# Unsteady State Heat Transfer Essay Sample

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Abstract

The objectives of the Unsteady State Heat Transfer laboratory were to study the rates of heat transfer for different materials of varying sizes, to develop an understanding of the concepts of forced and free convection and to determine the heat transfer coefficients for several rods. These objectives were met by heating several rods and allowing them to cool through free convection in air, free convection in water and forced convection in water- while monitoring their change in temperature over change in time. Seven heat transfer coefficients were determined during the laboratory for various rods. A copper rod underwent free convection in air, free convection in water and forced convection in water.

The measured heat transfer coefficients for the copper trials were 10.13 W/m2K, 438.43 W/m2K and 1715.69 W/m2K, respectively. These results supported theory that convection occurs for quickly in denser mediums and when it has a driving force. Two stainless steel rods underwent forced convection in water; the large rod had an experimental heat transfer coefficient of 1704.42 W/m2K while the small one had 1817.43 W/m2K. The smaller rod was expected to have the larger heat transfer coefficient since it has a smaller surface area. The results of the stainless steel rods therefore also supported theory.

The carbon steel rod possessed the smallest heat transfer coefficient for forced convection which was 370.25 W/m2K while the acrylic rod had the largest, 12 602.95 W/m2K. The heat transfer coefficients were calculated using the Lumped Heat Capacity Method and the Exact Method. The Lumped Heat Capacity Method is only viable for materials with high thermal conductivities and high external thermal resistances. The Exact Method had to be used for the acrylic and stainless steel rods so they were concluded to have low thermal conductivities and low external thermal resistances.

Test Methods

Objectives

The objectives of the Unsteady State Heat Transfer Lab were to study the rates of heat transfer for different materials of varying sizes, to develop an understanding of the concepts of forced and free convection and to determine the heat transfer coefficients for several rods.

Apparatus

In order to meet the objectives, some specific equipment was used from the Chemical Engineering laboratory. Several rods were used to investigate free and forced convection including a large copper rod with diameter of 3.1 cm and a length of 30.6 cm, two stainless steel rods of length 30.7cm and diameters of 3.21cm and 1.59cm, a thin acrylic rod and a thin carbon steel rod both with diameters and lengths of 1.6cm and 30.6 cm, respectively. A metal water basin insulated with Styrofoam was used and was divided into two smaller sections. The left basin was heated to approximately 65˚C with a Fisher Scientific Porta Temp. The water in the left basin was green due to an aniti-corrosive additive. The right section of the water basin was maintained near room temperature and was equipped with a Little Giant dual purpose pump, which provided circulation of 810 GPH for the forced convection trials. Thermocouples were used to measure the temperature of the centre of the rods during the experiments.

Hypotheses

Prior to performing the unsteady state heat transfer lab- it was hypothesized that the large copper rod would have the highest coefficient of heat transfer. This prediction was made based on the theory that a material’s heat transfer coefficient is proportional to its thermal conductivity. It was also hypothesized that forced convection would increase the heat transfer coefficient since the temperature gradient between the surface area and the surroundings will be greater due to constant turbulent flow. Lastly, it was predicted that convection would occur faster in water than air because water is denser and allows convection currents to occur more readily.

Procedures

The rods were initially placed in the left water basin to heat up to an initial temperature of approximately 65˚C. The room temperature or water temperature was recorded before each trial involving water or air. The rod being tested was connected to a thermocouple so the temperature could be measured throughout the experiment. Data was collected for the free convection of rods in air, water and also for the forced convection of rods in water by removing the rod from the hot bath and measuring the change in temperature over set time intervals in air or in the cold bath. To measure the forced convection in water the pump was turned on to circulate water in a turbulent flow around the surface of the rod.

Effects of Free and Forced Convection

Convection is one of the three primary methods of heat transfer. It is a process driven by the temperature gradient between two fluids or a fluid and a surrounding surface area. An external force may also influence convection.

In the Unsteady State Heat Transfer lab, students were required to differentiate between the effects of forced and free convection. Free convection is the transfer of heat that results from a temperature between two fluids or a fluid and an exposed surface area. In free convection, heat naturally disperses from a material when the surrounding fluid is stationary. The driving force for free convection is buoyancy- as the cooler fluid becomes heated it becomes less dense and rises and more cool fluid will thus replace it, creating a convection current. Free convection occurs more readily in water than air since water is more dense- it supplies a greater driving force. Forced convection occurs when an external force such as a fan or pump moves the fluid around and causes a transfer of heat.

