HEAT TRANSFER MECHANISM
When, τ = 0.1, the maximum and minimum values and position are almost the same for all values of Q. Based on the analysis, the following conclusions can be drawn: i) The solid-liquid thermal conductivity ratio (Kr) has a strong influence on thermal fields.
DIMENSIONLESS PARAMETERS
- Reynolds Number
- Richardson number
- Grashof number
- Prandtl number
DOUBLE-PIPE HEAT EXCHANGER
Maintaining the left and right vertical walls at a constant temperature in a lid-driven cavity with a heated circular hollow cylinder at the center of the cavity with magneto-hydrodynamic mixed convection is numerically studied by Farid et al. The analysis of the effect of mixed convective flow for different shapes and different boundary conditions to ensure efficient performance of heat transfer equipment. On the other hand, the maximum work of the mixed convection heat exchanger is performed in cavities or channels.
When Kr = 1.1 and τ = 0.1, the minimum value is close to the upper limit and the maximum value is close to the right limit. When Ri = 0.01 and 0.1 the isotherms show a temperature gradient near the right wall and at Ri = 5 and 10 the isotherm lines increase and join the heat generating isotherm lines. The flow field is almost symmetrical adjacent to the side walls for all values of Re.
PARTIALLY COOLED ENCLOSURE
APPLICATION
LITERATURE REVIEW
Using the commercial finite volume package FLUENT, Omari [33] studied steady laminar mixed convection flow and heat transfer in a lid-driven cavity for a computational fluid dynamics model. Ismael [18] numerically considered mixed convection in a lid-driven cavity with a moving arc-shaped wall. Consideration of different shapes of the hot bottom wall in a lid-driven cavity for mixed convection was studied by Yapici and Obut [42].
For mixed convective flow, the effect of Reynolds number on a heat-generating obstacle in a lid-driven cavity was investigated by Parvin et al. Filled with water-CuO nanofluid, a steady laminar mixed convective flow is established in a lid-driven cavity with wavy wall in a numerical model investigated by Nada and Chamkha [28]. A comparative study of mixed convective flow in a two-dimensional lid-driven square cavity filled with Cu-water nanofluid was investigated by Malik and Nayak [27].
MOTIVATION
The numerical solution of mixed convection in filled cavities for nanofluid field was investigated by Esfe et al.
OBJECTIVES
To investigate the effects of pertinent parameters, namely Prandtl number, Reynolds number, Richardson number, Nusselt number and the effects of physical parameters, namely solid-liquid conductivity ratio and length of cooling source on the flow and thermal fields in the enclosure.
OUTLINE OF THE THESIS
The solution of the governing equations together with the boundary conditions is obtained by the Galerkin finite element formulation. The results of the post-processing of the system are used to predict the flow rate and heat transfer rate through the heat exchanger. The average Nusselt number on the heated cylinder surface based on dimensional quantities can be expressed by.
The average Nusselt number at the heated surface of the cylinder based on the dimensionless quantities can be expressed by Nuh. As τ changes from 0.1 to 0.5, extra vorticity appears in the right corner of the cavity. The average temperature increases up to a certain level and then slowly decreases for the rest of the values of τ.
PHYSICAL MODEL
The left and right walls of the housing are kept adiabatic, as is the right wall of the housing. The heated part of the heat exchanger has a constant high temperature due to the hot fluid in the inner cylinder.
GOVERNING EQUATIONS ALONG WITH BOUNDARY CONDITIONS
The average Nusselt number can be used in process engineering design calculations to estimate the velocity transfer of the heated surface. After substituting the dimensionless variables into the equations we get the following dimensionless equations as. The dimensionless parameters appearing in equations (2.6) to (2.10) are the Reynolds number Re, Prandtl number Pr, Grashof number Gr, Richardson number Ri and the thermal conductivity ratio K of solid liquids.
Here N is the non-dimensional distance along the X and Y direction acting normal to the surface and Kr = ks kf is the thermal conductivity ratio of the solid-liquid.
NUMERICAL ANALYSIS
- FINITE ELEMENT FORMULATION AND COMPUTATIONAL
EFFECT OF THERMAL CONDUCTIVITY RATIO
Where ρ, u, l and μ are characteristic values of density, reference velocity, characteristic length and viscosity coefficient of the fluid flow respectively and the kinematics is -viscosity. The flow regime in free convection is determined by the dimensionless Grashof number which represents the ratio of the buoyancy to the viscous forces on the fluid. In heat transfer problems, the Prandtl number controls the velocity and the relative thickness of the thermal boundary layers.
This means that the thickness of the thermal boundary layer for liquid metals is much greater than the velocity boundary layer. In heat transfer problems, the Prandtl number controls the relative thickness of the momentum and thermal boundary layers. In their study, they found that the influence of angles and its variety of Richardson number on the change of the average Nusselt number.
