NUMERICAL STUDY FOR A THREE DIMENSIONAL LAMINAR NATURAL CONVECTION HEAT TRANSFER FROM AN ISOTHERMAL HEATED HORIZONTAL AND INCLINED SQUARE PLATE AND WITH A CIRCULAR HOLE

A theoretical study for a three-dimensional natural convection heat transfer from an isothermal horizontal , vertical and inclined heated square flat plates (with and without circular hole) has been done in the present work. The study involved the numerical solution of the transient Navier-Stokes and energy equations by using finite deference method (F.D.M.). The complete Navier-Stokes equation are transformed and expressed in terms of vorticity-vector potential. The Energy and Vorticity equations were solved by using an Alternating Direction Implicit (ADI) method because they are transient equations of parabolic portion, and the Vector potential is solved by using an equations Successive Over-Relaxation (S.O.R) method because it is from elliptic portion. The numerical solution is capable of calculating the Vector potential, three components of Vorticity and temperature field of the calculation domain. The numerical results were obtained in rang of Grashof number (103≤Gr≤5x104 ) with Prandtl number of (0.72) for square flat plate and the other consist a circle hole with ratio 0.6 and 0.8 diameter of the hole to main square side length. The numerical results showed that the main process of heat transfer is conduction for Grashof number less than 103 and convection for Grashof number larger than 103 and the results of local Nusselt number show fairly large dependence on inclination angle. For horizontal plate facing upward and downward, average Nusselt number is proportional to one-fifth power of Rayleigh number, and there is a significant difference in heat transfer rates between the upward and downward cases. For horizontal plate with circle hole facing upward for Grashof number 104 , the effect of core portion caused a limited increment in the heat transfer rate, where as for the facing downward case, the effect was larger and the maximum value of heat transfer rates is be for square flat plate with circle hole by ratio 0.6 for all inclination angles. With the increase of Grashof number to 5x104 heat transfer rates decrease except the square horizontal flat plate with circle hole by ratio 0.6 . The average Nusselt number increases with the increase of inclination of plates facing upward to reach to the higher average Nusselt number at vertical position then decrease with increase of inclination of plates. And the maximum value of average Nusselt number is depended on the ratio of diameter of the hole to main square side length, showed that the maximum temperature gradient occurs at the external edge of the horizontal plate (with and without circle hole) facing upward and at the lower external edge in inclined case. The numerical results was made through comparison with a previous numerical and experimental work, the agreement was good.

Experimental Study For a Laminar Natural Convection Heat Transfer From an Isothermal Heated Square Plate With and Without Circular Hole

An experimental investigation of natural convection heat transfer from an isothermal horizontal,vertical and inclined heated square flat plates with and without circular hole, were carried out in two cases, perforated plates without an impermeable adiabatic hole "open core" and perforated plates with an impermeable adiabatic hole "closed core" by adiabatic plug. The experiments covered the laminar region with a range of Rayleih number of (1.11x106 ≤RaLo≤4.39x106 ), at Prandtle number (Pr=0.7). Practical experiments have been done with variable inclination angles from horizon (Ф=0o ,45o,90o,135oand 180o),facing upward (0o≤Ф<90o), and downward (90o ≤Ф<180o). The results showed that the temperature gradient increases while the thermal boundary layer thickness decreases when Grashof number and perforation ratio (m) increase . The temperature gradient for inclined position facing upward is less than facing downward,while the thermal boundary layer thickness is greater. The temperature gradient decreases while the thermal boundary layer thickness increases for perforated plates with an adiabatic core as compared with perforated plates without an adiabatic core. The value of average Nusselt number increases with increasing perforation ratio, and Grashof number for all specimens with and without an adiabatic core, also increases by increase in inclination of plates approaching the higher value at vertical position (Ф=90o ), then decreases with increasing inclination of plates till horizontal position (Ф=180o). The average Nusselt number values for perforated plates with an adiabatic core are lower than for perforated plates without an adiabatic core for all perforation ratios. Maximum heat transfer rate occurs at perforated plate with perforation ratio of (m=0.1) without adiabatic core for vertical position (Ф=90o), at a range of Grashof number (1.576x106≤GrLo≤6.292x106 ), while the rate of heat transfer decreases with increasing perforation ratio for plates with and without adiabatic core for decrease in heat transfer rate area. The rate of heat transfer for perforated plates with circular hole is more than for perforated plates with square hole at the same perforation ratios (m=0.1,0.16,0.24 and 0.36). It found that the lack of core flow decreases the overall heat transfer rate by (6.477%) . There was a good agreement for the experimental present work results compared with other pervious results .

NUMERICAL AND EXPERIMENTAL INVESTIGATION ON THE EFFECT OF RESTRICTION SHAPE ON CHARACTERISTICS OF AIRFLOW IN A SQUARE DUCT

 Experimental and numerical investigation has been under taken to study turbulent flow of air through duct using restriction in different shapes and positions for Reynolds numbers ranges of (8.2x104 → 5.6x104).The numerical approach used in this work is the finite volume method for solution of elliptic partial differential equation for the modeling of turbulent (k-) model as well as wall function concept near the wall which was used to take the turbulent effects into consideration have been employed.The experimental test rigs were constructed from Perspex, and a fivehole pressure probe was used to measure the three component of air flow velocity vector in space.The results show that the total pressure drop depends on the shape and position of the restriction, and the pressure drop coefficient due to the restriction shape and position (kR) depends on two parameters; blockage area ratio (Ab) and the ratio between wetted perimeter to the free remainder perimeter (pe/Pe) and dose not depend on the Reynolds number ( for the same blockage area ratio Ab if the pe/Pe increases 40%, the coefficient kR increases 7% , and for the same pe/Pe, if the blockage area ratio increases 50% ,the coefficient kR increases 10%). But the pressure drop coefficient due to the friction (Cf) is a function of Reynolds.