Dynamic Response of Heat Exchangers Having Internal Heat Sources—Part IV

1961 ◽  
Vol 83 (3) ◽  
pp. 321-336 ◽  
Author(s):  
W. J. Yang ◽  
J. A. Clark ◽  
V. S. Arpaci
Keyword(s):  
Dynamic Response ◽  
Heat Exchangers ◽  
Nuclear Reactor ◽  
Amplitude Ratio ◽  
Internal Heat ◽  
Fluid Temperature ◽  
Dependent Rate ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Heterogeneous Nuclear Reactor

This paper investigates the dynamic response of a heat exchanger having a sinusoidally time-dependent rate of internal heat generation. Results for both the transient-periodic and the steady-periodic, or frequency response, are given. These results include the response of the wall and fluid temperatures and the wall-fluid temperature difference. A phenomena of resonance in the amplitude ratio and phase shift is disclosed. Analytical results are obtained through the use of the Laplace transform technique. Experimental results are presented which compare favorably with the theoretical analysis. Heat exchangers to which these results apply include the heterogeneous nuclear reactor.

Natural Convection Flow in Vertical Channel Due to Ramped Wall Temperature at One Boundary

2009 ◽  
Author(s):  
Narahari Marneni ◽  
Vijay R. Raghavan
Keyword(s):  
Natural Convection ◽  
Volume Flow Rate ◽  
Vertical Channel ◽  
The Other ◽  
Temperature Fields ◽  
Convection Flow ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
Laplace Transform Technique ◽  
The Laplace Transform

An exact solution to the problem of unsteady natural convective flow of a viscous and incompressible fluid in a vertical parallel plate channel due to ramp heating at one boundary is presented. The temperature at one of the channel plates increases linearly over a certain time period and then remains constant while that at the other plate is maintained at the initial fluid temperature. The Laplace transform technique has been used to obtain the expressions for the velocity and temperature fields by solving the dimensionless governing partial differential equations under appropriate boundary conditions. The influence of the physical parameters on the velocity field, the temperature field, rate of heat transfer, skin-friction and volume flow rate of the fluid are analyzed systematically. The shear stress at the plate with ramped temperature boundary condition is significantly higher than that at the other plate because of the steeper velocity profiles in the vicinity. The Nusselt number at the plate with ramped temperature is much higher than that at the other plate indicating that much of the energy released from the plate because of its increasing temperature with time is convected out by the fluid before it reaches the second plate. The natural convection due to ramp heating has also been compared with the baseline case of flow with constant temperature.

An Analytical Solution for Boundary Layer Flows Over a Moving-Flat Porous Plate With Viscous Dissipation

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
C. J. Toki
Keyword(s):  
Boundary Layer ◽  
Viscous Dissipation ◽  
Porous Plate ◽  
Fluid Temperature ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
Dissipation Parameter ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Layer Flow

The problem of boundary layer flow of an incompressible fluid over a moving porous flat plate is investigated, by taking into account the heat due to viscous dissipation. The governing boundary layer equations of this flow field were solved analytically using the Laplace transform technique. These new exact analytical solutions for velocity and temperature were obtained with arbitrary Prandtl number and dissipation parameter (or Eckert number Ec). The corresponding solutions for nonporous plate are discussed. Applying numerical values into the analytical expressions of the temperature and heat transfer coefficient, we also discussed the effects of the dissipation parameter in the cases of water, gas, and ammonia flow. We can finally deduce that the fluid temperature of the present problem will increase in the case of viscous dissipation with positive Ec, but this temperature will decrease with negative Ec.

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