The mathematical model of the system is derived from several sets of measurements, each recording the system's response (output) to different stimuli and disturbances (inputs). The triangular element with six nodes is used in this work to develop the finite element equations. Comparison of the streamlines between the present work (right) and Oztop et al.
Comparison of the isotherms between the present work (right) and that of Oztop et al.
EFFECT OF PRANDTL NUMBER
From figure 3.3(b) it is shown that the average Nusselt number remains unstable and eventually decreases for different values of Kr. The average Nusselt number increases rapidly with increasing Pr for the aforementioned values of τ. Here some maximum and minimum values are obtained for different values of heat generation parameter ratio.
From Figure 3.7 it is clear that the flow field remains almost the same at different values of τ for all values of Q. It is clearly observed that the isothermal lines are the same for the increasing values of Q with three different dimensionless time (τ) . When τ = 0.1, the isothermal lines near the right wall increase with increasing values of the cooling length.
50, the streamlines are thick, but with increasing values of Re, the streamlines become thinner. There is a significant effect on the currents, isothermal lines and heat transfer rates presented for different values of Ri.
EFFECT OF HEAT GENERATION PARAMETER RATIO
EFFECT OF COOLING LENGTH
A kidney-shaped cell is formed for τ = 0.1 on the right side of heat exchanger and it carries minimum values. Another cell is located on the right side near the right wall and it carries maximum values. Isotherms are distributed almost parallel to the horizontal wall from top to bottom of heat exchanger.
It can be seen from Figure 3.12(b) that the temperature in the cavity increases up to a certain value τ and then decreases for an increasing value τ.
EFFECT OF RICHARDSON NUMBER
The figure shows data on the influence of the Richardson number at different values of τ on the isotherms. For different dimensionless times (τ), the isotherm lines are almost parallel and distributed on the horizontal upper wall to the lower side of the generated solid. The isotherms along the right wall in the cooling section look like a shadow.
Again from Figure 3.15(b), when Ri = 0.01, the average Nusselt number decreases faster with time compared to when Ri = 0.1. It is higher for large New value and lower for small New value.
EFFECT OF REYNOLDS NUMBER
From figure 3.18(a) it is found that Re =0-300 with the increase of τ and decrease of Re, heat transfer rate decreases. From figure 3.18(b) it is observed that the average Nusselt number at the heated surface is primarily high for all values of Re, and as τ increases to a certain level, the average Nusselt number slowly decreases for the resting values of τ. Also note that Nuh is higher for Re = 500 and the lower value of Nuh.
Mixed convection heat transfer from a two-pipe heat exchanger in a partially cooled enclosure has been numerically investigated. The effect of various dimensionless parameters such as thermal conductivity ratio (Kr), Prandtl number (Pr), heat production parameter (Q), cooling length (Lc), Richardson number (Ri) and Reynolds number (Re) have been reported. Various ideas and results were discussed in more detail in the relevant chapter of the thesis.
SUMMARY OF THE MAJOR OUTCOMES
The average Nusselt number (Nuh) at the heat generating source decreases with increase in value of dimensionless time (τ). iv). There is a significant effect of cooling length (Lc) on streamlines, isotherms and heat transfer rate. Isotherms are distributed almost parallel to the horizontal wall and heat is trapped inside the cavity.
More elliptical cells are formed to increase τ and are elliptical in size. The average Nusselt number (Nuh), Ri decreases for increasing dimensionless time (τ). vi) As the values of τ are increasing, the vortices change their position for different Reynolds numbers. The flow field was almost symmetrical next to the sidewall cavity, which was heated from the center side with a higher concentration compared to the other boundaries of the cavity.
FURTHER WORKS
H., "Effect of Cavity Tilt on Mixed Convection Heat Transfer in a Lid Driven Cavity Flows", Computers and Fluids, Vol. 19] Ismael, M.A., Pop, I., and Chamkha, A.J., "Mixed Convection in a Lid-Driven Square Cavity with Partial Slip", International Journal of Thermal Science, Vol. J., "Multiple fluid flow and heat transfer solutions in a two-sided cover-driven cavity", International Journal of Heat and Mass Transfer, Vol.
J., “Mixed convective flow of a nanofluid in a lid-driven cavity with a wavy wall,” International Communications in Heat and Mass Transfer, Vol. 31] Oztop, H.F., Al-Salem, K., and Pop, I., “MHD mixed convection in a lid-driven cavity with corner heater”, International Journal of Heat and Mass Transfer, Vol. 33] Omari, R., “Numerical investigation of mixed convective flow in a lid-driven cavity”, American Journal of Computational Mathematics, Vol.
