scholarly journals Double‐diffusive flow in a porous right‐angle trapezoidal enclosure with constant heat flux

2021 ◽  
Author(s):  
Zafar H. Khan ◽  
Waqar A. Khan ◽  
Muhammad Qasim ◽  
Min Du
Keyword(s):  
Heat Flux ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Diffusive Flow ◽  
Trapezoidal Enclosure ◽  
Double Diffusive

scholarly journals Double-diffusive instabilities at a horizontal boundary after the sudden onset of heating

2018 ◽  
Vol 859 ◽  
pp. 126-159
Author(s):  
Oliver S. Kerr
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Salinity Gradient ◽  
Constant Heat Flux ◽  
Initial Time ◽  
Sudden Increase ◽  
Constant Heat ◽  
Diffusive Convection ◽  
Double Diffusive ◽  
Thermal Rayleigh Number

When a deep body of fluid with a stable salinity gradient is heated from below at a horizontal boundary a destabilizing temperature gradient develops and can lead to instabilities. We will focus on two variants of this problem: the sudden increase in the boundary temperature at the initial time and the sudden turning on of a constant heat flux. These generate time-dependent temperature profiles. We look at the growing phase of the linear instabilities as an initial value problem where the initial time for the instabilities is a parameter to be determined. We determine numerically the optimal initial conditions and the optimal starting time for the instabilities to ensure that the maximum growth occurs at some given later time. The method that is used is an extension of the method developed by Kerr & Gumm (J. Fluid Mech., vol. 825, 2017, pp. 1002–1034) in their investigation of the stability of developing temperature boundary layers at horizontal and vertical boundaries. This requires the use of an appropriate measure of the amplitude of the disturbances which is identified. The effectiveness of this approach is verified by looking at the classic problem of double-diffusive convection in a horizontal layer, where we look at both the salt-finger regime and the diffusive regime. We show that this approach is an effective way of investigating instabilities where the background gradients time dependent. For the problem of heating a salinity gradient from below, as the heat diffuses into the fluid the effective thermal Rayleigh number based on the instantaneous diffusion length scale grows. For the case of a sudden increase in the temperature by a fixed amount the effective thermal Rayleigh number is proportional to $t^{3/2}$, and for a constant heat flux it is proportional to $t^{2}$, where $t$ is the time since the onset of heating. However, the effective salt Rayleigh number also grows as $t^{2}$. We will show that for the constant temperature case the thermal Rayleigh number initially dominates and the instabilities undergo a phase where the convection is essentially thermal, and the onset is essentially instantaneous. As the salt Rayleigh number becomes more significant the instability undergoes a transition to oscillatory double-diffusive convection. For the constant heat flux the ratio of the thermal and salt Rayleigh numbers is constant, and the instabilities are always double diffusive in their nature. These instabilities initially decay. Hence, to achieve the largest growth at some given fixed time, there is an optimal time after the onset of heating for the instabilities to be initiated. These instabilities are essentially double diffusive throughout their growth.

Rate of Sublimation of Ice by Radiative Heating in Freeze-Etching

1980 ◽  
Vol 38 ◽  
pp. 618-619
Author(s):  
Yeshayahu Talmon
Keyword(s):  
Heat Flux ◽  
Freeze Fracture ◽  
Constant Heat Flux ◽  
Radiative Heating ◽  
Constant Heat ◽  
Entire Sample ◽  
Simplified Method ◽  
Freeze Etching ◽  
Sublimation Rates ◽  
Fractured Surface

To bring out details in the fractured surface of a frozen sample in the freeze fracture/freeze-etch technique,the sample or part of it is warmed to enhance water sublimation.One way to do this is to raise the temperature of the entire sample to about -100°C to -90°C. In this case sublimation rates can be calculated by using plots such as Fig.1 (Talmon and Thomas),or by simplified formulae such as that given by Menold and Liittge. To achieve higher rates of sublimation without heating the entire sample a radiative heater can be used (Echlin et al.). In the present paper a simplified method for the calculation of the rates of sublimation under a constant heat flux F [W/m2] at the surface of the sample from a heater placed directly above the sample is described.

scholarly journals The exact analytical solution of the dual-phase-lag two-temperature bioheat transfer of a skin tissue subjected to constant heat flux

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Hamdy M. Youssef ◽  
Najat A. Alghamdi
Keyword(s):  
Heat Flux ◽  
Analytical Solution ◽  
Exact Analytical Solution ◽  
Constant Heat Flux ◽  
Bioheat Transfer ◽  
Skin Tissue ◽  
Phase Lag ◽  
Dual Phase ◽  
Constant Heat ◽  
Two Temperature

Abstract This work is dealing with the temperature reaction and response of skin tissue due to constant surface heat flux. The exact analytical solution has been obtained for the two-temperature dual-phase-lag (TTDPL) of bioheat transfer. We assumed that the skin tissue is subjected to a constant heat flux on the bounding plane of the skin surface. The separation of variables for the governing equations as a finite domain is employed. The transition temperature responses have been obtained and discussed. The results represent that the dual-phase-lag time parameter, heat flux value, and two-temperature parameter have significant effects on the dynamical and conductive temperature increment of the skin tissue. The Two-temperature dual-phase-lag (TTDPL) bioheat transfer model is a successful model to describe the behavior of the thermal wave through the skin tissue.

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