# 1. cavity. The same geometry is analysed by

1. Introduction

Basak et al. 12, Wu et al. 37, Sarris et al. 4, Cheikh et al. 5, and Oztop et al. 6 has studied natural convection heat transfer in square cavities bounded by zero thickness solid walls. Free convection in enclosed cavities like square has got significant attention due its importance in many engineering applications such as fin type cooling (Banerjee et al. 11), material processing (Nazridoust et al. 10, Wang et al. 9 and Juel et al. 8), heat exchanger (Fitzgerald et al. 15, Asan et al. 13 and Prud’homme and Jasmin 14), nuclear reactor design (Espinosa et al. 17, Hassan et al. 19, Hirsch and Steinfeld 16 and Campbell et al. 18) and solar heating (Pangavhane et al. 12).

The work on conjugate heat transfer is scant and the problem is limited to boundary conditions such as heat flux and uniform temperature boundary conditions. Kaminski et al. 20 carried out numerical analysis on natural convection in a square cavity with the effect of conduction on one of the vertical walls having thickness (t). Liaqat and Baytas 21 numerically analysed the laminar natural convection flow in square cavity having thickness (t) on all sides of the cavity and containing volumetric sources.

Generally, heat is transferred by conduction through the walls of the enclosures having finite thickness. Thereby necessary to investigate the effect of conduction through solid on heat transfer by conduction/ convection through the fluid inside the enclosures. Conjugate convection heat transfer problems are complex and they have received less attention due to the physical modelling and simulation at the interface between the fluid regions and solid due to combined convection and conduction heat transfer. However, a few earlier works (Varol et al. 2325, Du and Bilgen 22, Das and Reddy 24) are carried out in this field of heat transfer with various enclosures.

Varol et al. 23 deliberate triangular porous enclosure with conjugate heat transfer via natural conduction and convection. Varol et al. 25 studied the effect of inclination angle in a partitioned square cavity on conjugate natural convection. Das and Reddy 24 studied the effect of inclination angle on heat transfer for a square enclosure with solid square block inside the cavity. The same geometry is analysed by McGarry et al. 31 and is determined that the choice of material for conducting solid block placed at the centre of the cavity does not have any impact on hot wall for heat removal.

Desrayaud et al. 26 numerically studied the free convection effects generated by cold vertical wall of a cavity with two openings on opposite wall of finite thickness and results are showcased in terms of temperature and velocity profiles for different Rayleigh numbers and aspect ratios of enclosure. Wansophark et al. 27 developed a combined FEM for solving heat conduction though a solid wall coupled with heat convection in viscous fluid flow (conjugate heat transfer problems). Saeid 28 carried out a numerical study of the steady conjugate natural heat transfer within two-dimensional porous enclosure having finite thickness. Mobedi 29 studied effect on Rayleigh number and conductivity ratio, of horizontal wall conduction on heat transfer rate through convection with in the enclosure. Hakyemez et al. 30 numerically studied the effect of the heat barrier located in the ceiling wall of a cavity on natural convection / conjugate conduction, where the horizontal walls are adiabatic and vertical walls are differentially heated.

In the previously mentioned examinations, investigation of conjugate free convection has been done utilizing streamlines and isotherms. Streamlines can magnificently clarify fluid flow; however, isotherms are deficient to examine energy flow disseminations particularly on account of conjugate convective heat transfer. Isotherms can just demonstrate the temperature distribution which might be adequate to consider the conduction heat transfer, where the heat flux lines are orthogonal to isotherms. The heat flow visualization in the event of convection heat transfer through a two-dimensional space is non-insignificant as heat flux lines are non-orthogonal to the isotherms to analyze the direction and intensity of the convective transport processes.

In the current investigation, an attempt is made to study the conjugate natural convection in a square cavity. The square cavity used in the current study is bounded by constant temperature / constant heat flux / convective boundary conditions at right solid wall of different thickness and, adiabatic top and bottom walls. Right wall is subjected to heat flux boundary condition q? or temperature boundary condition as Th. Also, having a convection boundary condition with ambient temperature T? and heat transfer co-efficient h, and left cold wall.

Right and left vertical walls of the square enclosure are maintained isothermally hot and cold, while the bottom walls are adiabatic. Each case is analysed for various parameters such as wall thickness (t = 0.2), Grashof numbers (Gr =103-107), conductivity ratios (kwL/kft = 5, 25 and 50) and Prandtl numbers (Pr = 0.7 6.08 and 17.08). In the present study, Grashof number are in the range (Gr =103-107) in order to show the effect of conduction (Gr =103), on set of convection (103 Gr 104) and dominant convective regimes (Gr 104). Also, wide range of Prandtl numbers has been chosen.