Heat and Mass Transfer: Fundamentals and Applications
Heat and Mass Transfer: Fundamentals and Applications
5th Edition
ISBN: 9780073398181
Author: Yunus A. Cengel Dr., Afshin J. Ghajar
Publisher: McGraw-Hill Education
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Chapter 2, Problem 51P

A spherical metal ball of radius ro is heated in an oven to a temperature of Ti throughout and is then take out of the oven and dropped into a large body of water at T where it is cooled by convection with an average convection heat transfer coefficient of h. Assuming constant thermal conductivity and transient one-dimensional heat transfer, express the mathematical formulation (the differential equation and the boundary and initial conditions) of this heat conduction problem. Do not solve.

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You are asked to estimate the maximum human body temperature if the metabolic heat produced in your body could escape only by tissue conduction and later on the surface by convection. Simplify the human body as a cylinder of L=1.8 m in height and ro= 0.15 m in radius. Further, simplify the heat transfer process inside the human body as a 1-D situation when the temperature only depends on the radial coordinater from the centerline. The governing dT +q""=0 dr equation is written as 1 d k- r dr r = 0, dT dr =0 dT r=ro -k -=h(T-T) dr (k-0.5 W/m°C), ro is the radius of the cylinder (0.15 m), h is the convection coefficient at the skin surface (15 W/m² °C), Tair is the air temperature (30°C). q" is the average volumetric heat generation rate in the body (W/m³) and is defined as heat generated per unit volume per second. The 1-D (radial) temperature distribution can be derived as: T(r) = q"¹'r² qr qr. + 4k 2h + 4k +T , where k is thermal conductivity of tissue air (A) q" can be calculated…
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Which formula is used to calculate the heat conduction in the AXIAL direction in a vertically located pipe segment whose inner and outer surfaces are perfectly insulated. Here r, is inner radius, r, outer radius, Tri pipe inner surface temperature, Tro pipe outer surface temperature, L is the length of the pipe, T the temperature on the lower surface, Ty the temperature on upper surface. Tu r; Tro r

Chapter 2 Solutions

Heat and Mass Transfer: Fundamentals and Applications

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 - Consider a large 3-cm-thick stainless steel plate...Ch. 2 - In a nuclear reactor, heat is generated uniformly...Ch. 2 - Prob. 18PCh. 2 - Prob. 19EPCh. 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. 23PCh. 2 - Prob. 24PCh. 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. 33PCh. 2 - Prob. 34PCh. 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. 42PCh. 2 - Prob. 43PCh. 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. 47PCh. 2 - Prob. 48PCh. 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. 52PCh. 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. 57PCh. 2 - Prob. 58PCh. 2 - Prob. 59PCh. 2 - Consider a 20-cm-thick concrete plane wall...Ch. 2 - Prob. 61PCh. 2 - Prob. 62PCh. 2 - Prob. 63PCh. 2 - Prob. 64PCh. 2 - Prob. 65EPCh. 2 - Prob. 66PCh. 2 - Consider a chilled-water pipe of length L, inner...Ch. 2 - Prob. 68EPCh. 2 - Prob. 69PCh. 2 - Prob. 70PCh. 2 - Prob. 71PCh. 2 - Prob. 72PCh. 2 - Prob. 73PCh. 2 - Prob. 74PCh. 2 - Prob. 75PCh. 2 - Prob. 76PCh. 2 - Prob. 77PCh. 2 - Prob. 78CPCh. 2 - Does heat generation in a solid violate the first...Ch. 2 - Prob. 80CPCh. 2 - Prob. 81CPCh. 2 - Prob. 82CPCh. 2 - Prob. 83PCh. 2 - Prob. 84PCh. 2 - Consider a large 3-cm thick stainless steel plate...Ch. 2 - Prob. 86PCh. 2 - Prob. 87EPCh. 2 - Prob. 88PCh. 2 - Prob. 89PCh. 2 - Prob. 90PCh. 2 - Heat is generated uniformly at a rate of 3 kW per...Ch. 2 - Prob. 92PCh. 2 - Prob. 93PCh. 2 - Prob. 94PCh. 2 - Prob. 95PCh. 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. 104CPCh. 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. 108CPCh. 2 - Prob. 109PCh. 2 - Prob. 110PCh. 2 - Prob. 111PCh. 2 - Consider a plane wall of thickness L whose thermal...Ch. 2 - Prob. 113PCh. 2 - Prob. 114PCh. 2 - A pipe is used for transporting boiling water in...Ch. 2 - Prob. 116PCh. 2 - Prob. 117PCh. 2 - Consider a spherical shell of inner radius r1 and...Ch. 2 - Prob. 119PCh. 2 - A spherical tank is filled with ice slurry, where...Ch. 2 - Prob. 121CPCh. 2 - Prob. 122CPCh. 2 - Can a differential equation involve more than one...Ch. 2 - Prob. 124CPCh. 2 - Prob. 125CPCh. 2 - Prob. 126CPCh. 2 - Prob. 127CPCh. 2 - How is integation related to derivation?Ch. 2 - Prob. 129CPCh. 2 - Prob. 130CPCh. 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. 138PCh. 2 - Prob. 139EPCh. 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. 142PCh. 2 - Prob. 143PCh. 2 - Consider a 20-cm-thick large concrete plane wall...Ch. 2 - Prob. 145PCh. 2 - Prob. 146PCh. 2 - Prob. 147EPCh. 2 - Prob. 148PCh. 2 - In a manufacturing plant, a quench hardening...Ch. 2 - Consider a water pipe of length L=17m, inner...Ch. 2 - Prob. 151PCh. 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. 163PCh. 2 - Prob. 164PCh. 2 - The temperatures at the inner and outer surfaces...Ch. 2 - The thermal conductivity of a solid depends upon...Ch. 2 - Prob. 167PCh. 2 - Prob. 168PCh. 2 - Prob. 169PCh. 2 - Prob. 170PCh. 2 - Prob. 171PCh. 2 - Write essay on heat generation in nuc1e e1 rods....Ch. 2 - Write an interactive computer program to calculate...Ch. 2 - Prob. 174P
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