# Bahaidarah, Haitham M. S. (2004-08). A numerical study of heat and momentum transfer over a bank of flat tubes. Doctoral Dissertation. Thesis

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### abstract

• The present study considers steady laminar two-dimensional incompressible flow over both in-line and staggered flat tube bundles used in heat exchanger applications. The effects of various independent parameters, such as Reynolds number (Re), Prandtl number (Pr), length ratio (L/Da), and height ratio (H/Da), on the pressure drop and heat transfer were studied. A finite volume based FORTRAN code was developed to solve the governing equations. The scalar and velocity variables were stored at staggered grid locations. Scalar variables (pressure and temperature) and all thermophysical properties were stored at the main grid location and velocities were stored at the control volume faces. The solution to a one-dimensional convection diffusion equation was represented by the power law. The locations of grid points were generated by the algebraic grid generation technique. The curvilinear velocity and pressure fields were linked by the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm. The line-by-line method, which is a combination of the Tri-Diagonal Matrix Algorithm (TDMA) and the Gauss-Seidel procedure, was used to solve the resulting set of discretization equations. The result of the study established that the flow is observed to attain a periodically fully developed profile downstream of the fourth module. The strength increases and the size of the recirculation gets larger as the Reynolds number increases. As the height ratio increases, the strength and size of the recirculation decreases because the flow has enough space to expand through the tube passages. The increase in length ratio does not significantly impact the strength and size of the recirculation. The non-dimesionalized pressure drop monotonically decreased with an increase in the Reynolds number. In general, the module average Nusselt number increases with an increase in the Reynolds number. The results at Pr = 7.0 indicate a significant increase in the computed module average Nusselt number when compared to those for Pr = 0.7. The overall performance of in-line configuration for lower height ratio (H/Da = 2) and higher length ratio (L/Da = 6) is preferable since it provides higher heat transfer rate for all Reynolds numbers except for the lowest Re value of 25. As expected the staggered configurations perform better than the in-line configuration from the heat transfer point of view.
• The present study considers steady laminar two-dimensional incompressible flow over both in-line and staggered flat tube bundles used in heat exchanger applications. The effects of various independent parameters, such as Reynolds number (Re), Prandtl number (Pr), length ratio (L/Da), and height ratio (H/Da), on the pressure drop and heat transfer were studied.
A finite volume based FORTRAN code was developed to solve the governing equations. The scalar and velocity variables were stored at staggered grid locations. Scalar variables (pressure and temperature) and all thermophysical properties were stored at the main grid location and velocities were stored at the control volume faces. The solution to a one-dimensional convection diffusion equation was represented by the power law. The locations of grid points were generated by the algebraic grid generation technique. The curvilinear velocity and pressure fields were linked by the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm. The line-by-line method, which is a combination of the Tri-Diagonal Matrix Algorithm (TDMA) and the Gauss-Seidel procedure, was used to solve the resulting set of discretization equations.
The result of the study established that the flow is observed to attain a periodically fully developed profile downstream of the fourth module. The strength increases and the size of the recirculation gets larger as the Reynolds number increases. As the height ratio increases, the strength and size of the recirculation decreases because the flow has enough space to expand through the tube passages. The increase in length ratio does not significantly impact the strength and size of the recirculation.
The non-dimesionalized pressure drop monotonically decreased with an increase in the Reynolds number. In general, the module average Nusselt number increases with an increase in the Reynolds number. The results at Pr = 7.0 indicate a significant increase in the computed module average Nusselt number when compared to those for Pr = 0.7. The overall performance of in-line configuration for lower height ratio (H/Da = 2) and higher length ratio (L/Da = 6) is preferable since it provides higher heat transfer rate for all Reynolds numbers except for the lowest Re value of 25. As expected the staggered configurations perform better than the in-line configuration from the heat transfer point of view.

• August 2004