Abstract
The impact of wall movements in different directions on mixed convection flow and thermal performance in a wavy chamber is reported. The wavy wall of the chamber is heated non-uniformly, and the upper wall is kept at a constant cold temperature, while the vertical walls of the chamber are adiabatic. Four different cases, namely Case-1, Case-2, Case-3 and Case-4, are considered on the basis of multi-directional movements of the walls of the chamber. Mathematical model of the flow physics consists of the Navier–Stokes (N-S) equations in streamfunction (\(\psi\)) —vorticity (\(\zeta\)) formulation including the energy transport equations which are solved by higher-order compact (HOC) scheme on curvilinear grids Pandit SK, Chattopadhyay A.(Comput Math Appl 74(6):1414–34 2017) [45]. It is found that the fluid flow and thermal performance are both influenced by the direction of moving lids and the undulations of the wavy bottom surface of the chamber. Optimum thermal performance is noticed when the wavy bottom surface of the chamber is employed with one undulation at low Richardson number (Ri). Moreover, for \(Ri=0.01\), Case-2, in which the upper lid is moving in left direction and the left lid is moving in upward direction, gives better heat transfer rate with maximum value of average Nusselt number for one undulation. Furthermore, it is noticed that among all the cases, the cases (Case-2 and Case-4) in which upper lid is moving in left direction produce minimum entropy generation for every undulations of the wavy surface with each of the Ri values. So, on the basis of better heat transfer rate and the minimum entropy generation, Case-2 and Case-4 may be recommended as optimum configurations.
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Abbreviations
- Be :
-
Bejan number
- Gr :
-
Grashof number \((g{\beta _\text{T}}'L^3(T'_\text{h}-T'_\text{c})/\nu ^2)\)
- g :
-
Gravitational acceleration (\(\hbox {ms}^{-2}\))
- k :
-
Thermal conductivity (Wm−1 K−1)
- L :
-
Side length of a square chamber (m)
- Nu :
-
Local Nusselt number
- \({\overline{Nu}}\) :
-
Average Nusselt number
- p :
-
Non-dimensional pressure
- \(U_0\) :
-
Non-dimensional velocity of the horizontal moving walls (ms−1)
- Pr :
-
Prandtl number \((\nu /\alpha )\)
- P :
-
Dimensionless pressure \((p/\rho U^2_0)\)
- Re :
-
Reynolds number \((U_0 L/\nu )\)
- \(S_T\) :
-
Total entropy generation number
- t :
-
Non-dimensional time
- \(T'\) :
-
Dimensional temperature (K)
- T :
-
Non-dimensional temperature \((T'-T'_\text{c})\)/\((T'_\text{h}-T'_\text{c})\)
- \(T_0\) :
-
Bulk temperature (K)
- \(T'_h\) :
-
Temperature on hot surface (K)
- \(T'_c\) :
-
Temperature on cold vertical wall (K)
- u, v :
-
Dimensional velocity components (ms−1)
- U, V :
-
Non-dimensional velocity components in x, y directions (\(u/U_{0}\), \(v/U_{0}\))
- x, y :
-
Dimensional Cartesian coordinates (m)
- X, Y :
-
Non-dimensional Cartesian coordinates (xL−1, yL−1)
- \(\alpha\) :
-
Thermal diffusivity (\(({\text{m}}^{{\text{2}}}\,{\text{s}}^{{ - 1}})\))
- \({\beta _T}'\) :
-
Thermal expansion coefficient (K−1)
- \(\nu\) :
-
Kinematic viscosity (\({\text{m}}^{{\text{2}}}\,{\text{s}}^{{ - 1}}\))
- \(\lambda\) :
-
Wave amplitude of the wavy wall
- \(\mu\) :
-
Dynamic viscosity (kgm−1 s−1)
- \(\tau\) :
-
Irreversibility distribution ratio
- \(\rho\) :
-
Density (\({\text{kgm}}^{{\text{3}}}\))
- \(\psi\) :
-
Stream function
- \(\zeta\) :
-
Vorticity
- \(\xi\) :
-
Non-dimensional horizontal coordinate in computational plane
- \(\eta\) :
-
Non-dimensional vertical coordinate in computational plane
- i, j :
-
Cell faces
- c :
-
Cold wall
- h :
-
Hot wall
- d :
-
Wave undulation of the wavy surface
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Chattopadhyay, A., Karmakar, H., Pandit, S.K. et al. Impact of moving walls on combined convection flow and thermal performance in a wavy chamber. J Therm Anal Calorim 147, 3731–3752 (2022). https://doi.org/10.1007/s10973-021-10663-z
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DOI: https://doi.org/10.1007/s10973-021-10663-z