Critical role of Prandtl number on multiple steady states during natural convection in square enclosures: Analysis of heat transfer rates, flow and thermal maps

This paper investigates natural convection heat transfer of generalized Oldroyd-B fluid in a porous medium with modified fractional Darcy's law. Nonlinear coupled boundary layer governing equations are formulated with time–space fractional derivatives in the momentum equation. Numerical solutions are obtained by the newly developed finite difference method combined with L1-algorithm. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Results indicate that, different from the classical result that Prandtl number only affects the heat transfer, it has remarkable influence on both the velocity and temperature boundary layers, the average Nusselt number rises dramatically in low Prandtl number, but increases slowly with the augment of Prandtl number. The maximum value of velocity profile and the thickness of momentum boundary layer increases with the augment of porosity and Darcy number. Moreover, the relaxation fractional derivative parameter accelerates the convection flow and weakens the elastic effect significantly, while the retardation fractional derivative parameter slows down the motion and strengthens the elastic effect.

Download Full-text

Numerical Study of Convective Heat Transfer From Expanding Annular Pipe Flows

Volume 8: Heat Transfer and Thermal Engineering ◽

10.1115/imece2016-67486 ◽

2016 ◽

Author(s):

Khaled J. Hammad

Keyword(s):

Heat Transfer ◽

Reynolds Number ◽

Prandtl Number ◽

Convective Heat Transfer ◽

Diameter Ratio ◽

Wall Heat Transfer ◽

Reattachment Point ◽

Transfer Rates ◽

Pipe Flows ◽

Annular Pipe

Convective heat transfer from suddenly expanding annular pipe flows are numerically investigated within the steady laminar flow regime. A parametric study is performed to reveal the influence of the annular diameter ratio, k, the Prandtl number, Pr, and the Reynolds number, Re, over the following range of parameters: k = {0, 0.5, 0.7}, Pr = {0.7, 1, 7, 100}, and Re = {25, 50, 100}. Heat transfer enhancement downstream of the expansion plane is only observed for Pr > 1. Peak wall-heat-transfer-rates always appear downstream of the flow reattachment point, in the case of suddenly expanding round pipe flows, i.e. k = 0. However, for suddenly expanding annular pipe flows, i.e., k = 0.5 and 0.7, peak wall-heat-transfer-rates always appear upstream of the flow reattachment point. The observed heat transfer augmentation is more dramatic for suddenly expanding annular flows, in comparison with the one observed for suddenly expanding pipe flows. For a given annular diameter ratio and Reynolds number, increasing the Prandtl number, always results in higher wall-heat-transfer-rates downstream the expansion plane.

Download Full-text

Three-Dimensional Natural Convection From Vertical Heated Plates With Adjoining Cool Surfaces

Journal of Heat Transfer ◽

10.1115/1.2911235 ◽

1992 ◽

Vol 114 (1) ◽

pp. 115-120 ◽

Cited By ~ 6

Author(s):

B. W. Webb ◽

T. L. Bergman

Keyword(s):

Heat Transfer ◽

Natural Convection ◽

Control Volume ◽

Three Dimensional ◽

Local Heat Transfer ◽

Local Heat ◽

Uniform Heat Flux ◽

Infrared Thermal Imaging ◽

Transfer Rates ◽

Thermal Boundary Conditions

Natural convection in an enclosure with a uniform heat flux on two vertical surfaces and constant temperature at the adjoining walls has been investigated both experimentally and theoretically. The thermal boundary conditions and enclosure geometry render the buoyancy-induced flow and heat transfer inherently three dimensional. The experimental measurements include temperature distributions of the isoflux walls obtained using an infrared thermal imaging technique, while the three-dimensional equations governing conservation of mass, momentum, and energy were solved using a control volume-based finite difference scheme. Measurements and predictions are in good agreement and the model predictions reveal strongly three-dimensional flow in the enclosure, as well as high local heat transfer rates at the edges of the isoflux wall. Predicted average heat transfer rates were correlated over a range of the relevant dimensionless parameters.

Download Full-text

Design of a Plane-Type Bidirectional Thermal Diode

Journal of Solar Energy Engineering ◽

10.1115/1.3268271 ◽

1988 ◽

Vol 110 (4) ◽

pp. 299-305 ◽

Cited By ~ 8

Author(s):

K. Chen

Keyword(s):

Heat Transfer ◽

Natural Convection ◽

Transfer Rate ◽

Reverse Bias ◽

Energy Utilization ◽

Heat Transfer Analysis ◽

Transfer Rates ◽

One Dimensional ◽

Plane Type ◽

Solar Energy Utilization

The design of a plane-type, bidirectional thermal diode is presented. This diode is composed of two vertical plates and several fluid-filled loops with their horizontal segments soldered to the vertical plates. This invention is simple in construction and low in cost. The direction of heat transfer in the invented thermal diode can be easily reversed. These features of the present invention make it very attractive to solar energy utilization. Natural convection analysis for thermosyphon operations was adopted for heat transfer calculations of the fluid-filled loops. A one-dimensional heat transfer analysis was employed to estimate the heat transfer rate and ratio of heat transfer rates of the diode under forward and reverse bias.

Download Full-text