HEAT+MASS TRANSFER:FUND.+APPL.
6th Edition
ISBN: 9780073398198
Author: CENGEL
Publisher: RENT MCG
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 2, Problem 23P
Starting with an energy balance on rectangular volume element, derive the one-dimensional transient heat conduction equation for a plane wall with constant thermal conductivity and no heat generation
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Starting with an energy balance on a disk volume element, derive the one-dimensional transient heat conduction equation for T(z, t) in a cylinder of diameter D with an insulated side surface for the case of constant thermal conductivity with heat generation.
Heat conduction
What does the assumption of one dimestional heat conduction mean? In the conduction what actual phenomena (heat transfer mechanisms) are being ignored to assume it, and where do they occur?
Derive the combined one-dimensional heat conduction equation.
Chapter 2 Solutions
HEAT+MASS TRANSFER:FUND.+APPL.
Ch. 2 - How does transient heat transfer from steady heat...Ch. 2 - Is heat transfer a scalar or a vector quantity?...Ch. 2 - Does a hear flux vector at a point P on an...Ch. 2 - From a heat transfer point of view, what is the...Ch. 2 - What is heat generation in a solid? Give examples.Ch. 2 - Heat generation is also referred to as energy...Ch. 2 - In order to size the compressor of a new...Ch. 2 - In order to determine the size of the heating...Ch. 2 - Consider a round potato being baked in an oven....Ch. 2 - Consider an egg being cooked in boiling water in a...
Ch. 2 - Prob. 11CPCh. 2 - Consider the cooking process of a roast beef in an...Ch. 2 - Consider heat loss from a 200-L cylindrical hot...Ch. 2 - Consider a cold canned drink left on a dinner...Ch. 2 - Heat flux meters use a very sensitive device know...Ch. 2 - Prob. 16PCh. 2 - Consider a large 3-cm-thick stainless steel plate...Ch. 2 - In a nuclear reactor, heat is generated uniformly...Ch. 2 - Prob. 19PCh. 2 - Prob. 20EPCh. 2 - Writer down the one-dimensional transient heat...Ch. 2 - Writer down the one-dimensional transient heat...Ch. 2 - Starting with an energy balance on rectangular...Ch. 2 - Prob. 24PCh. 2 - Prob. 25PCh. 2 - Consider a medium in which the heat conduction...Ch. 2 - Consider a medium in which the heat conduction...Ch. 2 - Consider a medium in which the heat conduction...Ch. 2 - Consider a medium in which the heat conduction...Ch. 2 - Consider a medium in which the heat conduction...Ch. 2 - Consider a medium in which the heat conduction...Ch. 2 - Consider a medium in which the heat conduction...Ch. 2 - Starting with an energy balance on a volume...Ch. 2 - Prob. 34PCh. 2 - Prob. 35PCh. 2 - What is a boundary condition? How many boundary...Ch. 2 - What is an initial condition? How many initial...Ch. 2 - What is a thermal symmetry boundary condition? How...Ch. 2 - How is the boundary condition on an insulated...Ch. 2 - It is claimed that the temperature profile in a...Ch. 2 - Why do we try to avoid the radiation boundary...Ch. 2 - Consider an aluminum pan used to cook stew on top...Ch. 2 - Prob. 43PCh. 2 - Prob. 44PCh. 2 - Heat is generated in a long wire of radius ro at a...Ch. 2 - Consider a long pipe of inner radius r1, Outer...Ch. 2 - A 2-kW resistance heater wire whose thermal...Ch. 2 - Prob. 48PCh. 2 - Prob. 49PCh. 2 - Consider a spherical shell of inner radius r1,...Ch. 2 - A container consists of two spherical layers, A...Ch. 2 - A spherical metal ball of radius ro is heated in...Ch. 2 - Prob. 53PCh. 2 - It is stated that the temperature in a plane wall...Ch. 2 - Consider one-dimensional heat conduction through a...Ch. 2 - Consider a solid cylindrical rod whose side...Ch. 2 - Consider a solid cylindrical rod whose ends are...Ch. 2 - Prob. 58PCh. 2 - Prob. 59PCh. 2 - Prob. 60PCh. 2 - Prob. 61PCh. 2 - Consider a 20-cm-thick concrete plane wall...Ch. 2 - Prob. 63PCh. 2 - Prob. 64PCh. 2 - Prob. 65PCh. 2 - Prob. 66PCh. 2 - Prob. 67PCh. 2 - Prob. 68EPCh. 2 - Prob. 69PCh. 2 - Consider a chilled-water pipe of length L, inner...Ch. 2 - Prob. 71EPCh. 2 - Prob. 72PCh. 2 - Prob. 73PCh. 2 - Prob. 74PCh. 2 - Prob. 75PCh. 2 - Prob. 