Pratibha Biswal

Analysis of Convective Heat Flow Visualization within Porous Right Angled Triangular Enclosures with a Concave/Convex Hypotenuse

Analysis of natural convection in porous right angled triangular enclosures with a concave/convex hypotenuse has been carried out using the Bejans heatlines approach. A generalized non-Darcy model without Forchheimer term is employed for fluid flow in a porous matrix and the governing equations are solved by the Galerkin finite element method. The cavity is subjected to a thermal boundary condition of an isothermal cold left wall, isothermal hot curved right wall, and adiabatic bottom wall. Due to intense closed loop heatlines, thermal mixing is higher in convex cases compared to the concave case for all parameters. Average heat transfer rate is found to be largest in the concave hypotenuse case.

Analysis of entropy generation during natural convection within entrapped porous triangular cavities during hot or cold fluid disposal

ABSTRACT Entropy generation analysis is carried out during natural convection within entrapped porous triangular cavities for two cases based on the heating or cooling of the inclined and horizontal walls (case 1: hot inclined walls with cold horizontal walls and case 2: cold inclined walls with hot horizontal walls). The results are plotted in terms of the isotherms (θ), streamlines (ψ), and entropy generation maps (Sθ and Sψ). The total entropy generation (Stotal), average Bejan number (Beav), and average Nusselt number ( or ) as a function of Darcy number (Dam) at a high Rayleigh number (Ram = 106) have been studied for both cases 1 and 2 and the optimal case is recommended based on least Stotal and largest or .

Analysis of exergy loss vs heat transfer rate for Rayleigh–Bénard convection of various fluids in enclosures with curved walls

ABSTRACT The investigation of entropy generation is highly desirable for the optimization of the thermal systems to avoid larger energy wastage and ensure higher heat transfer rate. The numerical investigation of natural convection within enclosures with the concave and convex horizontal walls involving the Rayleigh–Bénard heating is performed via entropy generation approach. The spatial distributions of the temperature (θ), fluid flow (ψ), entropy generation due to heat transfer and fluid friction (Sθ and Sψ) are discussed extensively for various Rayleigh numbers and Prandtl numbers involving various wall curvatures. A number of complex patterns of spatial distributions of fluid flow and temperature for cavities with concave or convex isothermal walls (top and bottom) have been obtained. The zones of high entropy generation for temperature and fluid flow are detected within cavities with concave and convex horizontal walls. The optimal situation involves the high heat transfer rate with moderate or low entropy generation. Overall, case 3 (highly concave) is found to be optimal over cases 1 and 2 (concave) and cases 1–3 (convex) for all Pr and Ra.

Analysis of differential versus Rayleigh–Bénard heating via heat flow visualization for thermal convection due to heating at enclosures with concave/convex walls

Abstract Natural convection within enclosures in the presence of isothermal curved walls involving (a) differential heating and (b) Rayleigh–Bénard heating is considered for investigation. The two heating strategies are compared based on the distributions of fluid flow, heat flow and local or average heat transfer rates for various Dam (modified Darcy number) and Prm (modified Prandtl number) at the high Ram (modified Rayleigh number). Unidirectional circulation cells occur for differential heating whereas four (combination of clockwise and anticlockwise) circulation cells occur for Rayleigh–Bénard heating. Consequently, unidirectional heatline cell occurs at the center for differential heating and four heatline circulation cells occur for Rayleigh–Bénard heating specially at the high . Multiple heatline cells lead to larger thermal mixing for Rayleigh–Bénard heating. The heat transfer rate is larger for differential heating case and the percentage enhancement of Nusselt number is calculated in terms of the gain in heat transfer rate for differential heating (E). The gain in heat transfer rate in terms of E involving concave and convex cavities (cases 1 and 2) is found to be the strong function of Dam and Prm at the high Ram.

Analysis of entropy generation during natural convection in porous enclosures with curved surfaces

ABSTRACT The natural convection is analyzed via the entropy generation approach in the differentially heated, porous enclosures with curved (concave or convex) vertical walls. The numerical simulations have been carried out for various fluids (Prandtl number: Prm = 0.015, 0.7, and 7.2) at various permeabilities (Darcy numbers: 10−5 ≤ Dam ≤ 10−2) for a high value of Rayleigh number (Ram = 106). The finite element method is employed to solve the governing equations and that is further used to calculate the entropy generation and average Nusselt number. The detailed spatial distributions of Sθ and Sψ are analyzed for all the wall curvatures. Overall, the case with the highly concave surfaces (case 3) is the optimal case at low Dam, whereas the cases with the less convex surfaces (cases 1 and 2) are the most efficient cases at high Dam.

Investigation of natural convection via heatlines for Rayleigh–Bénard heating in porous enclosures with a curved top and bottom walls

ABSTRACT The current study deals with the heatline-based analysis of natural convection in porous cavities with the curved top and bottom walls involving the Rayleigh–Bénard heating. The streamline cells are weak, and the wall-to-wall heatlines are observed for all the cases at the low Dam involving two test cases, Prm = 0.015 and 7.2. At the high Dam, the convective force takes the command, and multiple heatline cells are observed for all the concave (except for high wall concavity) and convex cases. The directions of the streamlines (for all Dam) and heatlines (at the high Dam) are exactly opposite for the concave and convex cases. The case 3 (concave) is the efficient case based on the largest heat transfer rate for Prm = 0.015 involving all Dam and for Prm = 7.2 involving the low Dam. At Prm = 7.2 and high Dam, the case 1 (concave or convex) may be the efficient cases compared with the cases involving high wall curvatures.

Role of various moving walls on entropy generation during mixed convection within entrapped porous triangular cavities

ABSTRACT The aim of the present investigation is to analyze the effect of the motion of horizontal walls on the entropy generation and heat transfer rates in an entrapped triangular porous cavity during mixed convection. Two different thermal boundary conditions are considered as follows: (i) hot inclined walls and cold horizontal walls and (ii) cold inclined walls and hot horizontal walls. Overall, Re = 100 may be recommended at Prm = 0.026, 7.2, Gr = 105, and Dam = 10−4 to 10−2 within the upper and lower cavities for cases 1 and 2.

Role of heatlines on thermal management during Rayleigh-Bénard heating within enclosures with concave/convex horizontal walls

Purpose This study aims to carry out the analysis of Rayleigh-Benard convection within enclosures with curved isothermal walls, with the special implication on the heat flow visualization via the heatline approach. Design/methodology/approach The Galerkin finite element method has been used to obtain the numerical solutions in terms of the streamlines (ψ ), heatlines (Π), isotherms (θ), local and average Nusselt number (Nut¯) for various Rayleigh numbers (103 ≤ Ra ≥ 105), Prandtl numbers (Pr = 0.015 and 7.2) and wall curvatures (concavity/convexity). Findings The presence of the larger fluid velocity within the curved cavities resulted in the larger heat transfer rates and thermal mixing compared to the square cavity. Case 3 (high concavity) exhibits the largest Nut¯ at the low Ra for all Pr. At the high Ra, Nut¯ is the largest for Case 3 (high concavity) at Pr = 0.015, whereas at Pr = 7.2, Nut¯ is the largest for Case 1 (high concavity and convexity). Practical implications The results may be useful for the material processing applications. Originality/value The study of Rayleigh-Benard convection in cavities with the curved isothermal walls is not carried out till date. The heatline approach is used for the heat flow visualization during Rayleigh-Benard convection within the curved walled enclosures for the first time. Also, the existence of the enhanced fluid and heat circulation cells within the curved walled cavities during Rayleigh-Benard heating is illustrated for the first time.