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Transient Heat Transfer Analysis in Insulated Pipe with Constant and Time-Dependent Heat Flux for Solar Convective Furnace

Conference paper
Part of the Springer Proceedings in Energy book series (SPE)

Abstract

The paper deals with heat transfer during the transportation of the hot air from receiver via an insulated pipe to solar convective furnace for metal processing. In the developed concept of solar convective furnace (SCF) hot air at a temperature of 300–600 °C is required for a duration of about 3–6 h. However, the availability of solar irradiance is 8–10 h per day, whereas, the typical required time for achieving the steady condition is in the order of hours. Thus, prediction of time-dependent air temperature development at the outlet of insulated pipe is required for a given flow condition. Considering these aspects, the developed and validated transient heat transfer analysis tool is used to analyze effect of (a) pipe length and thickness of insulation, (b) mass-flow-rate of air, (c) constant and variable inlet air temperature and (d) preheating of pipe. Following are the broad observations based on the performed analysis: (i) time to reach steady state for the considered insulated pipe and the ratio of the heat loss to input reduces with increasing mass-flow-rate; (ii) increasing insulation thickness beyond critical thickness reduces the heat loss that results in a higher temperature at outlet. However, it increases the required time to reach the steady state condition; (iii) the achieved maximum temperature corresponding to a solar irradiance is forward shifted in time.

Keywords

Insulated pipe 1-D numerical tool Experiment Preheating Steady state time Insulation thickness 

Nomenclature

Aa

Area of aperture (m2)

C

Concentration factor

Cpf

Specific heat capacity of fluid (J/kg K)

Cps

Specific heat capacity of pipe/absorber (J/kg K)

DNI

Direct normal irradiance (W/m2)

Ea

Net energy available at inlet (MJ)

Eph

Energy required for preheating the pipe (MJ)

Eu

Energy utilized (MJ)

hf

Heat transfer coefficient for internal heat transfer in fluid (W/m2 K)

hex

Natural convective heat transfer coefficient (W/m2 K)

Ki

Thermal conductivity of insulation (W/mK)

Ks

Thermal conductivity of pipe (W/mK)

Lc

Thermal development length (m)

Ls or L

Length of pipe (solid domain) (m)

\(\dot{m}_{\text{f}}\)

Mass flow rate (kg/s)

nth

Efficiency of receiver

Nuex,i

Nusselt number for natural convection at top of insulation domain (radial boundary)

Nuex,s

Nusselt number for natural convection at axial boundary of solid domain

Nz

Number of divisions in axial direction of pipe

Prf

Prandtl number of fluid

\(\dot{Q}_{\text{a}}\)

Power available at the inlet of pipe (W)

\(\dot{Q}_{\text{cond}}\)

Power conducted (W)

\(\dot{Q}_{\text{fts}}\)

Power transferred from fluid to solid (W)

\(\dot{Q}_{{\text{Nat}.\text{Conv}}}\)

Natural convective power losses from insulation surface (W)

\(\dot{Q}_{{\text{sti}}}\)

Power transferred to insulation from solid domain (W)

r

Radial direction of pipe

Ra

Rayleigh number

Re

Reynolds number

ri

Outer radius of insulation (m)

rs

Inner radius of pipe (m)

SST

Time to reach steady state (s)

T

Time axis

Ta

Ambient temperature (K)

th

Time (h)

Ti

Temperature of insulation (K)

Tm

Mean temperature of fluid (K)

Tm,in

Mean temp of fluid at inlet of pipe (K)

Tm,out

Mean temp of fluid at outlet of pipe (K)

Tm,out|steady state

Mean temp of fluid at outlet at steady state (K)

Tph

Preheat temp of pipe (K)

Ts

Temperature of pipe (K)

top

Total time of operation of the system (s)

\({{T_m}_{{i}} ^{n}}\)

Mean temp of fluid at ith node and nth time step (K)

\({{T_s}_{{i}}^{n}}\)

Temperature of solid domain at ith node and nth time step (K)

\({{T_{i}}_{i}^{n}}\)

Temperature of insulation at ith node and nth time step (K)

z

Axial direction of pipe

Greek Symbols

\(\alpha_{\text{i}}\)

Thermal diffusivity of fluid domain (m2/s)

\(\alpha_{\text{s}}\)

Thermal diffusivity of solid domain (m2/s)

\(\delta_{\text{i}}\)

Thickness of insulation (m)

\(\delta_{\text{s}}\)

Thickness of pipe (m)

\(\Delta{{r}}\)

Grid spacing in radial direction (m)

\(\Delta {{z}}\)

Finite difference element in axial direction (m)

\(\oslash\)

Porosity of absorber

\(\rho_{\text{s}}\)

Density of pipe (kg/m3)

\(\Delta {{z}}\)

Grid spacing in axial direction (m)

\(\Delta t\)

Time step (s)

Abbreviations

MFR

Mass flow rate

OVAR

Open volumetric air receiver

VNS

Von Neumann stability

Num

Numerical

POA

Power on aperture (W)

DNI

Direct normal irradiance (W/m2)

Exp

Experiment

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of Technology JodhpurJodhpurIndia
  2. 2.Department of Mechanical Engineering and Center for Solar EnergyIndian Institute of Technology JodhpurJodhpurIndia

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