76PCh. 2 - Prob. 77PCh. 2 - Prob. 78PCh. 2 - Prob. 79PCh. 2 - Prob. 80PCh. 2 - Prob. 81PCh. 2 - Prob. 82CPCh. 2 - Does heat generation in a solid violate the first...Ch. 2 - Prob. 84CPCh. 2 - Prob. 85CPCh. 2 - Prob. 86CPCh. 2 - Prob. 87PCh. 2 - Prob. 88PCh. 2 - Consider a large 3-cm thick stainless steel plate...Ch. 2 - Prob. 90PCh. 2 - Prob. 91EPCh. 2 - Prob. 92PCh. 2 - Prob. 93PCh. 2 - Prob. 94PCh. 2 - Heat is generated uniformly at a rate of 3 kW per...Ch. 2 - Prob. 96PCh. 2 - Prob. 97PCh. 2 - Prob. 98PCh. 2 - Prob. 99PCh. 2 - Prob. 100PCh. 2 - Prob. 101PCh. 2 - Prob. 102PCh. 2 - Prob. 103PCh. 2 - Prob. 104PCh. 2 - Prob. 105PCh. 2 - Prob. 106PCh. 2 - Prob. 107PCh. 2 - Prob. 108PCh. 2 - Prob. 109CPCh. 2 - When the thermal conductivity of a medium varies...Ch. 2 - The temperature of a plane wall during steady...Ch. 2 - Consider steady one-dimensional heat conduction in...Ch. 2 - Prob. 113CPCh. 2 - Prob. 114PCh. 2 - Prob. 115PCh. 2 - Prob. 116PCh. 2 - Consider a plane wall of thickness L whose thermal...Ch. 2 - Prob. 118PCh. 2 - Prob. 119PCh. 2 - A pipe is used for transporting boiling water in...Ch. 2 - Prob. 121PCh. 2 - Prob. 122PCh. 2 - Consider a spherical shell of inner radius r1 and...Ch. 2 - Prob. 124PCh. 2 - A spherical tank is filled with ice slurry, where...Ch. 2 - Prob. 126CPCh. 2 - Prob. 127CPCh. 2 - Can a differential equation involve more than one...Ch. 2 - Prob. 129CPCh. 2 - Prob. 130CPCh. 2 - Prob. 131CPCh. 2 - Prob. 132CPCh. 2 - How is integation related to derivation?Ch. 2 - Prob. 134CPCh. 2 - Prob. 135CPCh. 2 - How is the order of a differential equation...Ch. 2 - How do you distinguish a linear differential...Ch. 2 - How do you recognize a linear homogeneous...Ch. 2 - How do differential equations with constant...Ch. 2 - What kinds of differential equations can be solved...Ch. 2 - Consider a third-order linear and homogeneous...Ch. 2 - A large plane wall, with a thickness L and a...Ch. 2 - Prob. 143PCh. 2 - Prob. 144EPCh. 2 - A spherical vessel has an inner radius r1 and an...Ch. 2 - Consider a short cylinder of radius r0 and height...Ch. 2 - Prob. 147PCh. 2 - Consider a 20-cm-thick large concrete plane wall...Ch. 2 - Prob. 149PCh. 2 - Prob. 150PCh. 2 - Prob. 151PCh. 2 - Prob. 152PCh. 2 - Prob. 153PCh. 2 - Prob. 154EPCh. 2 - Prob. 155PCh. 2 - Consider a water pipe of length L=17m, inner...Ch. 2 - Prob. 157PCh. 2 - In a manufacturing plant, a quench hardening...Ch. 2 - Consider a spherical reactor of 5-cm diameter...Ch. 2 - Consider a cylindrical sheel of length L, inner...Ch. 2 - A pipe is used for transporting boiling water in...Ch. 2 - A metal spherical tank is filled with chemicals...Ch. 2 - The heat conduction equation in a medium is given...Ch. 2 - Consider a medium in which the heat conduction...Ch. 2 - Consider a large plane wall of thicness L, thermal...Ch. 2 - A solar heat flux qs is incident on a sidewalk...Ch. 2 - A plane wall of thickness L is subjected to...Ch. 2 - Consider steady one-dimensional heat conduction...Ch. 2 - The conduction eqution boundary condition for an...Ch. 2 - Prob. 170PCh. 2 - Prob. 171PCh. 2 - The temperatures at the inner and outer surfaces...Ch. 2 - The thermal conductivity of a solid depends upon...Ch. 2 - Prob. 174PCh. 2 - Prob. 175PCh. 2 - Prob. 176PCh. 2 - Prob. 177PCh. 2 - Prob. 178PCh. 2 - Write essay on heat generation in nuc1e e1 rods....Ch. 2 - Write an interactive computer program to calculate...Ch. 2 - Prob. 181P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- 2.29 In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation where = local rate of heat generation per unit volume at r = outside radius = rate of heat generation per unit volume at the centerline Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of if the rate of heat removal from its surface is 1.6 .arrow_forward2.9 In a large chemical factory, hot gases at 2273 K are cooled by a liquid at 373 K with gas-side and liquid-side convection heat transfer coefficients of 50 and , respectively. The wall that separates the gas and liquid streams is composed of a 2-cm thick oxide layer on the gas side and a 4-cm thick slab of stainless steel on the liquid side. There is a contact resistance between the oxide layer and the steel of . Determine the rate of heat loss from hot gases through the composite wall to the liquid.arrow_forward2.43 A turbine blade 6.3 cm long, with cross-sectional area and perimeter , is made of stainless steel . The temperature of the root, , is . The blade is exposed to a hot gas at , and the heat transfer coefficient is K. Determine the temperature of the blade tip and the rate of heat flow at the root of the blade. Assume that the tip is insulated.arrow_forward
