Analysis of Nonlinear Heat Transfer in a Cylindrical Solid with Two-Step Exothermic Kinetics and Radiative Heat Loss

2017 ◽  
Vol 377 ◽  
pp. 17-28
Author(s):  
Solomon Tahiru ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Thermal Stability ◽  
Heat Loss ◽  
Radiative Heat ◽  
Iteration Scheme ◽  
Regular Perturbation ◽  
Radiative Heat Loss ◽  
Nonlinear Heat Transfer ◽  
Cylindrical Solid ◽  
Exponential Factors

This paper examines the problem of nonlinear heat transfer in a cylindrical solid of combustible materials with two-step exothermic kinetics and radiative heat loss to the ambient surrounding. The reactant diffusion and temperature dependent pre-exponential factors with respect to sensitized, Arrhenius, and bimolecular kinetics are taken into account in the model energy balanced equation. Both regular perturbation method and numerical shooting technique coupled with Runge-Kutta-Fehlberg iteration scheme are employed to tackle the nonlinear model problem. The effects of various thermophysical parameters on the reactive cylindrical solid temperature, Nusselt number and thermal stability are discussed quantitatively with the help of computational illustrations. It is found that radiative heat loss enhances thermal stability of the material while the two-step exothermic kinetics promotes the onset of thermal instability.

Mechanisms of thermal stability during flight in the honeybee apis mellifera

1999 ◽  
Vol 202 (11) ◽  
pp. 1523-1533 ◽  
Author(s):  
S.P. Roberts ◽  
J.F. Harrison
Keyword(s):  
Thermal Stability ◽  
Heat Loss ◽  
Heat Production ◽  
Radiative Heat ◽  
Carbon Dioxide Production ◽  
Metabolic Heat Production ◽  
Evaporative Heat Loss ◽  
Radiative Heat Loss ◽  
Convective Heat Loss ◽  
Metabolic Heat

Thermoregulation of the thorax allows honeybees (Apis mellifera) to maintain the flight muscle temperatures necessary to meet the power requirements for flight and to remain active outside the hive across a wide range of air temperatures (Ta). To determine the heat-exchange pathways through which flying honeybees achieve thermal stability, we measured body temperatures and rates of carbon dioxide production and water vapor loss between Ta values of 21 and 45 degrees C for honeybees flying in a respirometry chamber. Body temperatures were not significantly affected by continuous flight duration in the respirometer, indicating that flying bees were at thermal equilibrium. Thorax temperatures (Tth) during flight were relatively stable, with a slope of Tth on Ta of 0.39. Metabolic heat production, calculated from rates of carbon dioxide production, decreased linearly by 43 % as Ta rose from 21 to 45 degrees C. Evaporative heat loss increased nonlinearly by over sevenfold, with evaporation rising rapidly at Ta values above 33 degrees C. At Ta values above 43 degrees C, head temperature dropped below Ta by approximately 1–2 degrees C, indicating that substantial evaporation from the head was occurring at very high Ta values. The water flux of flying honeybees was positive at Ta values below 31 degrees C, but increasingly negative at higher Ta values. At all Ta values, flying honeybees experienced a net radiative heat loss. Since the honeybees were in thermal equilibrium, convective heat loss was calculated as the amount of heat necessary to balance metabolic heat gain against evaporative and radiative heat loss. Convective heat loss decreased strongly as Ta rose because of the decrease in the elevation of body temperature above Ta rather than the variation in the convection coefficient. In conclusion, variation in metabolic heat production is the dominant mechanism of maintaining thermal stability during flight between Ta values of 21 and 33 degrees C, but variations in metabolic heat production and evaporative heat loss are equally important to the prevention of overheating during flight at Ta values between 33 and 45 degrees C.

Effect of radiative heat loss on steady hypersonic flow past a blunt body

1967 ◽  
Vol 29 (3) ◽  
pp. 485-494 ◽  
Author(s):  
M. I. G. Bloor
Keyword(s):  
Numerical Solution ◽  
Heat Loss ◽  
Blunt Body ◽  
Radiative Heat ◽  
Constant Density ◽  
Axially Symmetric ◽  
Radiative Heat Loss ◽  
Stagnation Region ◽  
Expansion Procedure ◽  
Axis Of Symmetry

Using the grey gas approximation, the effect of radiative heat loss on axially symmetric flows is studied. Using an expansion procedure about the axis of symmetry, a numerical solution for the stagnation region is found taking the shock to be spherical. The results of this calculation are compared with the results of Lighthill's non-radiative constant density solution.

scholarly journals Analysis of MHD Forced Convective Flow of Variable Fluid Properties over a Saturated Porous Medium with Thermal Radiation Effect

2016 ◽  
Vol 9 ◽  
pp. 47-65 ◽  
Author(s):  
Kolawole Sunday Adegbie ◽  
Adeyemi Isaiah Fagbade
Keyword(s):  
Porous Medium ◽  
Heat Loss ◽  
Convective Flow ◽  
Radiative Heat ◽  
Saturated Porous Medium ◽  
Fluid Velocity ◽  
Radiative Heat Loss ◽  
Variable Fluid Properties ◽  
Fluid Properties ◽  
Forced Convective Flow

The present paper addresses the problem of MHD forced convective flow in a fluid saturated porous medium with Brinkman-Forchheimer model, which is an important physical phenomena in engineering applications. The paper extends the previous models to account for effects of variable fluid properties on the forced convective flow through a porous medium in the presence of radiative heat loss using bivariate spectral relaxation method (BSRM). The dynamic viscosity and thermal conductivity of the newtonian fluid are assumed to vary linearly respectively, with temperature whereas the contribution of thermal radiative heat loss is based on Rosseland diffussion approximation. The flow model is described and expressed in form of a highly coupled nonlinear system of partial differential equations. The method of solution BSRM as proposed by Motsa [25] seeks to decouple the original system of PDEs to form a sequence of equations that can be solved in a computationally efficient manner. BSRM is an approach that applies spectral collocation independently in all underlying independent variable is executed to obtain approximate solutions of the problem. The proposed algorithm is supposed to be a very accurate, convergent and very effective in generating numerical results. The results obtained show a significant effects of the flow control parameters on the fluid velocity and temperature respectively. Consequently, the wall shear stress and local heat transfer rate of the present paper are compared with the available results in literatures. Remarkable impacts and a good agreement are found.

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