Heat and Mass Transfer

, Volume 44, Issue 4, pp 401–412 | Cite as

Convective drying analysis of three-dimensional porous solid by mass lumping finite element technique

  • K. Murugesan
  • D. C. Lo
  • D. L. YoungEmail author
  • C. W. Chen
  • C. M. Fan


A numerical analysis of convective drying of a 3D porous solid of brick material is carried out using the finite element method and mass lumping technique. The energy equation and moisture transport equations for the porous solid are derived based on continuum approach following Whitaker’s theory of drying. The governing equations are solved using the Galerkin’s weighted residual method, which convert the governing equations into discretized form of matrix equations. The resulting capacitance matrices are made diagonal matrices by following the classical row-sum mass lumping technique. Hence with the use of the Eulerian time marching scheme, the final equations are reduced to simple algebraic equations, which can be solved directly without using an equation solver. The proposed numerical scheme is initially validated with experimental results for 1D drying problem and then tested by application to convective drying of 3D porous solid of brick material for four different aspect ratios obtained by varying the cross section of the solid. The mass lumping technique could correctly predict the wet bulb temperature of the solid under evaporative drying conditions. A parametric study carried out for three different values of convective heat transfer coefficients, 15, 30 and 45 W/m2 K shows an increased drying rate with increase in area of cross section and convective heat transfer coefficient. The proposed numerical scheme could correctly predict the drying behavior shown in the form of temperature and moisture evolutions.


Heat Transfer Coefficient Mass Transfer Coefficient Moisture Transport Convective Heat Transfer Coefficient Surface Node 
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List of symbols


side (m)


width (m)


concentration (kg/m3), capacitance matrix


specific heat capacity (J/kg K)


moisture diffusion coefficient (m2/s)


convective heat transfer coefficient (W/m2 K)


convective mass transfer coefficient (m/s)


enthalpy (J/kg)


mass flux (kg/m2 s)


thermal conductivity (W/m K)


permeability (m2)


length (m)


rate of evaporation/condensation (kg/m2 s)


mass of solid (kg)


shape function


pressure (N/m2)


time (s)


temperature (K)


volume (m3)


moisture content (kg/kg of dry solid)


species velocity (m/s)

x, y, z

Cartesian coordinates

Greek symbols


dynamic viscosity (N s/m2)


relative humidity


density (kg/m3)


tortuosity factor





vapor diffusion








isothermal liquid moisture


isothermal vapor moisture


non-isothermal liquid moisture


non-isothermal vapor moisture




dry solid

ambient value



The National Science Council of Taiwan is gratefully acknowledged for providing financial support under the grant no. NSC 94-2211-E-002-071 to carry out the present research and greatly appreciated.


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • K. Murugesan
    • 1
  • D. C. Lo
    • 2
  • D. L. Young
    • 2
    Email author
  • C. W. Chen
    • 2
  • C. M. Fan
    • 2
  1. 1.Department of Mechanical and Industrial EngineeringIIT RoorkeeRoorkeeIndia
  2. 2.Department of Civil Engineering and Hydrotech Research InstituteNational Taiwan UniversityTaipeiTaiwan

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