- 3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on one side is and on the other side is . If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it takes for the copper plate to reach a temperature of 82°C.arrow_forwardOne end of a 0.3-m-long steel rod is connected to a wall at 204C. The other end is connected to a wall that is maintained at 93C. Air is blown across the rod so that a heat transfer coefficient of 17W/m2 K is maintained over the entire surface. If the diameter of the rod is 5 cm and the temperature of the air is 38C, what is the net rate of heat loss to the air?arrow_forwardThe handle of a ladle used for pouring molten lead is 30 cm long. Originally the handle was made of 1.9cm1.25cm mild steel bar stock. To reduce the grip temperature, it is proposed to form the handle of tubing 0.15 cm thick to the same rectangular shape. If the average heat transfer coefficient over the handle surface is 14 W/m K, estimate the reduction of the temperature at the grip in air at 21C.arrow_forward
- 1.10 A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.arrow_forwardShow that the rate of heat conduction per unit length through a long, hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with temperature, is given by qkL=TiTo(rori)/kmA where Ti = temperature at the inner surface To = temperature at the outer surface A=2(rori)/ln(ro/ri)km=ko[1+k(Ti+To)/2]L=lenthofcyclinderarrow_forwardEstimate the rate of heat loss per unit length from a 5-cm ID, 6-cm OD steel pipe covered with high-temperature insulation having a thermal conductivity of 0.11 W/(m K) and a thickness of 1.2 cm. Steam flows in the pipe. It has a quality of 99% and is at 150C. The unit thermal resistance at the inner wall is 0.0026(m2K)/W the heat transfer coefficient at the outer surface is 17W/(m2K) and the ambient temperature is 16C.arrow_forward
- An electronic device that internally generates 600 mW of heat has a maximum permissible operating temperature of 70C. It is to be cooled in 25C air by attaching aluminum fins with a total surface area of 12cm2. The convection heat transfer coefficient between the fins and the air is 20W/m2K. Estimate the operating temperature when the fins are attached in such a way that (a) there is a contact resistance of approximately 50 K/W between the surface of the device and the fin array and (b) there is no contact resistance (in this case, the construction of the device is more expensive). Comment on the design options.arrow_forwardThe interior wall of a large, commercial walk-in type meat freezer is covered under normal operating conditions with a 2-cm thick layer of ice. One day, a power outage cuts electricity to the refrigeration system of the freezer. Estimate the time required to melt this layer of ice if it has a mass density of 700kg/m3 and a latent heat of fusion of 334 kJ/kg. Consider the air temperature inside the freezer to be 20C with a heat transfer coefficient of 2W/m2K for convection from the freezer surface to air, and clearly state the assumptions made in your calculations.arrow_forward2.5 Derive an expression for the temperature distribution in a plane wall in which there are uniformly distributed heat sources that vary according to the linear relation where is a constant equal to the heat generation per unit volume at the wall temperature . Both sides of the plate are maintained at and the plate thickness is 2L.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Heat Transfer – Conduction, Convection and Radiation; Author: NG Science;https://www.youtube.com/watch?v=Me60Ti0E_rY;License: Standard youtube license