Variation of Heat Transfer Coefficient for Inside and Outside Closed Space with Respect to Temperature Gradient for Three Different Metals

- The heat transfer coefficient (h), is used in thermodynamics to calculate the heat transfer typically occurring by convection. A simple way to calculate (h) is to define it through the classical formula for convection, the present study includes correlations different natural convection can be used to calculate heat transfer coefficients theoretically for the experimental tests done inside and outside close system. All the results obtained from the experimental tests, theoretical calculations and from the literatures show that, heat transfer coefficients (h) are increasedwiththe temperature increasing. The experimental results for all the tested materials appears that there are similarity for the rules of sequence step in the change of heat transfer coefficient (h) with respect to the thermal conductivity coefficients (k) of these materials, and they are in a row from the highest value to the lowest value; Copper, Aluminum, Steel and Brick respectively for both of (k) and (h). The results show a good accuracy and compatibility of the comparison between numerical results with the present experimental work, also give a good agreement between the present experimental work and the numerical results with the experimental results obtained from literature approved in this study.


Introduction
Convection heat transfer takes place whenever a fluid is in contact with a solid surface that is at a different temperature than the fluid. If the fluid is moving past the solid surface because of an external driving force, then it is called forced convection .If fluid motion is due to density differences caused by temperature variation in the fluid, then it is called natural convection [1]. The convective heat transfer coefficient h is defined according to Newton's Law of Cooling as [2]: For convection, we use the convection heat transfer coefficient h, W/(m 2 .k). A different approach to define h is through the Nusselt number Nu, which is the ratio between the convective and the conductive heat transfer [3].
(2) Nusselt number is used directly to evaluate the convection coefficient according to (3): (3) Table 1 given value (Nu) Natural convection of isothermal flat plate ,The Nesselt number relies of geometrical shape of the body heat and the air flow.

Engineering and Technology Journal
Vol. 35, Part A. No. 5, 2017 535 Awbi [6] studied natural convection heat transfer in two-dimensional rooms by using computational fluid dynamics (CFD) technique. The room configurations included heated wall, heated floor and heated ceiling. Two kinds of CFD models were applied: a standard k −ε model with "wall functions" and the low Reynolds number k −ε model. Oetelaar and Johnston [7] studied natural convection processes inside terracotta flues as a part of a larger numerical study of ancient Roman baths, The five plenum temperatures were tested (60°C, 70°C, 80°C, 90°C, 100°C) and they found , that the average convective coefficient was 7.0 (w/m 2°C ). Roncati [8] used the iterative method to calculated accurately the temperature value for heat sink and better precision of heat transfer coefficient of finite elements software for thermal analysis. Conti et al. [9] introduced simplified model for measuring convection heat-transfer coefficient, the simplified model is valid for convective heattransfer coefficient of about 30 W m-2 K -1 and for ∆T<100K,that is when the energy exchange by radiation is negligible. Hatton and Awbi [10] made experiments to find convective heat transfer in room building simulation on room walls or aluminum plates. They found the mean convective heat of aluminum wall to be hc=1.57ΔT 0.31 . Where ΔT = (T -Ta); T is the measuring temperature of air tentacles with specimen face; Ta Aluminum specimen temperature. Ahmed and Chaichan [11] study of Free Convection in A solar Chimney Model. Shows Maximum heat transfer coefficient h was 31.83 W/m2 K. A maximum air temperature difference attained was 22 º C at mid-day through the solar chimney and Empirical equation that relates Nusselt and Rayleigh numbers was obtained. Mohammed [12] study experimental and numerical simulation for natural convection heat transfer formed by uniformly heated inclined elliptical cylinder concentrically located in an enclosed square cylinder subjected to the ambient have been investigated. Experiments have been carried out for Rayliegh number ranges from 0.9 ×10 6 to3.3×10 6 while a numerical simulation was conducted by using commercial Fluent CFD code to investigate the steady laminar natural convective heat transfer. The experimental results explained the heat transfer process improves with increases in Rayliegh number . In this paper, description of experiment and theoretical methods to measure and to calculate the convective heat-transfer coefficient, which is a characteristic constant of convection systems.

I. Experimental apparatus
Electrical france explains in Figure 1 utilized to calculate the transfer coefficient of the convection heat. The heater room is intended to hole the round and hollow samples sleeve of (140mm) length in gap in the rear mass of the heater, the samples are penetrated to embed the thermocouples so as to gauge the heat via the sample materials. To acquire sensible temperature consistency along the sample, an aluminum tube is used to place the sample holder in it. The experimental variables are different specimen materials and specification such as Aluminum, Copper and Steel, each specimen has outside diameter of (30mm) and length (40mm). In order to measure the temperature the heating process, we have inserted thermocouple type (k) inside specimen and measured the temperature of the specimen when temperatures furnace from 50°C to 500°C. Once the heat degree of the thermocouple is settled by switching on the heater that becomes in state of balance, accordingly, the reading is begun to show up.

II. Temperature Measurement
The temperature values have been automatically acquired by the software (PLC). The first temperature measured (T1) for the face of the specimen located in side furnace, the second temperature (T2) represented second face of specimen is located in outer side of furnace wall, the third temperature (T3) represented temperature near of furnace wall as shown in Figure 2.

III. Metal Selection
The composition of the used alloy are shown in Table 1, 2 and 3 its chemical analysis of sample Equipped by company inspection engineering (S.I.E.R) as it was given in Appendix

I .Calculation samples of convective heat transfer coefficient (h) of materials
An initial determine value for Tp then is set in Eq. 5 to define Garshof number. Once calculated the parameters Gr, Pr, Ra and Nu, then calculated value of (h) from is the equation (Eq.3) for estimation convection coefficient of copper inside furnace at temperature 100°C, the air properties at the mean temperature are evaluated as followed: According to average mean temperature (T F) , the physical properties of Air (k,pr and μ) got assessed. K= 0.03003 w/m °C, pr=0.697, μ =2.075x10 -5 kg/m.s Define air thermal expansion coefficient.  Table 7. These numerical formulas were derived by using the general polynomial, Taylor series and least square methods which give accurate results are closed on each other for all the three methods of solutions. The value of h for all the samples are expressed as follows which were derived from the general polynomial and solved by Gaussian eliminations: The general polynomial used was: (7) Which can be written as follows: Then after were finding the values of a1, a2 and a3 get the following empirical equations: Samples of Copper formula: (9) Samples of Aluminum formula: (10) Samples of Steel formula: -(11) Samples of Brick formula: (12) Then the heat transfer coefficients(h) of the thin layers of air at the surface of the samples Copper, Aluminum, Steel and Brick were calculated from measurements in the outside closed system,. The expressions given in Table 8 represent these values. These numerical formulas derived by using the general polynomial of infinite degree, taylor series and least square methods which give accurate results closed on each other for all the three methods of solutions. The value of h for all the samples are expressed as follows which were derived from the general polynomial of infinite degree and solved by Gaussian eliminations: The general polynomial used was: f(x) =a1+a2x + a3 (13) Which can be written as follows:

III.
A comparison between both experimental and theoretical results compared with the results get from the formula given in reference [10] Hatton and Awbi are illustrated in Figures 12 and 13.The results are approximately close to each other.