Natural convection flow in a square cavity with internal heat generation and a flush mounted heater on a side wall


  • Md. Mustafizur Rahman Dept. of Math, BUET
  • M. Arif Hasan Mamun
  • M. Masum Billah
  • Saidur Rahman



Finite Element Method, location of heater, length of heater, natural convection and square cavity.


In this study natural convection flow in a square cavity with heat generating fluid and a finite size heater on the vertical wall have been investigated numerically. To change the heat transfer in the cavity, a heater is placed at different locations on the right vertical wall of the cavity, while the left wall is considered to be cold. In addition, the top and bottom horizontal walls are considered to be adiabatic and the cavity is assumed to be filled with a Bousinessq fluid having a Prandtl number of 0.72. The governing mass, momentum and energy equations along with boundary conditions are expressed in a normalized primitive variables formulation. Finite Element Method is used in solution of the normalized governing equations. The parameters leading the problem are the Rayleigh number, location of the heater, length of the heater and heat generation. To observe the effects of the mentioned parameters on natural convection in the cavity, we considered various values of heater locations, heater length and heat generation parameter for different values of Ra varying in the range 102 to 105. Results are presented in terms of streamlines, isotherms, average Nusselt number at the hot wall and average fluid temperature in the cavity for the mentioned parameters. The results showed that the flow and thermal fields through streamlines and isotherms as well as the rate of heat transfer from the heated wall in terms of Nusselt number are strongly dependent on the length and locations of the heater as well as heat generating parameter.

DOI: 10.3329/jname.v7i2.3292



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Author Biographies

Md. Mustafizur Rahman, Dept. of Math, BUET

Assistant Professor, Dept. of Math, BUET

M. Arif Hasan Mamun

The Institute of Ocean Energy

Saga University, Japan

M. Masum Billah

Lecturer in Mathematics, Department of Business Administration

International Islamic University Chittagong (IIUC), Bangladesh

Saidur Rahman

Associate Professor, Department of Mechanical Engineering

University of Malaya, 50603 Kuala Lumpur, Malaysia




How to Cite

Rahman, M. M., Mamun, M. A. H., Billah, M. M., & Rahman, S. (2011). Natural convection flow in a square cavity with internal heat generation and a flush mounted heater on a side wall. Journal of Naval Architecture and Marine Engineering, 7(2), 37–50.