 1-7.
P. Cooper and P. F. Linden, Natural ventilation of an enclosure containing two buoyancy sources, J. Fluid mechanics 311 (1996) 153-176.
W. G. Brown and K. R. Solvason, Natural convection through rectangular opening in partition-I. Int. J. Heat and Mass Transfer 5 (1962a) 859-868.
W. G. Brown and K. R. Solvason, Natural convection heat transfer through rectangular openings in partitions-II, Int. J. Heat and Mass Transfer 5 (1962b) 869-878.
P. F. Linden, The Fluid Mechanics of Natural ventilation. Annu. Rev. Fluid Mech. 31 (1) (1999) 201-238.
Y. Tong, CFD and Field Testing of a naturally ventilated Full-scale Building. (Doctoral thesis) University of Nottingham, UK (2004).
A. L. Muhammad, M. Z. Ringim and L. A. Isma’il, Transient investigation of stack- driven airflow process through rectangular cross- ventilated building with two vents in the absence opposing flow in the upper opening, International Journal of Engineering and Technology (IJET) 7 (3) (2018) 1249-1256.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186