The two methods used to determine the heat transfer coefficient during the lab were the Lumped Heat Capacity Model and the Exact Model. The Lumped Heat Capacity Method assumes that the temperature is evenly distributed across the solid at any given time during the trial. It assumes that the material has a high thermal conductivity and high external thermal resistance. The Lumped Heat Capacity Method only functions if the Biot number is less than 0.1. If it is greater than 0.1 than the Exact Method is used to determine the heat transfer coefficient. Presentation and Discussion of Results

Heat Transfer Coefficients|

Rod Type| Convection Method| Experimental Coefficient|

Copper| Free, Air| 10.13W/m2K|

Copper| Free, Water| 438.43W/m2K|

Copper| Forced, Water| 1715.69W/m2K|

Carbon Steel| Forced, Water| 370.25W/m2K|

Acrylic| Forced, Water| 12 602.95 W/m2K|

Large Stainless Steel| Forced, Water| 1704.42W/ m2K|

Small Stainless Steel| Forced, Water| 1817.43W/ m2K|

Some of the results of this experiment met the expectations based on theory while others deviated. All of the experimental heat transfer coefficients fell within the ranges provided in Table 1.1 from the Heat Transfer Textbook. The results from the trials involving the copper rod support the hypothesis that forced convection occurs more quickly than free convection. When convection was forced upon the copper rod by the pump- the heat transfer coefficient was approximately 4 times greater than when the copper underwent free convection in water. All of the rods displayed higher heat transfer coefficients in water. This result was expected because water is denser than air thus allowing convective currents to occur more readily. The experimental coefficient for the forced convection of carbon steel was 370.25 W/m2K. This is smaller than the coefficient of free convection of copper in water, which was 438.43 W/m2K. This result was attributed to the fact that copper has a larger thermal conductivity than carbon steel.

The acrylic rod was expected to have a large heat transfer coefficient since it has a high specific heat capacity and small surface area, however; it exhibited a heat transfer coefficient of 12 602.95 W/m2K, which seems much too high. An overall hypothesis was that the copper rod would display the largest heat transfer coefficient since it has the largest thermal conductivity but the acrylic rod had an experimental coefficient that was over seven times greater than the copper rod under similar conditions. The coefficients calculated for the large and small stainless steel rods were 1704.42 W/m2K and 1817.43W/ m2K, respectively. Both rods underwent forced convection in water. This result supports theory that heat transfer coefficients are proportional to surface area- as the surface area of an object increases, the heat transfer coefficient decreases.

Conclusions

The Unsteady State Heat Transfer lab was a useful way for students to gain a more thorough understanding of heat transfer. The objectives of the lab were to study the rates of heat transfer of different materials of different sizes, to familiarize students with concepts of forced and free convection and to calculate experimental heat transfer coefficients. All of the objectives were met during the lab. The most valuable portion of the lab was the three trials involving copper. The hypotheses predicted that the coefficient of copper would be smallest in air and then increase when copper was experiencing free convection in water, and the coefficient would be largest when the rod was undergoing forced convection in water.

The experimental results for free convection in air, free convection in water and forced convection in water were 10.13W/m2K, 438.43 W/m2K and 1715.69 W/m2K, respectively. The heat transfer coefficients for carbon steel was 370.25 W/m2K and for acrylic it was 12 602.95 W/m2K. The trials involving the two stainless steel rods supported theory that heat transfer coefficient decreases with surface area.

The experimental coefficients for the large and small stainless steel rods were 1704.42 W/m2K and 1817.43W/ m2K, respectively. The heat transfer coefficients for acrylic and the stainless steel rods could not be determined using the Lumped Heat Capacity Method so they were concluded to have a low thermal conductivity and low external thermal resistance. This conclusion was made because the Lumped Heat Capacity Method is only applicable for materials with high thermal conductivity and high external thermal resistance.

References

Incropera/DeWitt/Bergman/Lavine. Introduction to Heat Transfer (5th edition). Wiley (2007). ChE3424 – Chemical Engineering Laboratory II: Laboratory Manual “Unsteady State Heat Transfer” (2011) Recommendations

A recommendation for this lab would be to have a class lecture explaining all of the major concepts prior to the performing the lab. It is more beneficial for students to be applying knowledge they have gained in lecture while in the lab so that they are able to make relations to what they have learned. It is difficult to perform a lab and then interpret the results based on research in a minimal amount of time.